Paper.ipynb

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    "# Solving the Shallow Water Equations using Finite Volumes and Lax-Friedrichs\n",
    "---\n",
    "Nathan Brei\n",
    "\n",
    "Technical University of Munich\n",
    "\n",
    "14 December 2017\n",
    "\n",
    "---\n",
    "\n",
    "This paper has three aims:\n",
    "- Briefly introduce shallow water equations\n",
    "- Explore the concept of numerical viscosity via Lax-Friedrich and Local-Lax-Friedrich methods\n",
    "- Demonstrate code organization using Julia"
   ]
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   "source": [
    "# Shallow Water Equations (1-D)\n",
    "\n",
    "The shallow water equations are a set of hyperbolic partial differential equations.\n",
    "\n",
    "Specifically, they describe mass and momentum conservation on a fluid in a channel of unit width, subject to the following assumptions:\n",
    "\n",
    "* Small vertical velocity\n",
    "* Pressure is determined by hydrostatic pressure $p=\\frac{1}{2}\\rho gh^2$\n",
    "* Constant horizontal velocity $u(x)$ across any cross section $x$\n",
    "\n",
    "$\\begin{bmatrix}h \\\\ hu \\end{bmatrix}_t + \\begin{bmatrix}hu \\\\ hu^2 + \\frac{1}{2}gh^2\\end{bmatrix}_x = 0 $\n",
    "\n",
    "\n",
    "Formulate as a general conservation law in differential form: $q_t(x,t) + f(q(x,t))_x = 0$\n",
    "\n",
    "$q := (h, hu) \\in Q$\n",
    "\n",
    "$f : (q_1, q_2) \\mapsto \\begin{bmatrix} q_2\\\\ q_2^2/q_1 + \\frac{1}{2}gq_1^2\\end{bmatrix}$\n",
    "\n",
    "How do we abstract this?\n",
    "- Need state space, flux, and wavespeed\n",
    "\n",
    "The first step to translating this into Julia is to use "
   ]
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    {
     "data": {
      "text/plain": [
       "Array{Q,1}"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "const Float = Float64\n",
    "const G = 9.81f0\n",
    "\n",
    "mutable struct Q\n",
    "    h :: Float\n",
    "    hu :: Float\n",
    "end\n",
    "\n",
    "QS = Array{Q,1}"
   ]
  },
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   "execution_count": 11,
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     "data": {
      "text/plain": [
       "f (generic function with 1 method)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function f(q :: Q)\n",
    "    Q(q.hu, q.hu^2/q.h + 0.5*G*q.h^2)\n",
    "end"
   ]
  },
  {
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   "source": [
    "\n",
    "\n",
    "## Types and Methods in Julia\n",
    "\n",
    "* Types are composed of primitives, structures, unions, tuples, abstract types\n",
    "* Types are parametric\n",
    "* Type annotations are optional\n",
    "* Inheritance is restricted to abstract types\n",
    "* Type system offers no encapsulation, but does support invariants and immutability\n",
    "* Methods resolved via multiple dispatch (using all arguments rather than the first)\n",
    "\n",
    "## Defining a vector space over Q"
   ]
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  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "* (generic function with 215 methods)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import Base.+\n",
    "import Base.-\n",
    "import Base.*\n",
    "\n",
    "function +(lhs::Q, rhs::Q)\n",
    "    Q(lhs.h + rhs.h, lhs.hu + rhs.hu)\n",
    "end\n",
    "\n",
    "function -(lhs::Q, rhs::Q)\n",
    "    Q(lhs.h - rhs.h, lhs.hu - rhs.hu)\n",
    "end\n",
    "\n",
    "function *(a::Real, q::Q)\n",
    "    Q(a*q.h, a*q.hu)\n",
    "end"
   ]
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   "source": [
    "The third place where the shallow water equations enter the numerical model is in the wavespeed function. The physical wave speeds are given by the eigenvalues of the flux Jacobian\n",
    "\n",
    "$f'(q) = \\begin{bmatrix}0 & 1 \\\\ -u^2 + gh & 2u \\end{bmatrix}$\n",
    "\n",
    "$\\lambda_{max} = \\max\\ \\lvert u \\pm \\sqrt{gh} \\rvert$\n",
    "\n",
    "- What does the wavespeed represent physically?\n",
    "These \n"
   ]
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   "cell_type": "code",
   "execution_count": 13,
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     "data": {
      "text/plain": [
       "wavespeed (generic function with 1 method)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function wavespeed(q :: Q)\n",
    "    u = q.hu / q.h\n",
    "    c = sqrt(G * q.h)\n",
    "    max(abs(u-c), abs(u+c))\n",
    "end"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "What is the CFL condition?\n",
    "\n",
    "* Necessary condition for numerical stability\n",
    "* Information propagates through the spatial domain at finite speeds\n",
    "* Need {true domain of dependence} $\\subset$ {numerical domain of dependence}\n",
    "\n",
    "- Intuitive meaning: Outrunning\n",
    "- Why is there a correction term? Linear vs nonlinear case\n",
    "\n",
    "$ \\nu := \\lvert\\frac{\\bar{u}\\Delta t}{\\Delta x} \\rvert = \\frac{\\Delta t}{\\Delta x} \\lvert \\lambda_{max} \\rvert  \\leq 1 $\n",
    "\n"
   ]
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   "cell_type": "code",
   "execution_count": 14,
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     "data": {
      "text/plain": [
       "cfl_dt (generic function with 2 methods)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "function cfl_dt(qs::Array{Q,1}, dx::Float, correction=1.0::Float)\n",
    "    lambda = map(wavespeed,qs) |> maximum\n",
    "    dx / lambda * correction\n",
    "end"
   ]
  },
  {
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     "slide_type": "slide"
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   "source": [
    "## Finite Volumes\n",
    "\n",
    "- What are finite volumes? \n",
    "- Advantages: Conserves physical quantities\n",
    "\n",
    "Let $C_i := (x_{i-1/2}, x_{i+1/2})$ represent a grid cell in our spatial domain. The conservation equations may be represented in integral form as:\n",
    "\n",
    "$$\\frac{d}{dt} \\int_{C_i} q(x,t) dx = f(q(x_{i-1/2},t)) - f(q(x_{1+1/2},t))$$\n",
    "\n",
    "- Define spatial domain in Julia\n",
    "-- Ghost cells, indexing, type aliasing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "Integrate both sides with respect to time:\n",
    "\n",
    "$$\\int_{C_i} q(x,t_{n+1})dx - \\int_{C_i} q(x,t_n) dx = \\int_{t_n}^{t_{n+1}} f(q(x_{i-1/2},t))dt - \\int_{t_n}^{t_{n+1}} f(q(x_{i+1/2},t))dt $$\n",
    "\n",
    "Let $Q_{i}^{n} \\approx \\frac{1}{\\Delta x} \\int_{C_i} q(x,t_n) dx $ be the appx. average $q$ in cell $i$ at time $n$.\n",
    "\n",
    "Let $F_{i+1/2}^{n} \\approx \\frac{1}{\\Delta t} \\int_{t_n}^{t_{n+1}} f(q(x_{i+1/2},t))dt$ be the appx. average flux $f$ from cell $i$ into $i+1$."
   ]
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   "source": [
    "Rearranging, we get a general update scheme\n",
    "\n",
    "$Q_{i}^{n+1} = Q_{i}^{n} - \\frac{\\Delta t}{\\Delta x}(F_{i+1/2}^{n} - F_{i-1/2}^{n}) $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "update_qs! (generic function with 1 method)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function update_qs!(qs::QS, Fl::QS, Fr::QS, ncells::Int,\n",
    "                    dx::Float, dt::Float)\n",
    "    \n",
    "    for x = 2:ncells+1\n",
    "        qs[x] -= dt/dx * (Fr[x] + Fl[x-1])\n",
    "    end\n",
    "end"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Math              | Code        | Description |\n",
    "|----------------   |-------------|-------------|\n",
    "|  $Q_{i}^{n}$      | ```qs[x]``` | 1D array of Q containing solution states\n",
    "|  $F_{i+1/2}^{n}$  | ```Fr[x]``` | 1D array of Q containing flux flowing right \n",
    "|  $F_{i-1/2}^{n}$  | ```Fl[x]``` | 1D array of Q containing flux flowing left\n",
    "\n",
    "* Each buffer is of length ```ncells+2```, accounting for ghost cells at either end\n",
    "* Functions suffixed with a ! update one or more of their buffers in-place"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Timestepping loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
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    {
     "data": {
      "text/plain": [
       "run_experiment (generic function with 1 method)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function run_experiment(stoptime, ncells::Int, choose_dt,\n",
    "                        compute_fluxes!, apply_bcs!, apply_ics)\n",
    "\n",
    "    qs = apply_ics(ncells)\n",
    "    Fl = QS(ncells+2)\n",
    "    Fr = QS(ncells+2)\n",
    "\n",
    "    currenttime = 0\n",
    "    timesteps = 0\n",
    "    dx = Float(1000.0/ncells)\n",
    "    \n",
    "    while currenttime < stoptime\n",
    "        apply_bcs!(qs)\n",
    "        dt = choose_dt(qs, dx)\n",
    "        compute_fluxes!(qs, Fl, Fr, ncells, dx, dt)\n",
    "        update_qs!(qs, Fl, Fr, ncells, dx, dt)\n",
    "        currenttime += dt\n",
    "        timesteps += 1\n",
    "    end\n",
    "    return (qs, currenttime, timesteps)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "# Timestepping loop for animations\n",
    "* Outer timesteps correspond to clean increments of physical time\n",
    "* An outer loop controls outer timesteps by iterating over stoptime\n",
    "* Inner timesteps correspond to increments of dt\n",
    "* Inner timesteps go up to stop time exactly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
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    {
     "data": {
      "text/plain": [
       "run_experiment! (generic function with 1 method)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function run_experiment!(qs, Fl, Fr, \n",
    "                         currenttime::Real, stoptime::Real, \n",
    "                         ncells::Int, \n",
    "                         choose_dt, compute_fluxes!, apply_bcs!)\n",
    "\n",
    "    timesteps = 0\n",
    "    dx = Float(1000.0/ncells)\n",
    "    \n",
    "    while currenttime < stoptime\n",
    "        apply_bcs!(qs)\n",
    "        dt = choose_dt(qs, dx)\n",
    "        if currenttime + dt > stoptime\n",
    "            dt = stoptime - currenttime\n",
    "        end\n",
    "        compute_fluxes!(qs, Fl, Fr, ncells, dx, dt)\n",
    "        update_qs!(qs, Fl, Fr, ncells, dx, dt)\n",
    "        currenttime += dt\n",
    "        timesteps += 1\n",
    "    end\n",
    "    return (qs, currenttime, timesteps)\n",
    "end"
   ]
  },
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   "source": [
    "# Lax-Friedrichs by accident\n",
    "\n",
    "Consider the simplest choice of F: \n",
    "\n",
    "$ F_{i-1/2} = \\frac{1}{2}[f(Q_{i-1} + f(Q_i)] $\n",
    "\n",
    "$ Q_i^{n+1} = Q_i^n - \\frac{\\Delta t}{2 \\Delta x} [f(Q_{i+1}^n) - f(Q_{i-1}^n)]$\n",
    "\n",
    "Unfortunately this is unstable. \n",
    "\n",
    "Instead, replace $Q_i^n$ with $\\frac{1}{2}(Q_{i-1}^n + Q_{i+1}^n)$\n",
    "\n",
    "$ Q_i^{n+1} = \\frac{1}{2}(Q_{i-1}^n + Q_{i+1}^n) - \\frac{\\Delta t}{2 \\Delta x} [f(Q_{i+1}^n) - f(Q_{i-1}^n)]$\n",
    "\n",
    "Rearrange to get a flux update function:\n",
    "\n",
    "$ F_{i-1/2} = \\frac{1}{2} [ f(Q_{i-1}) + f(Q_i) - a(Q_i - Q_{i-1})]$ \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Lax-Friedrichs Solver\n",
    "* Input:  Buffers for $q(x), F_l(x), F_r(x)$, cell and timestep sizes\n",
    "* Output: Updated inter-cell flux buffers\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "lxf! (generic function with 1 method)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function lxf!(qs::QS, Fl::QS, Fr::QS, ncells::Int, \n",
    "              dx::Float, dt::Float)\n",
    "    \n",
    "    a = dx/dt\n",
    "    \n",
    "    for x = 2:ncells+2\n",
    "\n",
    "        ql = qs[x-1]\n",
    "        qr = qs[x]\n",
    "        fl = f(ql)\n",
    "        fr = f(qr)        \n",
    "\n",
    "        Fr[x-1] = 0.5*((fr - fl) - a*(qr - ql))\n",
    "        Fl[x-1] = 0.5*((fr - fl) + a*(qr - ql))\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "plotxh! (generic function with 1 method)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Set up plotting infrastructure\n",
    "using Plots\n",
    "pyplot()\n",
    "\n",
    "function plotxh(qs, title)\n",
    "    xs = linspace(0,1,length(qs))\n",
    "    hs = map(q->q.h, qs)\n",
    "    plot(xs, hs, title=title, xlabel=\"x [m]\", ylabel=\"height [m]\", ylim=(0.,2.5), legend=false)\n",
    "end\n",
    "\n",
    "function plotxhul(qs, title)\n",
    "    p0 = plot(map(q->q.h, qs), xlabel=\"x [m]\", ylabel=\"height [m]\", title=title)\n",
    "    p1 = plot(map(q->q.hu, qs), xlabel=\"x [m]\", ylabel=\"hu\")\n",
    "    p2 = plot(map(wavespeed, qs), xlabel=\"x [m]\", ylabel=\"\\$\\\\lambda_{max}\\$ [m/s]\")\n",
    "    plot(p0,p1,p2,layout=(3,1),legend=false)\n",
    "end\n",
    "\n",
    "function plotxhs(qss, labels, title)\n",
    "    p = plot(title=title, xlabel=\"x [m]\", ylabel=\"height [m]\", ylim=(0.,2.5))\n",
    "    for i=1:length(qss)\n",
    "        x = linspace(0,1,length(qss[i])-2)\n",
    "        plot!(x, map(q->q.h, qss[i]), label=labels[i])\n",
    "    end\n",
    "    p\n",
    "end\n",
    "\n",
    "function plotxh(title)\n",
    "    plot(title=title, xlabel=\"x [m]\", ylabel=\"height [m]\", ylim=(0.,2.5))\n",
    "end\n",
    "\n",
    "function plotxh!(p, qs, label)\n",
    "    xs = linspace(0,1,length(qs))\n",
    "    hs = map(q->q.h, qs)\n",
    "    plot!(p, xs, hs, label=label)\n",
    "end\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Gaussian Initial Condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
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\" />"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function gaussian_ics(ncells::Int)\n",
    "    qs = QS(ncells+2)\n",
    "    mid = ncells / 2.0 + 1\n",
    "    for x = 1:ncells+2\n",
    "        pos_rel = (mid-x) / (ncells/10.0)\n",
    "        qs[x] = Q(exp(-pos_rel^2) + 1, 0.0)\n",
    "    end\n",
    "    return qs\n",
    "end\n",
    "plotxh(gaussian_ics(100), \"Gaussian initial conditions\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Breaking Dam Initial Conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img 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\" />"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function breakingdam_ics(ncells::Int)\n",
    "    [x < ncells/2+1 ? Q(2,0) : Q(1,0) for x in 1:ncells+2]\n",
    "end\n",
    "\n",
    "plotxh(breakingdam_ics(100), \"Breaking dam initial conditions\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Boundary Conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "reflecting_bcs! (generic function with 1 method)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "function outflow_bcs!(qs::QS)\n",
    "    qs[1] = qs[2]\n",
    "    qs[end] = qs[end-1]\n",
    "end\n",
    "\n",
    "function periodic_bcs!(qs::QS)\n",
    "    qs[1] = qs[end-1]\n",
    "    qs[end] = qs[2]\n",
    "end\n",
    "\n",
    "function reflecting_bcs!(qs::QS)\n",
    "    qs[1].h = qs[2].h\n",
    "    qs[1].hu = -qs[2].hu\n",
    "    qs[end].h = qs[end-1].h\n",
    "    qs[end].hu = -qs[end-1].hu\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Timestep strategies\n",
    "\n",
    "* Idea: Strategies are simply functions\n",
    "* Timestep strategy always has the signature $ ([q], \\Delta x) \\mapsto \\Delta t $\n",
    "* Use _currying_ to pass configuration information\n",
    "* Use _closures_ to hold any state that may change at runtime "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "make_lagging_dt (generic function with 1 method)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function make_const_dt(dt)\n",
    "    return (qs, dx) -> dt\n",
    "end\n",
    "\n",
    "function make_cfl_dt(correction::Float)\n",
    "    return (qs, dx) -> cfl_dt(qs, dx, correction)\n",
    "end\n",
    "\n",
    "function make_lagging_dt(dt0, correction)\n",
    "    dt = dt0\n",
    "    function lagging_dt(qs, dx)\n",
    "        result = dt\n",
    "        dt = cfl_dt(qs, dx, correction)\n",
    "        return result\n",
    "    end\n",
    "    return lagging_dt\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Lax-Friedrichs solutions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "\u001b[91mInterruptException:\u001b[39m",
     "output_type": "error",
     "traceback": [
      "\u001b[91mInterruptException:\u001b[39m",
      "",
      "Stacktrace:",
      " [1] \u001b[1m#_pycall#67\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Array{Any,1}, ::Function, ::PyCall.PyObject, ::IOStream, ::Vararg{IOStream,N} where N\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m/Users/nathanwbrei/.julia/v0.6/PyCall/src/PyCall.jl:663\u001b[22m\u001b[22m",
      " [2] \u001b[1m(::PyCall.#kw##_pycall)\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Array{Any,1}, ::PyCall.#_pycall, ::PyCall.PyObject, ::IOStream, ::Vararg{IOStream,N} where N\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m./<missing>:0\u001b[22m\u001b[22m",
      " [3] \u001b[1m#pycall#71\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Array{Any,1}, ::Function, ::PyCall.PyObject, ::Type{PyCall.PyAny}, ::IOStream, ::Vararg{IOStream,N} where N\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m/Users/nathanwbrei/.julia/v0.6/PyCall/src/PyCall.jl:675\u001b[22m\u001b[22m",
      " [4] \u001b[1m(::PyCall.#kw##pycall)\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Array{Any,1}, ::PyCall.#pycall, ::PyCall.PyObject, ::Type{PyCall.PyAny}, ::IOStream, ::Vararg{IOStream,N} where N\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m./<missing>:0\u001b[22m\u001b[22m",
      " [5] \u001b[1m#call#72\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Array{Any,1}, ::PyCall.PyObject, ::IOStream, ::Vararg{IOStream,N} where N\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m/Users/nathanwbrei/.julia/v0.6/PyCall/src/PyCall.jl:678\u001b[22m\u001b[22m",
      " [6] \u001b[1m(::PyCall.#kw#PyObject)\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Array{Any,1}, ::PyCall.PyObject, ::IOStream, ::Vararg{IOStream,N} where N\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m./<missing>:0\u001b[22m\u001b[22m",
      " [7] \u001b[1mshow\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::IOStream, ::MIME{Symbol(\"image/png\")}, ::Plots.Plot{Plots.PyPlotBackend}\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m/Users/nathanwbrei/.julia/v0.6/Plots/src/output.jl:208\u001b[22m\u001b[22m",
      " [8] \u001b[1mpng\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Plots.Plot{Plots.PyPlotBackend}, ::String\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m/Users/nathanwbrei/.julia/v0.6/Plots/src/output.jl:8\u001b[22m\u001b[22m",
      " [9] \u001b[1mframe\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Plots.Animation, ::Plots.Plot{Plots.PyPlotBackend}\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m/Users/nathanwbrei/.julia/v0.6/Plots/src/animation.jl:20\u001b[22m\u001b[22m",
      " [10] \u001b[1mframe\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Plots.Animation\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m/Users/nathanwbrei/.julia/v0.6/Plots/src/animation.jl:18\u001b[22m\u001b[22m",
      " [11] \u001b[1mmacro expansion\u001b[22m\u001b[22m at \u001b[1m/Users/nathanwbrei/.julia/v0.6/Plots/src/animation.jl:142\u001b[22m\u001b[22m [inlined]",
      " [12] \u001b[1mmacro expansion\u001b[22m\u001b[22m at \u001b[1m./In[24]:8\u001b[22m\u001b[22m [inlined]",
      " [13] \u001b[1mmacro expansion\u001b[22m\u001b[22m at \u001b[1m/Users/nathanwbrei/.julia/v0.6/Plots/src/animation.jl:152\u001b[22m\u001b[22m [inlined]",
      " [14] \u001b[1manonymous\u001b[22m\u001b[22m at \u001b[1m./<missing>:?\u001b[22m\u001b[22m",
      " [15] \u001b[1minclude_string\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::String, ::String\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m./loading.jl:515\u001b[22m\u001b[22m"
     ]
    }
   ],
   "source": [
    "ncells = 500\n",
    "t0 = 0\n",
    "qs = breakingdam_ics(ncells)\n",
    "Fl = QS(ncells+2)\n",
    "Fr = QS(ncells+2)\n",
    "a = @animate for t=0.0:4.0:2000.0\n",
    "    qs,t0,ts = run_experiment!(qs, Fl, Fr, t0, t, ncells, make_cfl_dt(1.0), lxf!, reflecting_bcs!)\n",
    "    plotxh(qs, \"Lax-Friedrichs, breaking dam, reflecting boundaries, t=$t\")\n",
    "end\n",
    "figure24 = gif(a, \"animations/breakingdam_lxf_reflecting.gif\", fps = 20);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"animations/breakingdam_lxf_reflecting.gif?0.8293374703371885>\" />"
      ],
      "text/plain": [
       "Plots.AnimatedGif(\"/Users/nathanwbrei/src/shallow_water/animations/breakingdam_lxf_reflecting.gif\")"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "figure24"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Breaking dam scenario with reflecting boundary conditions, $t=0..2000, ncells=500, x=1.0$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Lax-Friedrichs solutions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Plots.Animation(\"/var/folders/1k/q68xhskx4ks0dfs38lkh72y40000gn/T/tmpjRFmb9\", String[\"000001.png\", \"000002.png\", \"000003.png\", \"000004.png\", \"000005.png\", \"000006.png\", \"000007.png\", \"000008.png\", \"000009.png\", \"000010.png\"  …  \"000192.png\", \"000193.png\", \"000194.png\", \"000195.png\", \"000196.png\", \"000197.png\", \"000198.png\", \"000199.png\", \"000200.png\", \"000201.png\"])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ncells = 100\n",
    "t0 = 0\n",
    "qs = gaussian_ics(ncells)\n",
    "Fl = QS(ncells+2)\n",
    "Fr = QS(ncells+2)\n",
    "a = @animate for t=0:4:800\n",
    "    qs,t0,ts = run_experiment!(qs, Fl, Fr, t0, t, ncells, make_cfl_dt(1.0), lxf!, periodic_bcs!)\n",
    "    plotxh(qs, \"Lax-Friedrichs, gaussian, periodic boundaries, t=$t\")\n",
    "end\n",
    "anim22 = a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[36mINFO: \u001b[39m\u001b[22m\u001b[36mSaved animation to /Users/nathanwbrei/src/shallow_water/animations/gauss_lxf.gif\n",
      "\u001b[39m"
     ]
    }
   ],
   "source": [
    "figure22 = gif(anim22, \"animations/gauss_lxf.gif\", fps = 20);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"animations/gauss_lxf.gif?0.8756549720694768>\" />"
      ],
      "text/plain": [
       "Plots.AnimatedGif(\"/Users/nathanwbrei/src/shallow_water/animations/gauss_lxf.gif\")"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "figure22"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Gaussian scenario with periodic boundaries, $t=800, ncells=100, w=1.0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = plotxh(\"Breaking Dam for different \\$n_{cells}\\$\")\n",
    "for ncells = [100, 200, 400, 800]\n",
    "    qs,t,ts = run_experiment(50, ncells, make_cfl_dt(0.5), lxf!, outflow_bcs!, breakingdam_ics)\n",
    "    plotxh!(p, qs, \"\\$n_{cells}\\$=$ncells, \\$\\\\mu\\$=0.5, timesteps=$ts\")\n",
    "end\n",
    "display(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = plotxh(\"Gaussian scenario for different \\$n_{cells}\\$\")\n",
    "for ncells = [100, 200, 400, 800]\n",
    "    qs,t,ts = run_experiment(50, ncells, make_cfl_dt(0.5), lxf!, reflecting_bcs!, gaussian_ics)\n",
    "    plotxh!(p, qs, \"\\$n_{cells}\\$=$ncells, \\$\\\\mu\\$=0.5, timesteps=$ts\")\n",
    "end\n",
    "display(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Effect of timestep correction term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = plotxh(\"Gaussian with different correction terms\")\n",
    "for w = [0.1, 0.3, 0.5, 0.7, 0.9]\n",
    "    qs,t,ts = run_experiment(50, 500, make_cfl_dt(w), lxf!, periodic_bcs!, gaussian_ics)\n",
    "    plotxh!(p, qs, \"w=$w [$ts timesteps]\")\n",
    "end\n",
    "display(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Effect of timestep correction term"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = plotxh(\"Breaking Dam with different correction terms\")\n",
    "for mu = [0.1, 0.2, 0.4, 0.8]\n",
    "    qs,t,ts = run_experiment(50, 1000, make_cfl_dt(mu), lxf!, outflow_bcs!, breakingdam_ics)\n",
    "    plotxh!(p, qs, \"\\$\\\\mu\\$=$mu [$ts timesteps]\")\n",
    "end\n",
    "display(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Artificial Viscosity\n",
    "\n",
    "Idea: An approximate solution is often an exact solution to an approximate problem. \n",
    "\n",
    "Consider $q_t + {f_{SWE}(q)}_x = 0 \\implies F_{i+1/2} = 1/2 (f_{SWE}(Q_{i+1/2} + f_{SWE}(Q_{i-1/2})) $\n",
    "\n",
    "Consider $q_t = \\beta q_{xx} \\implies F_{i+1/2} = -\\frac{\\Delta x^2}{2 \\Delta t} \\frac{Q_{i+1/2} - Q_{i-1/2}}{\\Delta x}$\n",
    "\n",
    "Our Lax-Friedrichs solver looks like:\n",
    "\n",
    "$ F_{i-1/2} = \\frac{1}{2} [f(Q_{i-1}) + f(Q_i)] - \\frac{\\Delta x}{2\\Delta t}[Q_i - Q_{i-1}]$ \n",
    "\n",
    "Which can be decomposed to:\n",
    "\n",
    "$ q_t + f_{SWE}(q)_x = \\frac{(\\Delta x)^2}{2\\Delta t} q_{xx} $\n",
    "\n",
    "Apparent viscosity $\\beta = \\frac{(\\Delta x)^2}{2\\Delta t} = \\frac{a \\Delta x}{2}$\n",
    "\n",
    "Consistency: $\\beta \\to 0$ if $a = \\frac{\\Delta x}{\\Delta t}$ is held constant as $\\Delta x \\to 0$ \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Local Lax-Friedrichs / Rusanov Improvement\n",
    "\n",
    "For Lax-Friedrichs, the viscosity $a$ is constant over the whole domain\n",
    "\n",
    "* Idea: Viscosity should vary over spatial domain\n",
    "\n",
    "* Idea: Only need to smooth areas with high wave speeds\n",
    "\n",
    "Let $a_{i-1/2} = max(\\lvert f'(q) \\rvert) \\ \\forall q \\in (Q_{i-1}, Q_{i})$\n",
    "\n",
    "Then $ F_{i-1/2} = \\frac{1}{2}[f(Q_{i-1}) + f(Q_i) - a_{i-1/2}(Q_i - Q_{i-1})]$\n",
    "\n",
    "* This is strictly less viscous than ordinary LxF due to CFL:\n",
    "\n",
    "$\\lvert f'(q)\\rvert \\leq \\frac{\\Delta x}{\\Delta t}$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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\" />"
      ]
     },
     "execution_count": 229,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qs,t,ts = run_experiment(60, 100, cfl_dt, lxf!, periodic_bcs!, gaussian_ics)\n",
    "plotxhul(qs, \"State space and wavespeed, Gaussian scenario\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Local Lax Friedrichs (Rusanov) Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "llxf! (generic function with 1 method)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function llxf!(qs::QS, Fl::QS, Fr::QS, ncells::Int, \n",
    "               dx::Float, dt::Float)\n",
    "    \n",
    "    for x = 2:ncells+2\n",
    "\n",
    "        ql = qs[x-1]\n",
    "        qr = qs[x]\n",
    "        fl = f(ql)p\n",
    "        fr = f(qr)  \n",
    "\n",
    "        a = max(wavespeed(ql), wavespeed(qr))\n",
    "        \n",
    "        Fr[x-1] = 0.5*((fr - fl) - a*(qr - ql))\n",
    "        Fl[x-1] = 0.5*((fr - fl) + a*(qr - ql))\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img 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F18E8OCYl84jBQC3bt3S6JjvzLnzMNtHV06ePAnGmNyy5uZm2WU+6dQI8+bNg4GBAZYtW4YbN27I1WeMoaysTPZZ1+diV2zHGTNmAHgw513rS4EikQjvv/++XJ3eji4RdlOXLl1SOamfn58fpkyZola9t99+Gzt37sTOnTsxbtw4vPbaawAezFW1c+dOCAQCTJ06Fb/++iuMjIy0+h0sLCwwdOhQ/Prrr+DxeIiKipKVSUe37ty5g9GjR6vdt5+fH/r374/vv/8eJiYmcHFxAcdxeP3117Uau0AgwMsvv4ykpCQEBARg4sSJaGxsxJ49ezBixAgcOnRIq/21NmTIEHzxxRd49dVXMWjQIIwdOxZeXl64d+8e8vPzcerUKSQkJGDr1q16aU+Z9vaLstdsXLp0CS0tLXB0dMSYMWMwefJk9OnTBxkZGaipqZHdx/HKK6/giy++kJsfTTrapMmlsry8PLmZ3CsrK3H27Fn8/vvvsLW1xccff6zR99V0m77++uv45ZdfMGrUKDz//PMwNTXFyZMnUVpaiieeeKLDZJHjOGzZsgU8Hg9btmwBYwzff/+9Vi8XPvXUU5g6dSq+++47BAQEYMKECWhsbMTevXsxfPhwHDx4EDxex/8m78y587DbRxcmTJgAKysr2dyBzc3NOHbsGK5cuYJnn31WNp9gQEAANmzYgAULFmDw4MGYMGECBg4ciFu3buH06dP417/+JZvzTtfnYldsx8jISLz++uvYtGkThgwZgsmTJ4MxhgMHDqCkpAQLFizQ+B8sjyz9PcBIlOnosXIALCoqSu16+fn5zMrKijk7O7M7d+4o9Pfee+/Jpm5oG4MmU0Co8u677zIASh9Zl86ZIp3KQdl2UPY497lz51hUVBSztLSUfdeCgoJ2pwporz1VxGIxW7NmDfP09GTGxsbM09OTJSYmsry8PJ1O0yB14cIFNmXKFNa/f39mZGTE+vbty0JCQtjbb7/NcnJyZPXUnSJBG+11Zr8os3XrVgaAffPNN2zu3LnMysqKWVlZscmTJ7OioiL2wgsvMHNzc7n50hh7MK+QnZ0dc3d3Z83Nze1+39bxtv1jYmLCvLy82Kuvvspu3LihsJ62tyljjO3fv5+FhIQwMzMz1rdvX/b888+z69evsxkzZihsK1X9SyQS9tprrzEAbNKkSaypqandaRo03YfNzc3sww8/ZB4eHnLH/Pnz5xkA9sYbb7S7PaQ0OXe0uX0YYywpKYkBYElJSQplK1asYABYWlpah9/hiy++YHFxcWzgwIHM1NSU2dvbs2HDhrEtW7YonUcrLS2NPfPMM8zOzo4ZGxszFxcXNnnyZHb27FmFuro8F7W1HdvrgzHGvv76azZ06FBmZmbGzMzM2NChQ9WaqqI34RhrMwZKCCE6Nm/ePGzbtg05OTkavevszz//REBAAD7//HPMnz9fhxGS1v73v/9h9uzZstEXQkjH6B4sQkiXEwqFMDMzg6+vr0brpaenw8nJCTNnztRRZL3brVu3FO47Ki0txapVq5S+X5QQohqNYBFCulRLSwssLS0RGBio0ycbieYWLlyIw4cPIyIiAo6OjigqKsKhQ4dw7949rFy5EitWrNB3iIT0GHSTOyGkS129ehX19fX0KHc39PTTT+PKlSs4fPgwqqqqYGpqisDAQMyfPx9Tp07Vd3iE9Cg6HcFqaGjAlClTcOXKFfTp0weOjo7YsmULvL295eoVFhbCy8sLAQEBsmUHDhyAl5eXrkIjhBBCCNEZnSdYJ06cwJgxY8BxHDZv3oz9+/crPCpaWFgIPp+vlfebEUIIIYTom05vcjc1NcXYsWNl0/CPGDEChYWFuuySEEIIIUTvuvQerI0bN2L8+PFKy+rq6hAaGgrGGCZMmID33ntP9vqN1hhjuHv3LoyNjeXen2RiYiI3GSEhhBBCiL502VOEiYmJOHjwII4fPw4zMzO5ssbGRohEIjg6OqKyshLx8fGIiYnBkiVLFNqpqalROjP0kiVLsHTpUp3FTx5OTU0NvQC0h6F91vPQPutZaH/1PNLXgqmjS0aw1q5di+TkZKSmpiokV8CD0SfpW7nt7Owwc+ZMfPfdd0oTLKni4mK5A5NGsLo/TQ5M0j3QPut5aJ/1LLS/Hl06T7DWr1+P3bt3IzU1FTY2NkrrlJeXw9bWFkZGRmhsbERycrLsjd2qWFlZUeZPCCGEkG5Jpze5l5SUYNGiRaiuroZAIACfz8fw4cMBAMuXL5e90PLMmTMIDg5GUFAQQkJC0K9fP7z33nu6DI0QQgghRGd63Ezu0nuwRCIRjWD1IJWVlTQU3sPQPut5aJ/1LLS/Hm00kzshhBCdqq2tRVlZGSQSib5D6Vaqq6tV3jpD9IPH48HGxgZ9+/YFj/dwF/kowSKEEKIz586dw5tvvommpiZ9h9LtSCSSh/4lTnQjNDQUy5cvx4ABAzrdBiVYhBBCdKK2thZvvvkmwsLCMHv2bBgZGek7pG5FLBbD0JB+DXcnLS0tKCkpweeff44XXngBqampMDY27lRbtGcJIYToRFlZGZqamjB79my5d82SByjB6p4GDx4MJycnzJo1C0VFRQrvT1YXjU0SQgjRCek9VzRyRXoaU1NTAA+S4M6iBIsQQgghRMsowSKEEEII0TJKsAghhBANXbt2DeHh4fD19cXQoUNx+fJllXUXLFgAd3d3cByH7OxslfU4jkNAQACOHDkCAGhoaMCECRPg6+uLoKAgxMTEIC8vT1bf3d0dgwYNAp/PB5/Px549e2RlsbGxCAwMBJ/PR0REBIRCoazsyJEjCAkJAZ/Px5AhQ7Bjxw6l8axcuRINDQ1yy/h8Pu7du9f+xtECZX1rk0AggJ2dHTZs2KCzPsB6GJFIxAAwkUik71CIBioqKvQdAtEQ7bOep7vts5ycHBYaGspycnL0HYrWCQQClpSUxBhjbN++fSwsLExl3VOnTrHi4mI2cOBAJhQKZcubm5vl6gFgVVVVss/19fXs8OHDTCKRMMYY27RpE4uKipKVt22vtdbtJCcns8DAQMYYYxKJhNna2rKLFy8yxhgrKChgJiYmrKamRqGNtvF0pa7oe8aMGezTTz9VWqaNY5dGsAghhPQ6M2fOxPbt22Wf3333XSQmJqq1bnl5ObKysjBt2jQAwOTJk1FcXCw3utRaZGQkXFxcNI7R1NQUY8eOBcdxAIARI0agsLBQrXVbT2AqEolkbQAPRsqqq6sBPHg7ir29PUxMTOTWnzdvHgAgIiICfD4f5eXlCutyHIfVq1dj+PDhcHd3R0pKCtasWYOwsDD4+Pjg5MmTsvYyMzMRHR2NsLAwBAcHY9++fQCA+vp6xMfHw9/fH0FBQYiNjVXZt6o2pLEsW7YMwcHB8PX1xa5du1S231Xo+VBCCCFd5r6Y4Wq17tr3swHMDLkO62VlZWHBggVynxcvXgwAiI+PR25urtL1Dh48iPLycjg7O8umWOA4Dm5ubg/1SL86Nm7ciPHjx8stmz59OgBg2LBh+Oijj+Dg4CAre+mll5CWlgYAssuOHMdhz549mDRpEszNzVFVVYXk5GSFuZ62bt2Kbdu2IT09vd3Z5i0sLHD+/HkcP34c48ePx+bNm5GVlYV9+/bhrbfeQmZmJqqrqzFnzhwcOXIEzs7OuHv3LkJCQhAeHo4LFy6guroaV65cAfDP64Pa9t1eG9LJQDmOg1AoRH5+PsLCwjBy5EgIhUKF9rsKJViEEEK6zNVqIPSHzj/63pHfJhoipG/7derr61FQUIAhQ4b8s95vvyE0NBQA5O5lUkY6otKVEhMTkZeXh+PHj8uWnT59Gm5ubmhubsayZcswY8YMWSIFAN9++y0AYMeOHVi6dCmOHDkCsViMVatWITk5GZGRkcjMzERcXBwuXbqEvn072HBKxMfHAwDCwsJQV1eHKVOmAHiQ8F27dg0AkJGRgfz8fIwZM0Zu3dzcXAQFBSEnJwfz589HVFQUxo4dq7Sf9tqQJlizZs0CAHh6eiIyMhKnT5/GqFGj1GpfFyjBIoQQ0mX8bB4kQbpsvyNCoRCDBw+WjUDl5ubC0tIS9vb2ADoewXJ1dcXNmzdlE4UyxlBUVAQ3NzetfY/W1q5di+TkZKSmpsLMzEy2XNqfkZERFi5cCF9fX6Xrz5gxA/PmzUNFRQUKCgpQVlaGyMhIAMDQoUPh4uICoVCImJgYjWOTzhdlYGCg8Fk6hxRjDIMHD0ZGRobSNq5cuYITJ04gNTUVS5YsUfogQEdtKMNxHDw9PZW2b2trq9H37AxKsAghhHQZM0OuwxEmXcvKykJjYyMkEglaWlqwatUq8Pl8WXlHI1gAEBISgp07dyIhIQEHDhyAi4uLTi4Prl+/Hrt370Zqaqrcpbq6ujo0NzfLlu3evRvBwcEAHlxOu3//Pvr37w8ASElJgb29Pezs7CAWi3Hz5k3k5OTgscceQ15eHq5fv45BgwYp9G1paQmRSPTQL6QODw9HQUEBUlNT8dRTTwEAsrOz4e/vj/Lyctja2iIuLg5PP/00UlJSUFxcrNB3e21IL28mJSVh5cqVKCwsRHp6OjZs2ICSkhKl7VOCRQghhGhZVlYWPDw8wOfzYWZmhujoaHzzzTe4ePEigoKC1Gpj27ZtSEhIQGJiIqysrJCUlCQrmzVrFuLi4hAXFwcAmDt3Lg4fPoxbt25h9OjRsLS0VHlDfGslJSVYtGgRPD09IRAIAAAmJiY4f/48bt++jcmTJ6OlpQWMMXh6esouCYpEIjz33HOor68Hj8eDg4MDDh06BI7j4OTkhC+//BLPP/88eDweJBIJNm/erHT0bdGiRYiJiYGZmRl++eUXODo6qrVt2rK1tcXhw4exePFiLFq0CM3NzXBzc0NKSgouXbqEd955B4wxiMViTJ8+HYGBgUr7VtWGVEtLC4KDg1FXV4fPPvsM7u7uOHr0qNL2uwLHGGNd0pOW1NTUwNraGiKRCFZWVvoOh6hJeuMi6Tlon/U83W2fXb16FdOmTcPOnTvh5+en73Bk/P39sXfvXrl7sPSh7bsIOY5DVVXVQ48Y9Uad2XYJCQng8/lYuHChQpk2jl2apoEQQkivUVtbi9LSUvj7++s7FAVOTk6IioqSu1Gd6IZAIMCpU6dgbm6usz7oEiEhhJBew8LCAiKRSN9hKHXr1i19h9BjaXoxTjp9hS7RCBYhhBBCiJZRgkUIIYQQomWUYBFCCCGEaBklWIQQQgghWkYJFiGEEEKIllGCRQghhBCiZZRgEUIIIYRoGSVYhBBCCCFaRgkWIYQQQoiWUYJFCCGEaOjatWsIDw+Hr68vhg4disuXLyut19DQgAkTJsDX1xdBQUGIiYlR+aJnjuMQEBAg96qcBQsWwN3dHRzHITs7W+12Gxsb8e9//xs+Pj4ICAjAtGnTZGU//fQTwsLCEBgYiBEjRuDixYtK41m5ciUaGhrklvH5fNy7d6/jDfSQlPWtTQKBAHZ2dtiwYYPO+qAEixBCCNHQ3LlzMWfOHPz1119YunQpEhISVNadM2cOcnNzcfHiRYwfPx6zZs1SWTc9PR1jx46VfX722Wdx5swZDBw4UKN23377bXAch7/++guXLl3C2rVrAQBVVVV48cUXsWPHDvzxxx/45JNP8OKLLyqN5f3331dIcrKzs2Fpaakyfm1R1rc2paWlIS4uTmftA5RgEUII6YVmzpyJ7du3yz6/++67SExMVGvd8vJyZGVlyUaFJk+ejOLiYqUjU6amphg7diw4jgMAjBgxAoWFhWrHGRkZCRcXF43araurw1dffYXVq1fLyvv16wcAuH79Ouzt7TF48GAAQEREBIqKivD777/LtT9v3jxZOZ/PR3l5OYAHo2zV1dWyv69evRrDhw+Hu7s7UlJSsGbNGoSFhcHHxwcnT56UtZeZmYno6GiEhYUhODgY+/btAwDU19cjPj4e/v7+CAoKQmxsrMq+VbUhjWXZsmUIDg6Gr68vdu3apbL9rkIveyaEENJlJE0NEN8u1ln7hk6u4BmbdlgvKysLCxYskPu8ePFiAEB8fDxyc3OVrndiNmbmAAAgAElEQVTw4EGUl5fD2dkZhoYPfoVyHAc3NzcUFRXB29u73X43btyI8ePHq/t11Na63evXr8POzg6JiYlITU1Fnz59sHLlSjz55JPw8fFBRUUFMjIyEB4ejh9//BH37t1DYWEhQkJCZO1t3boV27ZtQ3p6OmxsbFT2a2FhgfPnz+P48eMYP348Nm/ejKysLOzbtw9vvfUWMjMzUV1djTlz5uDIkSNwdnbG3bt3ERISgvDwcFy4cAHV1dW4cuUKAKCyshJ2dnYKfbfXxoABAwA82A9CoRD5+fkICwvDyJEjIRQKFdrvKpRgEUII6TLi28UoX/e6ztp3XLQJxq4+7dapr69HQUEBhgwZIlv222+/ITQ0FACwZ8+edteXjqhoKjExEXl5eTh+/Hin1le3XbFYjBs3bsDf3x8fffQRhEIhYmJicPnyZTg5OWH//v145513UFtbi8cffxz+/v6yZFFT8fHxAICwsDDU1dVhypQpAIBhw4bh2rVrAICMjAzk5+djzJgxcuvm5uYiKCgIOTk5mD9/PqKiouQuj7bWXhvSBEt6idTT0xORkZE4ffo0Ro0apVb7ukAJFiGEkC5j6OQKx0WbdNp+R4RCIQYPHixLKnJzc2FpaQl7e3sAHY9gubq64ubNmxCLxTA0NARjDEVFRXBzc1PZ59q1a5GcnIzU1FSYmZl14pup366bmxt4PJ7s3qrg4GB4eHjg0qVLcHJygkAggEAgAPDgZvh+/frB39+/U/2bmj4YLTQwMFD4LBaLAQCMMQwePBgZGRlK27hy5QpOnDiB1NRULFmyRO5mfqmO2lCG4zh4enoqbd/W1laj79kZlGARQgjpMjxj0w5HmHQtKysLjY2NkEgkaGlpwapVq8Dn82XlHY1gAUBISAh27tyJhIQEHDhwAC4uLiovD65fvx67d+9Gampqu5fbNKWq3b59++LJJ5/Ezz//jLFjx6KgoAAFBQV47LHHAAA3b96Es7MzAODDDz9EdHS00tgtLS0hEokeOubw8HAUFBQgNTUVTz31FIAHN8v7+/ujvLwctra2iIuLw9NPP42UlBQUFxcr9N1eG8bGxgCApKQkrFy5EoWFhUhPT8eGDRtQUlKitP2uSLDoJndCCCG9SlZWFjw8PMDn8xEREQFXV1dcuHBB5XQFymzbtg3btm2Dr68vPvroIyQlJcnKZs2ahR9//BEAUFJSgkWLFqG6uhoCgQB8Ph/Dhw9Xu5+5c+fCxcUFJSUlGD16tCwR6qjdrVu34pNPPkFAQAAmTJiAbdu2yS6lLV++HH5+fvD29saNGzfw1VdfKe170aJFiImJkbvRvDNsbW1x+PBhJCYmIigoCP7+/nj77bchkUhw6dIljBw5EkFBQQgODsb06dMRGBio0Hd7bUi1tLQgODgYsbGx+Oyzz+Du7q6y/a7AMcZYl/SkJTU1NbC2toZIJIKVlZW+wyFqkt64SHoO2mc9T3fbZ1evXsW0adOwc+dO+Pn56TscGX9/f+zdu1fuHix9kF5ilOI4DlVVVVod5eotOrPtEhISwOfzsXDhQoUybRy7NIJFCCGk16itrUVpaWmn7znSJScnJ0RFRclNNEp0QyAQ4NSpUzA3N9dZH3QPFiGEkF7DwsICIpFI32EodevWLX2H0GNpejEuLS1NR5H8g0awCCGEEEK0jBIsQgghhBAtowSLEEIIIUTLKMEihBBCCNEySrAIIYQQQrSMEixCCCGEEC2jBIsQQgghRMsowSKEEEII0TJKsAghhBANXbt2DeHh4fD19cXQoUNx+fLlDtdJSkoCx3FISUlRWs5xHAICAuRmcm9sbMS///1v+Pj4ICAgANOmTZOVxcbGIjAwUPZORaFQKCtzd3fHoEGDwOfzwefzVb7AeuXKlWhoaJBbxufzce/evQ6/z8NS1rc2CQQC2NnZYcOGDTrroz00kzshhBCioblz52LOnDlISEjA/v37kZCQgMzMTJX1CwsLsX37dowYMaLddtPT0+Xep/f222+D4zj89ddf4DhObrb3vXv3yur+8MMPSEhIkHth9Z49e8Dn89vt7/3338fChQthamoqW5adnd3uOtqirG9tSktLQ0JCgk7aVgeNYBFCCOl1Zs6cie3bt8s+v/vuu0hMTFRr3fLycmRlZclGkyZPnozi4mLk5eUprS+RSDBr1ixs2rQJJiYmasdYV1eHr776CqtXrwbHcQCAfv36ycpbJ2IikUhWR13z5s0DAERERIDP56O8vBzAg5G06upq2d9Xr16N4cOHw93dHSkpKVizZg3CwsLg4+ODkydPytrLzMxEdHQ0wsLCEBwcjH379gEA6uvrER8fD39/fwQFBSE2NlZl36rakMaybNkyBAcHw9fXF7t27VLZfndAI1iEEEK6TIO4EUU1JTpr383KBaaGHScxWVlZWLBggdznxYsXAwDi4+ORm5urdL2DBw+ivLwczs7OMDR88CuU4zi4ubmhqKgI3t7eCuusX78eI0eORGhoqEbf5fr167Czs0NiYiJSU1PRp08frFy5Ek8++aSszksvvSR7r17bl0RPnz4dADBs2DB89NFHcHBwkCvfunUrtm3bpjBq1paFhQXOnz+P48ePY/z48di8eTOysrKwb98+vPXWW8jMzER1dTXmzJmDI0eOwNnZGXfv3kVISAjCw8Nx4cIFVFdX48qVKwCAyspK2NnZKfTdXhsDBgyQbWuhUIj8/HyEhYVh5MiREAqFCu13B5RgEUII6TJFNSWYffRNnbW/fcx6+Np5tVunvr4eBQUFGDJkiGzZb7/9JkuAVN2vJCUdbVHHn3/+iQMHDuD06dNqryMlFotx48YN+Pv746OPPoJQKERMTAwuX74MJycnAMC3334LANixYweWLl0qS7JOnz4NNzc3NDc3Y9myZZgxY4ZCAqau+Ph4AEBYWBjq6uowZcoUAA8St2vXrgEAMjIykJ+fjzFjxsitm5ubi6CgIOTk5GD+/PmIiorC2LFjlfbTXhvSBGvWrFkAAE9PT0RGRuL06dMYNWqUWu13NUqwCCGEdBk3KxdsH7Nep+13RCgUYvDgwbIRqNzcXFhaWsLe3h5AxyNYrq6uuHnzJsRiMQwNDcEYQ1FREdzc3BTqp6eno7CwED4+PgCAW7duYc6cObh58yZmz57d/ndxcwOPx8OLL74IAAgODoaHhwcuXbokS7CkZsyYgXnz5qGiogL29vayWIyMjLBw4UL4+vp2uF1Ukd4jZWBgoPBZLBYDABhjGDx4MDIyMpS2ceXKFZw4cQKpqalYsmSJ0vu8OmpDGY7j4OnpqbR9W1tbjb6n1rEeRiQSMQBMJBLpOxSigYqKCn2HQDRE+6zn6W77LCcnh4WGhrKcnBx9hyJn48aNjM/ns5aWFtbU1MSmTZvGxo8fr1EbUVFRLCkpiTHG2L59+1hoaKja6/3www+MMcaam5vlygCwqqoquWUxMTHs8OHDjDHG8vPzmb29PSspKWFVVVWstLRUVu+HH35gAwYMYBKJhNXW1sq1s27dOhYREaE0HktLS1ZYWKgyjtZ/v3fvHmudNhQXFzNzc3PGGGOVlZWsX79+7NixY7JyoVDIGhsbWXFxMautrWWMMdbY2MhcXV3ZxYsXFfpurw1pLCtWrGCMMVZQUMDs7OxYQUGByvYZY2zGjBns008/Vfrd26ONY5dGsAghhPQqWVlZ8PDwAJ/Ph5mZGaKjo/HNN9/g4sWLCAoKUquNbdu2ISEhAYmJibCyskJSUpKsbNasWYiLi0NcXNxDx7p161a88sorWLp0KXg8HrZt24YBAwbgxo0beO6551BfXw8ejwcHBwccOnQIHMfh9u3bmDx5MlpaWsAYg6enp+xSYluLFi1CTEwMzMzM8Msvv8DR0bFTcdra2uLw4cNYvHgxFi1ahObmZri5uSElJQWXLl3CO++8A8YYxGIxpk+fjsDAQKV9q2pDqqWlBcHBwairq8Nnn30Gd3d3HD16VGn7+sb9nRX2GDU1NbC2toZIJIKVlZW+wyFqkt7USHoO2mc9T3fbZ1evXsW0adOwc+dO+Pn56TscGX9/f+zdu1fuHix9kF5ilOI4DlVVVe3ecN6bdWb7JCQkgM/nY+HChRr1pY1jl6ZpIIQQ0mvU1taitLQU/v7++g5FgZOTE6Kiojp9MzqRJxAIcOrUKZibm+ulf7pESAghpNewsLCASCTSdxhKtZ5ElCjS9IKbdPoKfaERLEIIIYQQLdNpgtXQ0IAJEybA19cXQUFBiImJUTnT7aFDh+Dn5wcfHx9MmjQJNTU1ugyNEEIIIURndD6CNWfOHOTm5uLixYsYP368bJKw1mpra/HKK68gJSUF165dQ//+/fHhhx/qOjRCCCGEEJ3QaYJlamqKsWPHyt6PNGLECBQWFirUO3r0KIKDg2V36s+fPx+7d+/WZWiEEEIIITrTpTe5b9y4EePHj1dYXlRUhIEDB8o+u7u7y82S21bc2Hjs2fEjDA2NZMs4HgeOk88Xub//tF2ocJscxwFg4BRry7fAAW3X5sAp7YS1qsdT2uyDha1bk/Xfpj7XtldlXaqIvnVfqtqWkvXR5oWhnOIiKG6XNh841mpdDk1NzTAyNlKs124fyvrhWn1kMDbgYGxiBFNTU1ibWcDC3AbmxmYwNTQF7+/jwdDMACa2RjA0NVDWASGEEKJ1XZZgJSYmIi8vD8ePH3/ott4a9B5QoIWgyCOlFkAtagAov3/P0JIHM1cTWPn3gaWPKTgDzd4839tUVVXpOwSioe62z6qrqyGRSCAWi2WvVCH/oG3SfYnFYkgkElRXV8u9PFqTeea6JMFau3YtkpOTkZqaCjMzM4VyNzc3HDt2TPa5sLBQ7k3lbcVsGY7zmb/BwtICwIORF2MDY5iY/FOfMaYwUsUkTO4xTyb9b9tl8ov+/jv7p36rAiZXp9XfW/fPlKz7dz1ZPHIxKKknHwz+WU3Fem2/g7SGXNOsbUhgTKK43WSdyS9jbZcpjg0CkgfL6+7fh7mZmfx2aP0/1jZ+JVtMVp/JQm8Qt+B+QxMa79ej7n4NRLVVaKq7g+bmu2hBFSpMxag0Mod1sy38Gj3hXx6Amiv1MLY2xMAx/eAYZgNO6RAjATT7YUK6h+60z2xsbMDj8WBoaKjy53lvR9ulezI0NASPx4ONjU2nzymd79n169dj9+7dSE1NVTn76tNPP43XXnsNV69ehZ+fH7744gvZ27qVaWioh7vbAJrJvQfRxwzTd+olOJ9TiuvCX9FSnYrrFkLs75eCgY6umHr/BTR9L8bt85XwneYKU1vjLo2NEELIo02nCVZJSQkWLVoET09PCAQCAICJiQnOnz+P5cuXo3///pg3bx4sLS3xv//9DxMmTIBYLMaQIUOwY8cOXYZGegGHPjw8E+IKhLiirvk5pGQWwS19J6qMz2GNw38R1GcIniudguy1efCb4QYbXwt9h0wIIeQRodOnCF1cXMAYw/Xr15GdnY3s7GycP38eAPDBBx9g3rx5srpxcXG4evUq8vLykJKSAmtra12GRnoZcyMOL4YPxOtvvQv/iC8xqcgf91v+wAceq1BheQeXtxfgjrBa32ESQnqIa9euITw8HL6+vhg6dCguX76ssu6RI0cQEhICPp/f7gACx3EICAiQe1VObGwsAgMDwefzERERAaFQKCtbsGAB3N3dwXEcsrOzO9XnypUr0dDQILeMz+fj3r17HW6Dh6Wsb20SCASws7PDhg0bdNZHu1gPIxKJGAAmEon0HQrRQEVFhb5DkFPbJGGf7v+Vrf/oWfbkjgksKXEvS//PH6zs7F19h9ZtdLd9RjrW3fZZTk4OCw0NZTk5OfoOResEAgFLSkpijDG2b98+FhYWprSeRCJhtra27OLFi4wxxgoKCpiJiQmrqalhzc3NcnUBsKqqKrllrT8nJyezwMBA2edTp06x4uJiNnDgQCYUCtXqsy1lfXaVruh7xowZ7NNPP9V4PW0cu/SqHNIrmRtxWDh5BB5/fjvGlvkgxen/kOV4Htf3l+H2he71JBYhRPtmzpyJ7du3yz6/++67SExMVGvd8vJyZGVlYdq0aQCAyZMno7i4WOWbSjiOQ3X1gxHympoa2Nvbw8TERK2+Wt+7LBKJZPNKAkBkZCRcXFw63af0KlJERAT4fD7Ky8sV1uU4DqtXr8bw4cPh7u6OlJQUrFmzBmFhYfDx8cHJkydl7WVmZiI6OhphYWEIDg7Gvn37AAD19fWIj4+Hv78/goKCEBsbq7JvVW1IY1m2bBmCg4Ph6+uLXbt2qWy/O6DHF0ivNsLDBj5vfARJ0tcQ2v4/cC08YA8Dz5iDA1/5QxmEkM5raZKgvrxRZ+33cTSBgXHHYwdZWVlYsGCB3OfFixcDAOLj45Gbm6t0vYMHD6K8vFzuSXeO4+Dm5oaioiJ4e3vL1ec4Dnv27MGkSZNgbm6OqqoqJCcnw9jYWO1pGl566SXZi4tbXz5Upb0+W9u6dSu2bduG9PR0lQ+hAQ9ekH3+/HkcP34c48ePx+bNm5GVlYV9+/bhrbfeQmZmJqqrqzFnzhwcOXIEzs7OuHv3LkJCQhAeHo4LFy6guroaV65cAfDPQ09t+26vjQEDBsi+m1AoRH5+PsLCwjBy5EgIhUKF9rsDSrBIr2ffh4c3X30Fnx/wwJ8tm2AoMQLbCRhbGcHa01zf4RHySKkvb0T2euUjPdrAf9MbFi592o+hvh4FBQUYMmSIbNlvv/2G0NBQAMCePXvaXV862qIOsViMVatWITk5GZGRkcjMzERcXBwuXbrUblLT2rfffgsA2LFjB5YuXdphktVen3379lU7dqn4+HgAQFhYGOrq6mRP+Q8bNgzXrl0DAGRkZCA/Px9jxoyRWzc3NxdBQUHIycnB/PnzERUVhbFjxyrtp702pAmW9HV7np6eiIyMxOnTpzFq1Ci12u9qlGARAoDHcXj92Sex61Q/ZP6xApbNVsB2htD/+MHMUb2hfEJIx/o4moD/pnfHFR+i/Y4IhUIMHjxYNgKVm5sLS0tL2NvbA+h4BMvV1VXubSOMMRQVFcHNzU2hfnZ2NsrKyhAZGQkAGDp0KFxcXCAUCmVP16trxowZmDdvHioqKmSxKtNenzExMRr1CTx47R0AGBgYKHyWjsIxxjB48GBkZGQobePKlSs4ceIEUlNTsWTJEoWb8tVpQxmO4+Dp6am0fVtbW42+p7bRPViEtPJi1GCMHfkxhH334A53B799noOmezTbMiHaYmDMg4VLH539UffyYGNjIyQSCZqbm7Fq1Srw+XxZ+Z49e2RPvrf94+rqCkdHR4SEhGDnzp0AgAMHDsDFxUXh8iAAWTKWk5MDAMjLy8P169cxaNCgDuOsrq5GWVmZ7HNKSgrs7e07nFNQkz4tLS0hEok6jKUj4eHhKCgoQGpqqmxZdnY2mpqaUFJSAo7jEBcXh7Vr14IxhuLiYoW+22tDKikpCcCDCcnT09MRERGhsn19oxEsQtqIDfGCgfHHOHJ8JZ4qfQXnP7+EkYuCwDOif48Q8ijIysqCh4cH+Hw+zMzMEB0djW+++QYXL15EUFCQWm1s27YNCQkJSExMhJWVlewXP/DgMlZcXBzi4uLg5OSEL7/8Es8//zx4PB4kEgk2b94MNze3Du/BEolEeO6551BfXw8ejwcHBwccOnRIdqP73LlzcfjwYdy6dQujR4+GpaUl8vLy2u2zrUWLFiEmJgZmZmb45Zdf4OjoqMGW/IetrS0OHz6MxYsXY9GiRWhuboabmxtSUlJw6dIlvPPOO2CMQSwWY/r06QgMDFTat6o2pFpaWhAcHIy6ujp89tlncHd3x9GjR5W2r28cY0zJ+026r5qaGlhbW0MkEtFM7j2IPmZyf1jpV4pw5Of/YnTJTJj48TBiVpDcEzyPup64z3q77rbPrl69imnTpmHnzp3w8/PTdzgy/v7+2Lt3r9w9WPogvcQoxXEcqqqq1L43q7fpzPZJSEgAn8/HwoULNepLG8cu/ZOcEBUi/N0wLvY/OOP0I1pyDPDH4Sv6DokQ8pBqa2tRWloKf39/fYeiwMnJCVFRUWo9KUg6JhAIcOrUKZib6+dhJbpESEg7wgd7oa7pOQgPn0HQiREoGHADHsED9R0WIaSTLCwstHLPkS7cunVL3yF0a5pecJNObaEvlGAR0oGY4MGoqa1B0bECNH7XD1ZOlrDv330uwxBCCOl+6BIhIWqYHPE42DBjNBg0In3z72i4r7uJEgkhhPR8lGARoqbpz4zFrcFlsGqyxQ9rj2o8XE0IIaT3oASLEA3Mnv4Cctz+gGu1F3Z+tlff4RDSrfF4D37FNDc36zkSQjTT0NAAAHJPeWqK7sEiREPzX0/A/xJ3wffGEOzf/SOefSFO3yER0i31798fxsbG2L59O2bPng0jIyN9h9SttJ2mgehfS0sLSkpKsHnzZpiZmSmdO0xdNA8W6RLdbX6eh1V3vwGH1hyDTYMDjOKA6IgR+g5J6x61fdYbdMd9du7cObz55ptys3GTByQSiWyUj3QvoaGhWL58uewdiJ1BCRbpEt3xB//DKi69gz8+y0G9wX34vzII/l4e+g5Jqx7Fffao6677rLa2FmVlZZBIJPoOpVuprq6mSUW7GR6PB1tbW9jb2z908ktjk4R0kusAB9yeWI57+yzw686z6Pcfe9hR0k+IAgsLC/j6+uo7jG6nuybERDtobJKQhxA2YjAah9VhkCgI336R1OG7xQghhPQOlGAR8pCejo/AbZcyBJdH4bOtm/UdDiGEkG6AEixCtGDiG7GosriLx4qG4cvd3+g7HEIIIXpGCRYhWsAz4BD75khwAKwuO+DQqVR9h0QIIUSPKMEiREvMbPog4BUv9Kvvj6LTRfjj2l/6DokQQoieUIJFiBYNGOQEy5g+CKwaiiPJ+3G3qlrfIRFCCNEDSrAI0bLQp/3Q6FuPEeVj8EXSx2hupicLCSGkt6EEixAdEMwKQ4N1PcJuP4O1/1ul73AIIYR0MUqwCNEBniEP0QuHwgiGcC0LxZbvt+k7JEIIIV2IEixCdMTYyghhc/3het8Vjdc5/L+Tv+g7JEIIIV2EEixCdMjW0xKuz/RFWMXj+O23DAiv5uo7JEIIIV2AEixCdMzjiQEwGWKA6LI4fP/TZty+W6XvkAghhOgYJViE6BjHcQid7gfYARG3nsfG795FY1OzvsMihBCiQ5RgEdIFeEY8PD5/CMxhjkEVo/HJV8sgkUj0HRYhhBAdoQSLkC5iYmuMkFm+8LjnASPRQGzZvUXfIRFCCNERSrAI6ULW3hbwGO+MkeURKCy/ieRjP+s7JEIIITpACRYhXcwl0gHWQWYYWzIJJ3KTceHPHH2HRAghRMsowSKki3EcB/8XPGDqYIzRJVOxM201Sm5X6DssQgghWkQJFiF6YGDMQ/AcX1hzNuBXTMTm7xfhfkOjvsMihBCiJZRgEaInpnbGCHzZCz41PrBsDMOnX72HFnqykBBCHgmUYBGiRza+FvB4xhlRt6JwV2yGLf/3ub5DIoQQogWUYBGiZwMEfdF3qDUmFE3En7V/Ye+RI/oOiRBCyEOiBIsQPeM4Dr7PucDS3QyTCqchrWAfzv7+p77DIoQQ8hAowSKkG+AZ8hAw0wsWVmYYXTId+8+swV/Fd/QdFiGEkE6iBIuQbsLI3BDB83xhD3vwK57Dt/sX43ZNg77DIoQQ0gmUYBHSjfRxMEHgLG941HrAvv4JbP/qHdQ2tug7LEIIIRqiBIuQbsbayxyD4l0x9G4YGlucsXn7GjS30PQNhBDSk1CCRUg35DTMDs7R9hhdNgZ3xPXY9M2XYIzpOyxCCCFqogSLkG7K81/OsAuxQFzxcyi8n4vt+w7oOyRCCCFqogSLkG6K4zj4veAOK28zTLjxIv64fQx7f0rTd1iEEELUQAkWId0Yz4BD4EwvWPQzwzPFCTh7bQcOns3Wd1iEEEI6QAkWId2cgYkBguf5wsrCAtFlCTjx2yc49nuevsMihBDSDkqwCOkBjCwMEfLaINgb2OLx29PxU/pynL1cqO+wCCGEqEAJFiE9hKm9MYLn+8JZ4oywO9OQkvoufv+rVN9hEUIIUYISLEJ6EPP+fRA83xcuzQMQdPcF7D3yFv64flvfYRFCCGmDEixCehgL1z4IetUHbo1ueKzqeXz/45sQ5t/Vd1iEEEJaoQSLkB7Iyt0MQfO84XHfA96iSdjz/xYg81qZvsMihBDyN0qwCOmhrD3NETjbC9513vCvise+I4tw/nKBvsMihBACSrAI6dFsfC0Q9Ko33BvdEXxnOvalvofU33L1HRYhhPR6hgDw+++/d2plf39/mJqaajUgQohmrD3NEfK6L7jPAaPbL+PI2VWorFmA5wVD9R0aIYT0WoYAEBYWBo7j1F6JMQaO45CZmYmQkJB26y5YsAA//vgjbty4AaFQCD6fr1CnsLAQXl5eCAgIkC07cOAAvLy81I6JkN7MwqUPQt8YhN8/B54snYufuf9BVFGMWZMnanRuE0II0Q5D6V82b94Mf39/tVYSi8WIjY1Vq+6zzz6LJUuWYNSoUe3Ws7S0RHY2vQKEkM4y62eKoYv9kb3tL0y4MQeHJHuw7stCzH/5DZgZG+g7PEII6VVkCVZoaCiGDRum1kotLS1gjKlVNzIysnOREUI0ZmJthLA3HsOfO/Mx8fI0nHA+hk8+X4gZU1fB3cla3+ERQkivYQgA9fX1MDExUXslAwMDjdfpSF1dHUJDQ8EYw4QJE/Dee+/BwED1v7pramrkPpuYmGg1HkJ6KgMTHgJf9kL+0ZuIPh6DPMvr2Lp7AUaEvIEJke1f0ieEEKIdhgA6lZhoM5lxdnZGaWkpHB0dUVlZifj4eKxbtw5LlixRuY6rq6vc5yVLlmDp0qVai4loV1VVlb5D6HVsHzeFkVNfSA60wLlsLk6yPbh8+Rimjnszg68AAB4KSURBVJsBazPjDtenfdbz0D7rWWh/9Tx2dnZq1zVUVVBTU4OSkhI0NDQolHV0Y7umTExM4OjoCOBB8DNnzsR3333XboJVXFwMKysruTZoBKt70+TAJNphZwf083XAH7vy8My1abhifQX/27cMgwNexpQnw8Hr4AZ42mc9D+2znoX216NLIcEqLS3FK6+8gmPHjilUlj492NLSotUgysvLYWtrCyMjIzQ2NiI5ORnBwcHtrmNlZSWXYBFClDO2MkLoPD/cuVgN8d5meJd6I6vhV6z8cy8iI+biyZDH6ElDQgjRMoUEa8aMGfjrr7/w2WefwdfXF8bGHV9KaM/cuXNx+PBh3Lp1C6NHj4alpSXy8vKwfPly9O/fH/PmzcOZM2ewfPlyGBgYQCwWIzo6Gu+9995D9UsI+QfHcXDk28JukBWu/VyEYWdGogUjcOmnMzh7Kgm+/jGIi34S5vS0ISGEaAXH2jwOaGlpiZ07d2L8+PH6iqldNTU1sLa2hkgkohGsHqSyspKGwruR5loxco8V4Pa5apg0m6KsTxnKzHLQZN6Afr6PYfTjAhgxMe2zHobOs56F9tejTWEEy9vbG83NzfqIhRDSRYwsDDFkog/8x0lQln0Xtaeq0fdmBIwrjCEuFiMtIx31hlVoNGoA6wMYm5vD3NIM5tZWsLaxhkUfU1iYmcDE2AQmpqYwNjGGAY+DAQdA6eVG9aZ1kenkFUuu1Ypc20Y6arOD6g++VjuNcCo/gONxqqtqHBun8pKuWNyE5uamv+v/XYdTXf/B7uKkrdKlYkK0SCHBWrt2LRYtWoTAwED4+vrqIyZCSBfhGfLgEuYIlzBHSMQSVBXfw8XzV2CQz8G6zgHm9y1hXmGpsN59tOA+7gO43/VBk3ZJcLvdctZBssu4DsrB5PI91qZUvi3FtVV94lTExnE8GBkYwaSPEZxH2sP1Kcd24yOku1BIsJ588kk89dRT8Pf3R//+/WFjYyNXznEcLl682GUBEkK6Bs+QB3sPa0R7PA7gn8sXLWIJqiurUVhyGxV3K1BXcw9NzWI0NbdA0iKGpEUMSBjAODCm8ViVWvWZyg+tF6tuifv7N71asTHFvyqMhrWpLs1JlLbfYaeajRq1neO5dWwSiaTNk6EclH0h6VJOuoD9vfUY5Ouj9RdjaPtfThYPU+jrn/0hbYMDp7CX/un/n+3AHqwtFsNQXIcGwybcMuUQ2SccTUfEsBlkAUtXMxDS3SkkWEuXLsX69esRGhqqlZvcCSE9m4EhD/aOdrB3pHtFurtH7Z6eO/USfPn1D7Cp/xrrrM7jQ6sPced3ESVYpEdQSLC+/PJLfPDBB1i2bJk+4iGEEEIAAA59eJj+0kSc+e9pMKcbqLWpgWU5JVekZ+C1XWBsbIzhw4frIxZCCCFEjpslDzd9noHvvRaU/v/27j04qvpw//hzkk02IEkgQNKE3OQSIhBCQmEQR0sZK9jqIEgFOwIB5FIsMoz8gE7LpYW2WKAtULk4WBCxdkQYbKkZZapYvKBmuFkKEi4hCURREhKCue3m/P6g5EvYEDZwds8ueb9mMrCbz559Mp9AnpzL54QUq+rrGrsjAV7xKFhTpkzR1q1b7cgCAICH9IED1POSqS/MfFWX1qreVW93JOCmPA4RRkVFac+ePRo8eLAefPDBJk9ynz17tt8CAgBat/u7RutMXSd9HVkq1Ut1lW4523vsHwACikfBmj9/vqQr9/rbt2+fxwsoWAAAf4oKN1Tr7Krq0POSJFe1W06F2ZwKaJ5HwaqvZ9crACCwhMf0Uk39GUmSu8ra++ECvsA+VgBAwOuQkKS27ipJkouChSAQIknnzp2Ty+Vq0QvPnTsnt5tvcgCA73VOSKBgIaiESFJSUpL279/v9YvcbreSkpJY0R0A4BfJXeLUzl0nt+GW61sKFgKfQ5JM09SePXtUXFzs1Ys4TwsA4E+pHcLkqG+j6tBquar5GYTA13CS+9WrBwEACDThoYbCzLtUFVrFSe4ICg5JOn369C29OCEhwdIwAADcSJgRrarQKtV8W2d3FOCmHJKUkpJidw4AAJoVFt5BdSF1qqnmdjkIfCzTAAAICs6ITqoLqVNtTcuuegfsQMECAASFyMhOqgtxyVVTa3cU4KYoWACAoNChfZxcIXWqreYcLAQ+ChYAICh0bh+ruhCX6mq4ihCBz6NgbdmyRRcuXGhycGlpqbZs2eLzUAAAXK99+/aSalVfxzpYCHweBWvixIk6efJkk4NPnz6tiRMn+jwUAADXi+kQKcN0yeQcdwQBj4JlmuYNB5eVlSkyMtKngQAAaErH6LtkqE6G27A7CnBTDknKzc1Vbm5uw5MrV65UXFxco4HV1dV699131a9fP/8mBABAUkRYqCS3Quo5fRiBzyFJx48f1z/+8Q9JkmEY2rt3r5xOZ6OB4eHh6tOnj37729/6PyUAAJJk1CvUdNx8HGAzhyTNmjVLs2bNkiTdfffd2rlzpzIzM20NBgDA9UxDctQ7ZJqmDINDhQhcHr8G3Op9CQEA8DlDMmTIdJsyHBQsBK4m97OWlZUpNzdXxcXFqq6ubvQ5wzC0YMECv4QDAOBahiNUklRfZyqEI4UIYB7fnu+8845Gjx6tyspKtWnTRuHh4Y0+T8ECANgl1BEmSVfWwmoTanMa4MY8LsV47rnnNGDAAJ0+fVqXL19WWVlZo4/S0lI7cgIAoND//dJfw/0IEeA8CtapU6c0f/58paSk2JEHAIAbcka0kSRdvFRpcxKgeR4FKzs7W0VFRXZkAQCgWRFt75IkfXXhos1JgOZ5FKx169Zp9erVevvtt+VycT8CAEDgiGrXTpJ0oZSChcDmkKTIyMhG64nU1tbqhz/8oUJCQtSmTZtGLzAMQ+Xl5f5NCQCApJgOMaqXVFHBzyEENod05cR2FmwDAAS6uI4xKtG3+vbyt3ZHAZrlkKTFixfbHAMAgJtLiItViQpUU11ldxSgWdwxEwAQNJxRV87BctXW2JwEaJ7HQqNDhw694eCQkBBFR0crKytLEydOVJcuXXwaDgCAa4WEGqqXW/W1XISFwOaxBys6OlonTpzQ3r17VVFRoYiICFVUVGjv3r06fvy4ysrKtHLlSvXq1Uv79++3IzMAoBVzhbhlut12xwCa5VGwfvzjH6t9+/Y6ceKE8vLy9NZbbykvL0/5+fmKjo7WhAkTdOrUKXXv3l0///nP7cgMAGjF3Ead5DbtjgE0y6Ng/epXv9LixYs9VnJPTU3VokWLtGTJEnXo0EFz5szRvn37/BYUAABJcoe4ZdCvEOA8ClZhYeENl2wwDENnz56VJCUkJLAQKQDA7+oNtwyTpYUQ2DwK1oABA7Rw4UKP2+WcOXNGixYt0sCBAyVJBQUFnOQOAPC7+pB6GWao3TGAZnlcRbh+/Xr94Ac/ULdu3ZSRkaHOnTvr66+/1uHDhxUXF6dt27ZJkr766itNnTrV74EBAK2bGWoqxHSoymWqjYM9WQhMHgWrV69eOnnypP7yl78oLy9PJSUlyszM1NNPP62JEycqIiJCkjR37ly/hwUAwAiVDDl04bJLidFhdscBmuRRsCQpIiJCM2bM8HcWAABuKiTMkOEK0zdlFUqM7mh3HKBJrOQOAAgqDmeowurDdb70G7ujADfkkKSoqCi999576t+/vyIjI5u98bNhGCov5y7mAAB7ONs65CwP1/myryX1tDsO0CSHJD333HOKj4/X1b83V7AAALBTRGQbOYudKrn4ld1RgBtySNKiRYsanli8eLFdWQAAuClnuzZyup26XPm13VGAG2r2HKyioiJ99NFHunz5sr/yAADQrLZ3tZGz3qnqbylYCFxNFqwXX3xRXbp0UUpKiu6//3598cUXkqSRI0dq1apVfg0IAMC12rVrK6fbqdraC3ZHAW7Io2D96U9/0syZMzV+/Hi98847Ms3/u+HTkCFDGhYaBQDADg6nQyEKkbueoysIXB7rYK1Zs0YLFizQL3/5S7nd7kaf69mzZ8PeLAAA7OCIuLJvIMSsU2m1qZgILsxC4PHYg3X27FkNHjy4ycFhYWGqrKz0eSgAAG4kNOLKfQhNQzpxodrmNEDTPApWSkqKPv300yYHf/LJJ0pLS/N5KAAAbiTUeeVH12VHhM4UnrM5DdA0j4I1ZcoULV26VC+99JIqKiokSXV1dfrnP/+p5cuXa9q0aX4PCQDAVY62V/ZgVYXcpbOnT9qcBmiaR8GaM2eOJk2apKlTp6pz586SpPvuu08jRozQuHHjWnyPwmeffVapqakyDEMHDx684bhdu3YpPT1dPXr00KhRoxrKHQAA13JGh0khUofajqr68jO74wBNanKZhtWrVys/P18vvPCCli5dqj//+c86evSoVq9e3eI3GD16tD744AOlpKTccExlZaUmT56snTt3Kj8/XwkJCVqyZEmL3wsAcOczQg05O4apU3VHhdce0cnyersjAR48riK8qmvXrpYcDnzggQduOiY3N1dZWVlKT0+XJM2YMUMPPfSQli9fftvvDwC489wVG6HUkiS91/GSduzO0/8bPdDuSEAjTRYst9utTz75RMXFxaqu9rxCY/z48ZaGKCwsbLSHKzU1VSUlJXK5XHI4mu6A1x9CdDqdcjqdluYCAASmqNS7FH8sUSHtMxRyYqv++MJhdeoUq7YREQp3hCn0lu+pa0h+uh9vTU21nM4Iv7wXrPHDh2++0+gqj/ayf/9+jRo1SkVFRY0WGb3KMAzLC9atSEpKavR47ty5mjdvnk1pcDNlZWV2R0ALMWfBpzXNmbOXoYjPwvTkqSevPHFeEue7w9ce9n6oR8H66U9/qujoaL388svq1auXwsPDrYzWpOTkZO3evbvhcUFBgeLj42+490q6cp/EqKiohsfswQp8MTExdkdACzFnwac1zVmnuR1Vc7FOdVV1ulD5jcouVuhydZWqaut0/f4Bs4m/Xc+UZDTzeatVVVerTYQP9mD570vw51sFHY8Gc+TIEW3btk3f+973/BZi+PDheuaZZ3Ts2DGlp6dr7dq1Gjt2bLOviYqKalSwAACtixFiKCImXBEKV6TuUqrdgVqotLS0VRXi1sbjKsK0tDRLl0iYNm2aEhMTVVxcrGHDhql79+6SpIULF2r9+vWSpMjISG3cuFGPPfaYunfvruLiYi1YsMCyDAAAAP5kmNedaPX+++9r1qxZ+tvf/tZwVV8gqaioUHR0tMrLy9mDFUT4TS34MGfBhzkLLszXnc0hSRkZGTKuuWqipKREffr0UUJCgtq3b9/oBYZh6NChQ/5NCQAAEEQcktS/f/9GBQsAAAC3ziFJmzdvtjkGAADAnaPJW+UAAADg1lGwAAAALEbBAgAAsBgFCwAAwGIULAAAAItRsAAAACxGwQIAALAYBQsAAMBiFCwAAACLUbAAAAAsRsECAACwGAULAADAYhQsAAAAi1GwAAAALEbBAgAAsBgFCwAAwGIULAAAAItRsAAAACxGwQIAALAYBQsAAMBiFCwAAACLUbAAAAAsRsECAACwGAULAADAYhQsAAAAi1GwAAAALEbBAgAAsBgFCwAAwGIULAAAAItRsAAAACxGwQIAALAYBQsAAMBiFCwAAACLUbAAAAAsRsECAACwGAULAADAYhQsAAAAi1GwAAAALEbBAgAAsBgFCwAAwGIULAAAAItRsAAAACxGwQIAALAYBQsAAMBiFCwAAACLUbAAAAAsRsECAACwGAULAADAYhQsAAAAi1GwAAAALEbBAgAAsBgFCwAAwGIULAAAAItRsAAAACxGwQIAALAYBQsAAMBiPi9Y+fn5Gjx4sNLS0jRgwAAdOXLEY0xBQYFCQ0PVr1+/ho+TJ0/6OhoAAIBPOHz9BtOmTdPUqVOVk5OjN954Qzk5Ofrss888xkVGRurgwYO+jgMAAOBzPt2Ddf78eeXl5empp56SJD3++OMqKirSiRMnfPm2AAAAtvJpwSoqKlJ8fLwcjis7ygzDUHJysgoLCz3GXr58Wf3791d2drZ+/etfy+12N7vtioqKRh81NTU++RoAAABayueHCL0RHx+vs2fPKjY2VqWlpRozZoxWrlypuXPn3vA1SUlJjR7PnTtX8+bN83VU3KKysjK7I6CFmLPgw5wFF+Yr+MTExHg91qcFKykpSSUlJXK5XHI4HDJNU4WFhUpOTm40zul0KjY2VtKV8JMmTdJf//rXZgtWUVGRoqKiGm3D6XT65guBJVryjYnAwJwFH+YsuDBfdy6fHiKMjY1Vdna2tm7dKknavn27EhMT1b1790bjzp8/r7q6OklSTU2NduzYoaysrGa3HRUV1eiDcgUAAAKFz5dp2LBhgzZs2KC0tDQtW7ZMmzZtkiQtXLhQ69evlyR98MEHysrKUmZmprKzs/Wd73xHv/jFL3wdDQAAwCcM0zRNu0O0REVFhaKjo1VeXt7oECECW2lpKbvCgwxzFnyYs+DCfN3ZWMkdAADAYhQsAAAAi1GwAAAALEbBAgAAsBgFCwAAwGIULAAAAItRsAAAACxGwQIAALAYBQsAAMBiFCwAAACLUbAAAAAsRsECAACwGAULAADAYhQsAAAAi1GwAAAALEbBAgAAsBgFCwAAwGIULAAAAItRsAAAACxGwQIAALAYBQsAAMBiFCwAAACLUbAAAAAsRsECAACwGAULAADAYhQsAAAAi1GwAAAALEbBAgAAsBgFCwAAwGIULAAAAItRsAAAACxGwQIAALAYBQsAAMBiFCwAAACLUbAAAAAsRsECAACwGAULAADAYhQsAAAAi1GwAAAALEbBAgAAsBgFCwAAwGIULAAAAItRsAAAACxGwQIAALAYBQsAAMBiFCwAAACLUbAAAAAsRsECAACwGAULAADAYhQsAAAAi1GwAAAALEbBAgAAsBgFCwAAwGIULAAAAItRsAAAACxGwQIAALAYBQsAAMBiQVewampqGv2JwFdTU6Pnn3+eOQsizFnwYc6CC/MVfGpqarR48WKv58wwTdP0ZaD8/HxNmDBB33zzjaKjo7V582b17t3bY9yuXbs0Z84cud1uZWRkaPPmzYqKivIYV1xcrKSkJBUVFSkxMdGX0WGRiooKRUdHq7y8vMk5ReBhzoIPcxZcmK/g09I58/kerGnTpmnq1Kk6fvy45s2bp5ycHI8xlZWVmjx5snbu3Kn8/HwlJCRoyZIlvo4GAADgEz4tWOfPn1deXp6eeuopSdLjjz+uoqIinThxotG43NxcZWVlKT09XZI0Y8YMvfbaa76MBgAA4DMOX268qKhI8fHxcjiuvI1hGEpOTlZhYaG6d+/eMK6wsFApKSkNj1NTU1VSUiKXy9Xw2quuHtEsKSlp9LzT6ZTT6fTVl4LbUFFR0ehPBD7mLPgwZ8GF+Qo+V+fK2zOrfFqwfKGurk6SNHDgQJuToKWSkpLsjoAWYs6CD3MWXJiv4FNbW+vVOJ8WrKSkpEZ7okzTVGFhoZKTkxuNS05O1u7duxseFxQUNNrzda3U1FSdPHlSYWFhMgyj4Xn2YAEAAF+LjIz0apzPryIcMmSIcnJylJOTozfeeEPLli1TXl5eozGXLl1St27d9O9//1vp6en62c9+poiICK1YscKX0QAAAHzC5wXriy++UE5Oji5cuKCoqCht2rRJGRkZWrhwoRISEjR9+nRJ0t///nfNnTtXLpdLffr00csvv6zo6GhfRgMAAPAJnxcsAACA1iZgV3LPz8/X4MGDlZaWpgEDBujIkSNNjtu1a5fS09PVo0cPjRo1iisybOTNnH3++ed64IEHlJ6erj59+mjSpEmqqqqyIS0k7/+dXZWTkyPDMHTx4kU/JcS1vJ2vwsJCPfroo+rZs6d69eqlNWvW+DkprvJ2zp5//nn16tVL/fr106BBg/Tpp5/6OSkk6dlnn1VqaqoMw9DBgwdvOM6r7mEGqO9///vmpk2bTNM0zW3btpnf/e53PcZcunTJjI2NNY8ePWqapmk+88wz5pw5c/wZE9fwZs6OHz9uHjp0yDRN03S5XOYTTzxhLlq0yI8pcS1v5uyq7du3m08//bQpySwrK/NTQlzLm/mqr683s7Ozzddff73huS+//NJfEXEdb+bswIEDZnJysnnp0iXTNE3zlVdeMQcMGODPmPif999/3ywqKjJTUlLMAwcONDnG2+4RkAXrq6++MiMjI826ujrTNK/8hxEXF2fm5+c3Gvf666+bw4YNa3h85MgRs0uXLn7Niiu8nbPrLV++3JwwYYIfEuJ6LZmzL7/80uzfv79ZUVFBwbKJt/O1e/du895777UjIq7j7ZwdPHjQjI+PbyjCa9asMUeOHOn3vPg/zRUsb7tHQB4ibG6B0ms1t0Ap/MvbObvW5cuXtXHjRo0YMcJfMXGNlszZlClT9Pvf/97ry5NhPW/n67///a86d+6ssWPHKisrSyNHjtSpU6fsiNzqeTtnmZmZmj17tu6++24lJibqj3/8I4d1A5i33SMgCxbufLW1tRozZoweeughjRw50u44aMbGjRuVnJysoUOH2h0FXnC5XHr33Xe1YMECHThwQMOGDdMTTzxhdyw04/Tp09qxY4dOnDih4uJizZ49W2PGjLE7Fm5TQBasaxcoldTsAqVnzpxpeNzcAqXwLW/nTLqyGv+YMWMUHx+vVatW+Tsq/sfbOXvvvff05ptvKjU1VampqZKkvn376sCBA/6O3Kq15P/FrKws9e7dW5I0btw47d+/v+EuGPAfb+ds+/btysjIUEJCgiRp4sSJ+vDDD71eMRz+5W33CMiCFRsbq+zsbG3dulXSlW++xMTERvcvlKThw4dr//79OnbsmCRp7dq1Gjt2rN/zwvs5c7lcGjt2rGJiYvTiiy82Wo0f/uXtnL366qsqKipSQUGBCgoKJEmHDx9WVlaWvyO3at7O18MPP6zi4mKdPXtWkvTWW2/pnnvuUVhYmN8zt3bezlnXrl314YcfqrKyUtKVK9TS0tIUHh7u98y4Oa+7hy9ODrPCsWPHzEGDBpk9evQw+/fvbx4+fNg0TdNcsGCBuW7duoZxb775ptmzZ0+zW7du5ogRI8yLFy/aFbnV82bOtm7dakoy+/bta2ZmZpqZmZnmjBkz7Izdqnn77+xa4iR323g7X2+//baZmZlp9u3b17z//vsbxsH/vJmz+vp6c/78+WbPnj3Nvn37mvfee6+Zl5dnZ+xWa+rUqWaXLl3M0NBQMzY21uzWrZtpmrfWPVhoFAAAwGIBeYgQAAAgmFGwAAAALEbBAgAAsBgFCwAAwGIULAAAAItRsAAAACxGwQJwx0pNTZVhGDIMo2Gxx9s1aNCghm2uWLHCkm0CuPNQsADc0UaPHq2PP/5Yw4cPt2R7L730kj7++GNLtgXgzsVN+wDc0eLi4jRo0CDLtnf1Hn8A0Bz2YAEIaBUVFUpJSdHo0aMbPT99+nR17NhR586da/E2hwwZokceeUSvvfaaevToobZt2+rRRx9VWVmZzpw5o2HDhqldu3bq3bu39uzZY9FXAqA1oWABCGhRUVHatGmTduzYoVdeeUWSlJubqw0bNmjt2rVKSEi4pe0eOHBAq1at0ooVK7R+/Xrt3btXU6ZM0ejRo/XII49ox44dio2N1ahRoxpuwgsA3uIQIYCAN3ToUM2cOVMzZ85URkaGJk+erCeffFJjxoy55W2Wl5fr0KFD6tSpkyTp8OHDWrlypdatW6fp06dLkhISEpSRkaF//etfGjFihCVfC4DWgT1YAILCsmXLFB8fr0GDBikkJEQvvPDCbW2vX79+DeVKktLS0iRJDz74oMdzRUVFt/VeAFofChaAoNCmTRs99thjqqmp0U9+8hN16NDhtrbXvn37Ro/Dw8M9nr/6XHV19W29F4DWh4IFICgcPnxYf/jDH5SVlaU1a9bo6NGjdkcCgBuiYAEIeLW1tRo3bpwGDhyoffv2qU+fPho/frxcLpfd0QCgSRQsAAFv4cKFOnnypDZv3qzw8HBt2bJF//nPf7R06VK7owFAkyhYAALaRx99pOXLl2vlypXq1q2bJOmee+7R7373O/3mN79RXl6ezQkBwJNhmqZpdwgA8IXU1FT96Ec/0qpVqxQaGirDMG57m263W6ZpKiwsTMuXL9ecOXMsSArgTsMeLAB3tLVr1yosLEyvvvqqJdu77777FBYWZsm2ANy52IMF4I71+eefq6amRpLUtWtXxcTE3PY2jx071rCye1JSkuLi4m57mwDuPBQsAAAAi3GIEAAAwGL/H1dZKMH09t+RAAAAAElFTkSuQmCC\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = plotxh(\"LLxF with different \\$\\\\mu\\$, Breaking dam scenario\")\n",
    "for mu = [0.1, 0.2, 0.4, 0.8]\n",
    "    qs,t,ts = run_experiment(50, 1000, make_cfl_dt(mu), llxf!, outflow_bcs!, breakingdam_ics)\n",
    "    plotxh!(p, qs, \"\\$\\\\mu\\$=$mu [$ts timesteps]\")\n",
    "end\n",
    "display(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Comparing Lax-Friedrich to Local-Lax-Friedrich"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "q1,t,ts = run_experiment(50, 500, make_cfl_dt(0.3), llxf!, outflow_bcs!, breakingdam_ics)\n",
    "q2,t,ts = run_experiment(50, 500, make_cfl_dt(0.3), lxf!, outflow_bcs!, breakingdam_ics)\n",
    "p = plotxh(\"Breaking Dam using LxF vs Local-LxF\")\n",
    "plotxh!(p, q1, \"LLxF [$ts timesteps]\")\n",
    "plotxh!(p, q2, \"LxF [$ts timesteps]\")\n",
    "figure1 = p;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[36mINFO: \u001b[39m\u001b[22m\u001b[36mSaved animation to /Users/nathanwbrei/src/shallow_water/animations/breakingdam_reflecting_cmp.gif\n",
      "\u001b[39m"
     ]
    }
   ],
   "source": [
    "ncells = 200\n",
    "\n",
    "t0 = 0\n",
    "qs = breakingdam_ics(ncells)\n",
    "Fl = Array{Q,1}(ncells+2)\n",
    "Fr = Array{Q,1}(ncells+2)\n",
    "\n",
    "t0l = 0\n",
    "qsl = breakingdam_ics(ncells)\n",
    "Fll = Array{Q,1}(ncells+2)\n",
    "Frl = Array{Q,1}(ncells+2)\n",
    "\n",
    "a = @animate for t=0.0:4.0:1000.0\n",
    "    p = plotxh(\"Breaking dam, reflecting boundaries, t=$t\")\n",
    "    q,t0,ts = run_experiment!(qs, Fl, Fr, t0, t, ncells, make_cfl_dt(0.4), lxf!, reflecting_bcs!)\n",
    "    ql,t0l,tsl = run_experiment!(qsl, Fll, Frl, t0l, t, ncells, make_cfl_dt(0.4), llxf!, reflecting_bcs!)\n",
    "    plotxh!(p, q, \"LxF w=0.4, timesteps=$ts\")\n",
    "    plotxh!(p, ql, \"LLxF w=0.4, timesteps=$tsl\")\n",
    "end\n",
    "figure31 = gif(a, \"animations/breakingdam_reflecting_cmp.gif\", fps = 20);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"animations/breakingdam_reflecting_cmp.gif?0.19035386887478944>\" />"
      ],
      "text/plain": [
       "Plots.AnimatedGif(\"/Users/nathanwbrei/src/shallow_water/animations/breakingdam_reflecting_cmp.gif\")"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "figure31"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Run breaking dam scenario with $t=0..1000, ncells=200, correction=0.4$\n",
    "* Both waves propagate at the same speed, no apparent loss of conserved quantities\n",
    "* Local-Lax-Friedrich dissipates less than Lax-Friedrich for the same correction factor\n",
    "* Local-Lax-Friedrich is smooth, whereas Lax-Friedrich exhibits stairstepping"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Comparing Lax-Friedrich to Local-Lax-Friedrich"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "p = plotxh(\"LxF vs Local-LxF, Breaking dam scenario\")\n",
    "for w = [0.1, 0.4, 0.9]\n",
    "    qs,t,ts = run_experiment(50, 200, make_cfl_dt(w), lxf!, outflow_bcs!, breakingdam_ics)\n",
    "    plotxh!(p, qs, \"LxF \\$\\\\mu\\$=$w [$ts timesteps]\")\n",
    "end\n",
    "qs,t,ts = run_experiment(50, 200, make_cfl_dt(0.4), llxf!, outflow_bcs!, breakingdam_ics)\n",
    "plotxh!(p, qs, \"LLxF \\$\\\\mu\\$=0.4 [$ts timesteps]\")\n",
    "figure2 = p;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img 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\" />"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "figure2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "a = @animate for w = 0.1:0.1:1.0\n",
    "    qll,t,tsl = run_experiment(50, 200, make_cfl_dt(w), llxf!, outflow_bcs!, breakingdam_ics)\n",
    "    ql,t,ts   = run_experiment(50, 200, make_cfl_dt(w), lxf!, outflow_bcs!, breakingdam_ics)\n",
    "    p = plotxh(\"Breaking Dam comparison of LxF vs Local-LxF\")\n",
    "    plotxh!(p, qll, \"LLxF w=$w\")\n",
    "    plotxh!(p, ql, \"LxF w=$w\")\n",
    "end\n",
    "llxf_w_lt_1 = a;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[36mINFO: \u001b[39m\u001b[22m\u001b[36mSaved animation to /Users/nathanwbrei/src/shallow_water/animations/llxf_w_lt_1.gif\n",
      "\u001b[39m"
     ]
    }
   ],
   "source": [
    "figure3 = gif(llxf_w_lt_1, \"animations/llxf_w_lt_1.gif\", fps = 10);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"animations/llxf_w_lt_1.gif?0.1747817274746899>\" />"
      ],
      "text/plain": [
       "Plots.AnimatedGif(\"/Users/nathanwbrei/src/shallow_water/animations/llxf_w_lt_1.gif\")"
      ]
     },
     "execution_count": 211,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "figure3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "* For Lax-Friedrich, $w$ affects dissipation\n",
    "* For Local-Lax-Friedrich, $w$ affects dissipation much less\n",
    "* Lax-Friedrich approaches Local-Lax-Friedrich as $w \\to 1.0$\n",
    "* Both methods are unstable for $w > 1.0$ due to CFL violation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Comparing Lax-Friedrich to Local-Lax-Friedrich"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[36mINFO: \u001b[39m\u001b[22m\u001b[36mSaved animation to /Users/nathanwbrei/src/shallow_water/animations/gaussian_cmp.gif\n",
      "\u001b[39m"
     ]
    }
   ],
   "source": [
    "ncells = 200\n",
    "\n",
    "t0 = 0\n",
    "qs = gaussian_ics(ncells)\n",
    "Fl = Array{Q,1}(ncells+2)\n",
    "Fr = Array{Q,1}(ncells+2)\n",
    "\n",
    "t0l = 0\n",
    "qsl = gaussian_ics(ncells)\n",
    "Fll = Array{Q,1}(ncells+2)\n",
    "Frl = Array{Q,1}(ncells+2)\n",
    "\n",
    "a = @animate for t=0.0:4.0:1000.0\n",
    "    p = plotxh(\"Gaussian, periodic boundaries, t=$t\")\n",
    "    q,t0,ts = run_experiment!(qs, Fl, Fr, t0, t, ncells, make_cfl_dt(0.4), lxf!, periodic_bcs!)\n",
    "    ql,t0l,tsl = run_experiment!(qsl, Fll, Frl, t0l, t, ncells, make_cfl_dt(0.4), llxf!, periodic_bcs!)\n",
    "    plotxh!(p, q, \"LxF w=0.4, timesteps=$ts\")\n",
    "    plotxh!(p, ql, \"LLxF w=0.4, timesteps=$tsl\")\n",
    "end\n",
    "figure32 = gif(a, \"animations/gaussian_cmp.gif\", fps = 20);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"animations/gaussian_cmp.gif?0.845637128379553>\" />"
      ],
      "text/plain": [
       "Plots.AnimatedGif(\"/Users/nathanwbrei/src/shallow_water/animations/gaussian_cmp.gif\")"
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "figure31"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Run gaussian scenario with $t=0..1000, ncells=200, correction=0.4$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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\" />"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 200\n",
    "p = plotxh(\"LxF vs Local-LxF, Gaussian scenario\")\n",
    "for w = [0.1, 0.4, 0.9]\n",
    "    qs,t,ts = run_experiment(t, 200, make_cfl_dt(w), lxf!, reflecting_bcs!, gaussian_ics)\n",
    "    plotxh!(p, qs, \"LxF \\$\\\\mu\\$=$w [$ts timesteps]\")\n",
    "end\n",
    "qs,t,ts = run_experiment(t, 200, make_cfl_dt(0.4), llxf!, reflecting_bcs!, gaussian_ics)\n",
    "plotxh!(p, qs, \"LLxF \\$\\\\mu\\$=0.4 [$ts timesteps]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Implementation Details -- Spatial Discretization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "scrolled": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "p = plotxh(\"Gaussian for different ncells\")\n",
    "for ncells = [100,200,300,400,500,600]\n",
    "    qs,t,ts = run_experiment(2000, ncells, 1.0, periodic_bcs!, gaussian_ics)\n",
    "    plotxh!(p, qs, \"ncells=$ncells [$ts timesteps]\")\n",
    "end\n",
    "display(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "# Implementation Details -- Staircase instability from incorrect dt\n",
    "\n",
    "* The existing code skeleton does not use the $\\Delta t$ obtained from the CFL condition inside Lax-Friedrichs\n",
    "* Instead, it uses the $\\Delta t$ from the previous timestep\n",
    "* The initial value $\\Delta t_0 = 0.4\\frac{ncells}{a_{adv}}$ where $a_{adv} = 0.25$\n",
    "* This leads to a staircase instability:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "q1,t,ts1 = run_experiment(800, 200, make_cfl_dt(0.4), lxf!, outflow_bcs!, breakingdam_ics)\n",
    "q2,t,ts2 = run_experiment(800, 200, make_lagging_dt(0.4), outflow_bcs!, breakingdam_ics)\n",
    "\n",
    "p = plotxh(\"Breaking Dam comparison of LxF vs LxF-staircase\")\n",
    "plotxh!(p, q1, \"LLxF w=0.7 [$ts1 timesteps]\")\n",
    "plotxh!(p, q2, \"LLxF_staircase w=0.7 [$ts2 timesteps]\")\n",
    "display(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "# Thank you!\n",
    "\n",
    "---\n"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Julia 0.6.0",
   "language": "julia",
   "name": "julia-0.6"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}