22.06.07 Navier stokes Hirt VOF method.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8f6ea07f-f858-48a6-8479-316d0730e860",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "04c3b3ac-5e25-4dec-82a2-ee3ee2d8e706",
   "metadata": {},
   "outputs": [],
   "source": [
    "L_x = 100\n",
    "g = 9.81\n",
    "H = 100\n",
    "\n",
    "N_x = 301\n",
    "dx = L_x/(N_x - 1)\n",
    "dt = 0.002\n",
    "N_t = 50000\n",
    "err = 1e-4\n",
    "x = np.linspace(0,L_x,N_x)\n",
    "h = np.zeros(N_x)\n",
    "u = np.zeros(N_x)\n",
    "D = 100\n",
    "slope = lambda x: 0.7*(x>700)*(x-700)\n",
    "# slope = lambda x: 0.2*x\n",
    "\n",
    "b = slope(x)\n",
    "H = D - b\n",
    "b_ = np.zeros(N_x)\n",
    "# b = np.zeros(N_x)\n",
    "# h = 10*np.exp(-((x)**2/(2*(0.05E+3)**2)))\n",
    "h[int(1*N_x/16):int(2*N_x/8)] = 50\n",
    "nu = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4616dd39-a6aa-4493-acfb-d8087427248c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = np.ones(N_x)*0.5\n",
    "\n",
    "h[:300]= 2\n",
    "slope = lambda x,b,L: (x>=b)*(x-b)*(L/(L_x-b))\n",
    "dam  = lambda x,a,b,L: ((x>=a)&(x<=b))*L\n",
    "\n",
    "u = np.zeros(N_x)\n",
    "z = np.ones(N_x)*0.5\n",
    "s = slope(x,90,2)\n",
    "d = dam(x,20,30,3)\n",
    "z = z\n",
    "z_ = np.zeros(N_x)\n",
    "\n",
    "h = np.where(h>=z,h-z,0)\n",
    "plt.plot(h)\n",
    "plt.show()\n",
    "# z[150:200]=0\n",
    "fig, (axh,axu) = plt.subplots(2, 1,facecolor ='white')\n",
    "line_u,=axu.plot(x,u)\n",
    "line_h,=axh.plot(x,h+z)\n",
    "fill_=axh.fill_between(x,z,z_,color ='tab:orange')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "525e380d-945d-4414-a44b-78c2948fbdef",
   "metadata": {},
   "outputs": [],
   "source": [
    "N_x = 200-1 # for Fx,and Px\n",
    "N_z = 200-1  # for Fz,and Pz\n",
    "\n",
    "U_x = N_x + 2 \n",
    "U_z = N_z\n",
    "\n",
    "W_x = N_x\n",
    "W_z = N_z + 2\n",
    "\n",
    "L_x = 100\n",
    "L_z = 100\n",
    "\n",
    "# U = np.zeros((U_x,U_y+2)) # N_x+2, N_y    , N_x [0,last] =0,and if you N_y +2 for convinient, so -1, max+ 1 also 0 for BC\n",
    "# V = np.zeros((V_x+2,V_y)) # N_x  , N_y + 2, N_y [0,last] =0,and if you N_x +2 for convinient, so -1, max+ 1 also 0 for BC\n",
    "\n",
    "\n",
    "# x = np.linspace(0,L_x,U_x,endpoint=True) # contain the boundary, make the all area\n",
    "# y = np.linspace(0,L_y,V_y,endpoint=True) # contain the boundary, make the all area\n",
    "# X,Y = np.meshgrid(x,y,indexing='ij')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6d00a672",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "U = np.zeros((U_x,U_z+2)) # N_x+2, N_z    , N_x [0,last] =0,and if you N_z +2 for convinient, so -1, max+ 1 also 0 for BC\n",
    "W = np.zeros((W_x+2,W_z)) # N_x  , N_z + 2, N_z [0,last] =0,and if you N_x +2 for convinient, so -1, max+ 1 also 0 for BC\n",
    "\n",
    "\n",
    "x = np.linspace(0,L_x,U_x,endpoint=True) # contain the boundary, make the all area\n",
    "z = np.linspace(0,L_z,W_z,endpoint=True) # contain the boundary, make the all area\n",
    "X,Z = np.meshgrid(x,z,indexing='ij')\n",
    "dx, dz = L_x/(N_x-1), L_z/(N_z-1)\n",
    "slope = lambda x,b,L: (x>=b)*(x-b)*(L/(L_x-b))\n",
    "B_X = slope(X,10,20)\n",
    "# plt.plot(x,slope(x,0,20))\n",
    "height = lambda x,b,h1,h2: (x<=b)*(h1) + (x>b)*(h2)\n",
    "H_X = height(X,10,30,20)\n",
    "BC = np.where(((X==0)|(X == L_x)|(Z==0)|(Z==L_z)))\n",
    "FC = np.where(((X==0)|(Z==0)|(Z<=H_X)|(Z<=B_X)))\n",
    "FC_not = np.where(~((X==0)|(X == L_x)|(Z==0)|(Z==L_z)|(Z<=H_X)|(Z<=B_X)))\n",
    "TC = np.where(((X==0)|(Z==0)|(Z<=B_X))|(((Z==L_z)|(X==L_x)))) # Topology condition\n",
    "\n",
    "HC = np.where((Z<=H_X)&(Z>B_X))\n",
    "\n",
    "# plt.imshow(x, height(x,10,10,20))\n",
    "# plt.imshow(H_x.T,vmin=0, vmax= 100)\n",
    "F = np.zeros_like(U)\n",
    "F[FC] = 1\n",
    "# F[HC] = 1\n",
    "plt.subplot(121)\n",
    "plt.imshow(F.T,extent=[0,L_x,0,L_z],origin='lower')\n",
    "plt.colorbar(orientation=\"horizontal\")\n",
    "# set pressure by height\n",
    "P = np.zeros_like(U)\n",
    "P = -g*dz*0.1*P\n",
    "P[HC] = -g*dz\n",
    "# P[TC_not] = 0\n",
    "for i in range(N_z-1,0,-1):\n",
    "\n",
    "    P[:,i-1]+=P[:,i]\n",
    "P[TC] = 0\n",
    "plt.subplot(122)\n",
    "plt.imshow(P.T[1:,1:],extent=[0,L_x,0,L_z],origin='lower')\n",
    "plt.colorbar(orientation=\"horizontal\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "bb2188c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set pressure by height\n",
    "\n",
    "F = np.zeros_like(U)\n",
    "F[TC] = 1\n",
    "F[HC] = 1\n",
    "# BC = np.where(Y<B_X)\n",
    "# U[BC] = 0\n",
    "plt.subplot(121)\n",
    "plt.imshow(F.T,extent=[0,L_x,0,L_z],origin='lower')\n",
    "plt.colorbar(orientation=\"horizontal\")\n",
    "# set pressure by height\n",
    "P = np.zeros_like(U)\n",
    "P[HC] = -g*dz\n",
    "# P[TC_not] = 0\n",
    "for i in range(N_z-1,-1,-1):P[:,i-1]+=P[:,i]\n",
    "P[TC] = 0\n",
    "plt.subplot(122)\n",
    "plt.imshow(P.T,extent=[0,L_x,0,L_z],origin='lower')\n",
    "plt.colorbar(orientation=\"horizontal\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "262e2d7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from numba import jit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "161daf48",
   "metadata": {},
   "outputs": [],
   "source": [
    "def padding_2D(UC,axis='x',HOW ='edge'):\n",
    "    if axis == 'x':\n",
    "        if HOW == 'constant':\n",
    "            U_pad = np.pad(UC,((1,1),(0,0)),'constant',constant_values = 0)\n",
    "        else:\n",
    "            U_pad = np.pad(UC,((1,1),(0,0)),'edge')\n",
    "        UW = U_pad[:-2,:]\n",
    "        UE = U_pad[2:,:]\n",
    "        return UW,UC,UE\n",
    "    if axis == 'z':\n",
    "        if HOW == 'constant':\n",
    "            U_pad = np.pad(UC,((0,0),(1,1)),'constant',constant_values = 0)\n",
    "        else:\n",
    "            U_pad = np.pad(UC,((0,0),(1,1)),'edge')\n",
    "        UN = U_pad[:,2:]\n",
    "        US = U_pad[:,:-2]\n",
    "        return US,UC,UN\n",
    "\n",
    "\n",
    "def set_dt(U,W,dx,dz,dt,c_num,err=1e-5):\n",
    "    dx_u = dx/np.max(U)\n",
    "    dz_w = dz/np.max(W)\n",
    "    newdt = min(c_num*dx_u,c_num*dz_w,dt)\n",
    "    newdt = max(newdt,err)\n",
    "    return newdt\n",
    "\n",
    "def NS_solver(U,W,P,F,dx,dz,dt,nu,beta0=1.7,c_num = 0.7,g=g):\n",
    "\n",
    "    # UC[TC] = 0\n",
    "    # WC[TC] = 0\n",
    "    \n",
    "    PN = P.copy()\n",
    "    UW,UC,UE = padding_2D(U.copy(),'x','constant')\n",
    "    US,UC,UN = padding_2D(U.copy(),'z','constant')\n",
    "    WW,WC,WE = padding_2D(W.copy(),'x','constant')\n",
    "    WS,WC,WN = padding_2D(W.copy(),'z','constant')\n",
    "    \n",
    "    UiC = (UC + UW)/2\n",
    "    UiCE = (UE + UC)/2\n",
    "    WiC = (WC + WS)/2\n",
    "    WiCN = (WN + WC)/2\n",
    "    UUup = np.where(UiC>=0,UW,UC)\n",
    "    UUupE = np.where(UiCE>=0,UC,UE)\n",
    "    \n",
    "    FUX = (UiCE*UUupE - UiC*UUup)*dx\n",
    "    \n",
    "    UWup = np.where(WiC>=0,US,UC)\n",
    "    UWupN = np.where(WiCN>=0,UC,UN)\n",
    "    \n",
    "    FUZ = (WiCN*UWupN-WiC*UWup)*dz\n",
    "    \n",
    "\n",
    "    WUup = np.where(UiC>=0,WW,WC)\n",
    "    WUupE = np.where(UiCE>=0,WC,WE)\n",
    "    \n",
    "    FWX = (UiCE*WUupE - UiC*WUup)*dx\n",
    "    \n",
    "    Wup = np.where(WiC>=0,WS,WC)\n",
    "    WupN = np.where(UiCE>=0,WC,WN)\n",
    "    \n",
    "    FWZ = (WiCN*WupN-WiC*Wup)*dz\n",
    "    \n",
    "    VISX = nu*((1/(dx*dx))*(UE - 2*UC + UN) + (1/(dz*dz))*(UN - 2*UC + UW))\n",
    "    VISZ = nu*((1/(dx*dx))*(WE - 2*WC + WN) + (1/(dz*dz))*(WN - 2*WC + WW))\n",
    "    \n",
    "    PW,PC,PE = padding_2D(P.copy(),'x','constant')\n",
    "    PS,PC,PN = padding_2D(P.copy(),'z','constant')\n",
    "    PX = (PC - PW)/dx\n",
    "    PZ = (PC - PS)/dz\n",
    "    \n",
    "    U = UC + dt*(-PX - FUX - FUZ + VISX) \n",
    "    W = WC + dt*(-PZ - FWX - FWZ + VISZ - g) \n",
    "    \n",
    "    # UW,UC,UE = padding_2D(U.copy(),'x','constant')\n",
    "    # WS,WC,WN = padding_2D(W.copy(),'z','constant')\n",
    "    # D = (-(1/dx)*(UC - UW) + (1/dz)*(WC-WS))\n",
    "    # beta = beta0/(2*dt*(1/(dx*dx) + 1/(dz*dz)))\n",
    "    # dP = beta*D\n",
    "    # dPW,dPC,dPE = padding_2D(dP,'x','constant')\n",
    "    # dPS,dPC,dPN = padding_2D(dP,'z','constant')\n",
    "    # P = PN+dP\n",
    "    # # P[TC] = 0\n",
    "    # U = UC + (dt/dx)*(dPC - dPW)\n",
    "    # W = WC + (dt/dz)*(dPC - dPS)\n",
    "    \n",
    "    new_dt = set_dt(U,W,dx,dz,dt,c_num)\n",
    "    \n",
    "    P[TC] = 0\n",
    "    U[TC] = 0\n",
    "    W[TC] = 0\n",
    "    # U[TC]=-U[TC[0],TC[1]+1] \n",
    "\n",
    "    # W[TC]=-W[TC[0]+1,TC[1]] \n",
    "    return U,W,P,new_dt\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c66c3d83-0d1b-41dd-9479-75db5402ba49",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x2197e4ab190>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "UW,UC,UE = padding_2D(U.copy(),'x')\n",
    "WS,WC,WN = padding_2D(W.copy(),'z')\n",
    "PN = P.copy()\n",
    "D = (-(1/dx)*(UC - UW) + (1/dz)*(WC-WS))\n",
    "beta0 = 1.7\n",
    "beta = beta0/(2*dt*(1/(dx*dx) + 1/(dz*dz)))\n",
    "dP = beta*D\n",
    "plt.imshow((PN).T, origin='lower')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "d280bd0c-6f3c-4695-86c7-7cc82930023f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x2197f849000>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Unew,Wnew,Pnew, newdt = NS_solver(U,W,P,F,dx,dz,dt,nu,1e-6,c_num=0.1)\n",
    "\n",
    "plt.figure(figsize=(15,5))\n",
    "plt.subplot(131)\n",
    "plt.imshow(Unew.T,origin='lower')\n",
    "plt.colorbar(orientation=\"horizontal\")\n",
    "plt.subplot(132)\n",
    "plt.imshow(Wnew.T,origin='lower')\n",
    "plt.colorbar(orientation=\"horizontal\")\n",
    "plt.subplot(133)\n",
    "plt.imshow(Pnew.T,origin='lower')\n",
    "plt.colorbar(orientation=\"horizontal\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "0b673626",
   "metadata": {},
   "outputs": [],
   "source": [
    "T_list =[]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6ed3bbc8-1b44-4959-833c-d327ab255f58",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\kim9y\\AppData\\Local\\Temp\\ipykernel_35004\\3377654964.py:61: RuntimeWarning: overflow encountered in multiply\n",
      "  FWZ = (WiCN*WupN-WiC*Wup)*dz\n",
      "C:\\Users\\kim9y\\AppData\\Local\\Temp\\ipykernel_35004\\3377654964.py:61: RuntimeWarning: invalid value encountered in subtract\n",
      "  FWZ = (WiCN*WupN-WiC*Wup)*dz\n",
      "C:\\Users\\kim9y\\AppData\\Local\\Temp\\ipykernel_35004\\3377654964.py:40: RuntimeWarning: invalid value encountered in add\n",
      "  WiC = (WC + WS)/2\n",
      "C:\\Users\\kim9y\\AppData\\Local\\Temp\\ipykernel_35004\\3377654964.py:41: RuntimeWarning: invalid value encountered in add\n",
      "  WiCN = (WN + WC)/2\n",
      "C:\\Users\\kim9y\\AppData\\Local\\Temp\\ipykernel_35004\\3377654964.py:50: RuntimeWarning: invalid value encountered in multiply\n",
      "  FUZ = (WiCN*UWupN-WiC*UWup)*dz\n",
      "C:\\Users\\kim9y\\AppData\\Local\\Temp\\ipykernel_35004\\3377654964.py:56: RuntimeWarning: invalid value encountered in multiply\n",
      "  FWX = (UiCE*WUupE - UiC*WUup)*dx\n",
      "C:\\Users\\kim9y\\AppData\\Local\\Temp\\ipykernel_35004\\3377654964.py:61: RuntimeWarning: invalid value encountered in multiply\n",
      "  FWZ = (WiCN*WupN-WiC*Wup)*dz\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x2197fcbc430>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(1000):\n",
    "    T_list.append(newdt)\n",
    "    Unew,Wnew,Pnew, newdt = NS_solver(Unew,Wnew,Pnew,F,dx,dz, newdt,nu,1e-6,c_num=0.1)\n",
    "\n",
    "plt.figure(figsize=(15,5))\n",
    "plt.subplot(131)\n",
    "plt.imshow(Unew.T,origin='lower')\n",
    "plt.colorbar(orientation=\"horizontal\")\n",
    "plt.subplot(132)\n",
    "plt.imshow(Wnew.T,origin='lower')\n",
    "plt.colorbar(orientation=\"horizontal\")\n",
    "plt.subplot(133)\n",
    "plt.imshow(Pnew.T,origin='lower')\n",
    "plt.colorbar(orientation=\"horizontal\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e6026735",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(np.cumsum(T_list))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "3dbf08ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "N_x = 51 # for Fx,and Px\n",
    "N_z = 51  # for Fz,and Pz\n",
    "\n",
    "U_x = N_x  \n",
    "U_z = N_z\n",
    "\n",
    "W_x = N_x\n",
    "W_z = N_z \n",
    "\n",
    "L_x = 100\n",
    "L_z = 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b8f53530",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "U = np.zeros((U_x,U_z)) # N_x+2, N_z    , N_x [0,last] =0,and if you N_z +2 for convinient, so -1, max+ 1 also 0 for BC\n",
    "W = np.zeros((W_x,W_z)) # N_x  , N_z + 2, N_z [0,last] =0,and if you N_x +2 for convinient, so -1, max+ 1 also 0 for BC\n",
    "\n",
    "\n",
    "x = np.linspace(0,L_x,U_x,endpoint=True) # contain the boundary, make the all area\n",
    "z = np.linspace(0,L_z,W_z,endpoint=True) # contain the boundary, make the all area\n",
    "X,Z = np.meshgrid(x,z,indexing='ij')\n",
    "dx, dz = L_x/(N_x-1), L_z/(N_z-1)\n",
    "slope = lambda x,b,L: (x>=b)*(x-b)*(L/(L_x-b))\n",
    "B_X = slope(X,0,0)\n",
    "# plt.plot(x,slope(x,0,20))\n",
    "height = lambda x,b,h1,h2: (x<=b)*(h1) + (x>b)*(h2)\n",
    "H_X = height(X,10,30,20)\n",
    "BC = np.where(((X==0)|(X == L_x)|(Z==0)|(Z==L_z)))\n",
    "FC = np.where(((X==0)|(Z==0)|(Z<=H_X)|(Z<=B_X)))\n",
    "FC_not = np.where(~((X==0)|(X == L_x)|(Z==0)|(Z==L_z)|(Z<=H_X)|(Z<=B_X)))\n",
    "TC = np.where(((X==0)|(Z==0)|(Z<=B_X))&(~((Z==L_z)|(X==L_x)))) # Topology condition\n",
    "\n",
    "HC = np.where((Z<=H_X)&(Z>B_X))\n",
    "\n",
    "# plt.imshow(x, height(x,10,10,20))\n",
    "# plt.imshow(H_x.T,vmin=0, vmax= 100)\n",
    "F = np.zeros_like(U)\n",
    "F[FC] = 1\n",
    "# F[HC] = 1\n",
    "plt.subplot(121)\n",
    "plt.imshow(F.T,extent=[0,L_x,0,L_z],origin='lower')\n",
    "plt.colorbar(orientation=\"horizontal\")\n",
    "# set pressure by height\n",
    "P = np.zeros_like(U) +-g*dz*0.01\n",
    "P[HC] = -g*dz\n",
    "# P[TC_not] = 0\n",
    "for i in range(N_z-1,0,-1):\n",
    "\n",
    "    P[:,i-1]+=P[:,i]\n",
    "P[TC] = 0\n",
    "plt.subplot(122)\n",
    "plt.imshow(P.T[1:,1:],extent=[0,L_x,0,L_z],origin='lower')\n",
    "plt.colorbar(orientation=\"horizontal\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x2197ff79c60>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "temp = np.zeros_like(U)\n",
    "temp[HC]=1\n",
    "for i in range(N_z-1,0,-1):\n",
    "    temp[:,i-1]+=temp[:,i]\n",
    "temp[TC]=0\n",
    "temp[TC]=-temp[TC[0],TC[1]+1] \n",
    "# temp[TC]=0\n",
    "# temp[TC]=-temp[TC[0]+1,TC[1]] \n",
    "\n",
    "\n",
    "# for i in range(N_z-1,0,-1):\n",
    "#     print(i)\n",
    "#     temp[:,i-1]+=temp[:,i]\n",
    "plt.imshow(temp.T,origin='lower')\n",
    "plt.colorbar()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "765af65b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def set_dt(U,W,dx,dz,dt,c_num,err=1e-5):\n",
    "    dx_u = dx/np.max(U)\n",
    "    dz_w = dz/np.max(W)\n",
    "    newdt = min(c_num*dx_u,c_num*dz_w,dt)\n",
    "    newdt = max(newdt,err)\n",
    "    return newdt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "15d4a6a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def NS_solver(U,W,P,F,dt,dx,dz,nu,beta0=1.7,g=9.81,c_num=0.7):\n",
    "    UC = U.copy()\n",
    "    WC = W.copy()\n",
    "    PC = P.copy()\n",
    "    UCpad = np.pad(UC,((0,1),(0,1)),'constant',constant_values=0)\n",
    "    WCpad = np.pad(WC,((0,1),(0,1)),'constant',constant_values=0)\n",
    "    PCpad = np.pad(PC,((0,1),(0,1)),'constant',constant_values=0)\n",
    "    UUin = (UCpad[1:,:-1] + UCpad[:-1,:-1])/2\n",
    "    UWUin = (UCpad[:-1,1:] + UCpad[:-1,:-1])/2\n",
    "    UWWin = (WCpad[1:,:-1] + WCpad[:-1,:-1])/2\n",
    "    UU = (1/dx)*(((UUin[1:,:])**2-(UUin[:-1,:]))**2)[:,1:]\n",
    "    UW = (1/dz)*((((UWWin*UWUin)[:,1:])**2-((UWWin*UWUin)[:,:-1])**2))[1:,:]\n",
    "    PU = (1/dx)*((PCpad[1:,:-1]-PCpad[:-1,:-1]))[1:,1:]\n",
    "    VISUX = (nu/(dx*dx))*(UCpad[2:,:-1]-2*UCpad[1:-1,:-1]+UCpad[:-2,:-1])[:,1:]\n",
    "    VISUZ = (nu/(dz*dz))*(UCpad[:-1,2:]-2*UCpad[:-1,1:-1]+UCpad[:-1,:-2])[1:,:]\n",
    "    \n",
    "    WWin = (WCpad[:-1,1:] + WCpad[:-1,:-1])/2\n",
    "    WUUin = (UCpad[:-1,1:] + UCpad[:-1,:-1])/2\n",
    "    WUWin = (WCpad[1:,:-1] + WCpad[:-1,:-1])/2\n",
    "    WU = (1/dx)*((((UWWin*UWUin)[1:,:])**2-((UWWin*UWUin)[:-1,:])**2))[:,1:]\n",
    "    WW = (1/dx)*(((WWin[:,1:])**2-(WWin[:,:-1]))**2)[1:,:]\n",
    "    PW = (1/dz)*((PCpad[:-1,1:]-PCpad[:-1,:-1]))[1:,1:]\n",
    "    VISWX = (nu/(dx*dx))*(WCpad[2:,:-1]-2*WCpad[1:-1,:-1]+WCpad[:-2,:-1])[:,1:]\n",
    "    VISWZ = (nu/(dz*dz))*(WCpad[:-1,2:]-2*WCpad[:-1,1:-1]+WCpad[:-1,:-2])[1:,:]\n",
    "    \n",
    "    UC[1:,1:]  = UC[1:,1:] + dt*(-UU-UW-PU+VISUX+VISUZ)\n",
    "    WC[1:,1:]  = WC[1:,1:] + dt*(-WW-WU-PW+VISWX+VISWZ-g)\n",
    "    \n",
    "    D = -(1/dx)*(UC[1:,1:]-UC[:-1,1:]) + (1/dz)*(WC[1:,1:]-WC[1:,:-1])\n",
    "    beta = beta0/(2*dt*(1/(dx*dx) + 1/(dz*dz)))\n",
    "    dP = beta*D\n",
    "    dPpad = np.pad(dP,((0,1),(0,1)),'constant',constant_values=0)\n",
    "    UC[1:,1:] = UC[1:,1:] - (dt/dx)*(dPpad[1:,:-1]-dPpad[:-1,:-1])\n",
    "    WC[1:,1:] = WC[1:,1:] - (dt/dz)*(dPpad[:-1,1:]-dPpad[:-1,:-1])\n",
    "    PC[1:,1:] = PC[1:,1:] + dP\n",
    "    \n",
    "    UC[TC]=-UC[TC[0],TC[1]+1] \n",
    "    UC[TC]=0\n",
    "\n",
    "    WC[TC]=-WC[TC[0]+1,TC[1]] \n",
    "    WC[TC]=0\n",
    "    \n",
    "    \n",
    "    dx_u = dx/np.max(np.abs(UC))\n",
    "    dz_w = dz/np.max(np.abs(WC))\n",
    "    dt = min(c_num*dx_u,c_num*dz_w,dt)\n",
    "    dt = max(newdt,1e-8)\n",
    "    return UC,WC,PC,dt\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "db16e435",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.002\n"
     ]
    }
   ],
   "source": [
    "UC = U.copy()\n",
    "WC = W.copy()\n",
    "PC = P.copy()\n",
    "UCpad = np.pad(UC,((0,1),(0,1)),'constant',constant_values=0)\n",
    "WCpad = np.pad(WC,((0,1),(0,1)),'constant',constant_values=0)\n",
    "PCpad = np.pad(PC,((0,1),(0,1)),'constant',constant_values=0)\n",
    "UUin = (UCpad[1:,:-1] + UCpad[:-1,:-1])/2\n",
    "UWUin = (UCpad[:-1,1:] + UCpad[:-1,:-1])/2\n",
    "UWWin = (WCpad[1:,:-1] + WCpad[:-1,:-1])/2\n",
    "UU = (1/dx)*(((UUin[1:,:])**2-(UUin[:-1,:]))**2)[:,1:]\n",
    "UW = (1/dz)*((((UWWin*UWUin)[:,1:])**2-((UWWin*UWUin)[:,:-1])**2))[1:,:]\n",
    "PU = (1/dx)*((PCpad[1:,:-1]-PCpad[:-1,:-1]))[1:,1:]\n",
    "VISUX = (nu/(dx*dx))*(UCpad[2:,:-1]-2*UCpad[1:-1,:-1]+UCpad[:-2,:-1])[:,1:]\n",
    "VISUZ = (nu/(dz*dz))*(UCpad[:-1,2:]-2*UCpad[:-1,1:-1]+UCpad[:-1,:-2])[1:,:]\n",
    "WWin = (WCpad[:-1,1:] + WCpad[:-1,:-1])/2\n",
    "WUUin = (UCpad[:-1,1:] + UCpad[:-1,:-1])/2\n",
    "WUWin = (WCpad[1:,:-1] + WCpad[:-1,:-1])/2\n",
    "WU = (1/dx)*((((UWWin*UWUin)[1:,:])**2-((UWWin*UWUin)[:-1,:])**2))[:,1:]\n",
    "WW = (1/dx)*(((WWin[:,1:])**2-(WWin[:,:-1]))**2)[1:,:]\n",
    "\n",
    "PW = (1/dz)*((PCpad[:-1,1:]-PCpad[:-1,:-1]))[1:,1:]\n",
    "VISWX = (nu/(dx*dx))*(WCpad[2:,:-1]-2*WCpad[1:-1,:-1]+WCpad[:-2,:-1])[:,1:]\n",
    "VISWZ = (nu/(dz*dz))*(WCpad[:-1,2:]-2*WCpad[:-1,1:-1]+WCpad[:-1,:-2])[1:,:]\n",
    "\n",
    "UC[1:,1:]  = UC[1:,1:] + dt*(-UU-UW-PU+VISUX+VISUZ)\n",
    "WC[1:,1:]  = WC[1:,1:] + dt*(-WW-WU-PW+VISWX+VISWZ-g)\n",
    "\n",
    "D = -(1/dx)*(UC[1:,1:]-UC[:-1,1:]) + (1/dz)*(WC[1:,1:]-WC[1:,:-1])\n",
    "beta = beta0/(2*dt*(1/(dx*dx) + 1/(dz*dz)))\n",
    "dP = beta*D\n",
    "dPpad = np.pad(dP,((0,1),(0,1)),'constant',constant_values=0)\n",
    "UC[1:,1:] = UC[1:,1:] - (dt/dx)*(dPpad[1:,:-1]-dPpad[:-1,:-1])\n",
    "WC[1:,1:] = WC[1:,1:] - (dt/dz)*(dPpad[:-1,1:]-dPpad[:-1,:-1])\n",
    "PC[1:,1:] = PC[1:,1:] + dP\n",
    "\n",
    "UC[TC]=-UC[TC[0],TC[1]+1] \n",
    "UC[TC]=0\n",
    "\n",
    "WC[TC]=-WC[TC[0]+1,TC[1]] \n",
    "WC[TC]=0\n",
    "MAXW = np.max(np.abs(WC))\n",
    "MAXU = np.max(np.abs(UC))\n",
    "dx_u = dx/MAXU\n",
    "dz_w = dz/MAXW\n",
    "newdt = min(0.7*dx_u,0.7*dz_w,dt)\n",
    "newdt = max(newdt,1e-8)\n",
    "print(newdt)\n",
    "# dPx.shape\n",
    "# UC.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "a42d4cc9",
   "metadata": {},
   "outputs": [],
   "source": [
    "Unew,Wnew,Pnew,newdt = NS_solver(U,W,P,F,dt,dx,dz,nu,beta0=1.7,g=9.81,c_num=0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "acc99601",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x2190301ac50>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(Pnew.T,origin='lower')\n",
    "plt.colorbar(orientation='horizontal')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "1d987c20",
   "metadata": {},
   "outputs": [],
   "source": [
    "T_list =[]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "e1a65f0e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\kim9y\\AppData\\Local\\Temp\\ipykernel_35004\\230166934.py:11: RuntimeWarning: overflow encountered in square\n",
      "  UU = (1/dx)*(((UUin[1:,:])**2-(UUin[:-1,:]))**2)[:,1:]\n",
      "C:\\Users\\kim9y\\AppData\\Local\\Temp\\ipykernel_35004\\230166934.py:12: RuntimeWarning: overflow encountered in square\n",
      "  UW = (1/dz)*((((UWWin*UWUin)[:,1:])**2-((UWWin*UWUin)[:,:-1])**2))[1:,:]\n",
      "C:\\Users\\kim9y\\AppData\\Local\\Temp\\ipykernel_35004\\230166934.py:12: RuntimeWarning: invalid value encountered in subtract\n",
      "  UW = (1/dz)*((((UWWin*UWUin)[:,1:])**2-((UWWin*UWUin)[:,:-1])**2))[1:,:]\n",
      "C:\\Users\\kim9y\\AppData\\Local\\Temp\\ipykernel_35004\\230166934.py:20: RuntimeWarning: overflow encountered in square\n",
      "  WU = (1/dx)*((((UWWin*UWUin)[1:,:])**2-((UWWin*UWUin)[:-1,:])**2))[:,1:]\n",
      "C:\\Users\\kim9y\\AppData\\Local\\Temp\\ipykernel_35004\\230166934.py:20: RuntimeWarning: invalid value encountered in subtract\n",
      "  WU = (1/dx)*((((UWWin*UWUin)[1:,:])**2-((UWWin*UWUin)[:-1,:])**2))[:,1:]\n",
      "C:\\Users\\kim9y\\AppData\\Local\\Temp\\ipykernel_35004\\230166934.py:21: RuntimeWarning: overflow encountered in square\n",
      "  WW = (1/dx)*(((WWin[:,1:])**2-(WWin[:,:-1]))**2)[1:,:]\n",
      "C:\\Users\\kim9y\\AppData\\Local\\Temp\\ipykernel_35004\\230166934.py:26: RuntimeWarning: invalid value encountered in subtract\n",
      "  UC[1:,1:]  = UC[1:,1:] + dt*(-UU-UW-PU+VISUX+VISUZ)\n",
      "C:\\Users\\kim9y\\AppData\\Local\\Temp\\ipykernel_35004\\230166934.py:29: RuntimeWarning: invalid value encountered in subtract\n",
      "  D = -(1/dx)*(UC[1:,1:]-UC[:-1,1:]) + (1/dz)*(WC[1:,1:]-WC[1:,:-1])\n",
      "C:\\Users\\kim9y\\AppData\\Local\\Temp\\ipykernel_35004\\230166934.py:29: RuntimeWarning: invalid value encountered in add\n",
      "  D = -(1/dx)*(UC[1:,1:]-UC[:-1,1:]) + (1/dz)*(WC[1:,1:]-WC[1:,:-1])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x219036a22f0>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    T_list.append(newdt)\n",
    "    Unew,Wnew,Pnew, newdt = NS_solver(Unew,Wnew,Pnew,F,newdt,dx,dz,nu,1e-6,c_num=0.7)\n",
    "\n",
    "plt.figure(figsize=(15,5))\n",
    "plt.subplot(131)\n",
    "plt.imshow(Unew.T,origin='lower')\n",
    "plt.colorbar(orientation=\"horizontal\")\n",
    "plt.subplot(132)\n",
    "plt.imshow(Wnew.T,origin='lower')\n",
    "plt.colorbar(orientation=\"horizontal\")\n",
    "plt.subplot(133)\n",
    "plt.imshow(Pnew.T,origin='lower')\n",
    "plt.colorbar(orientation=\"horizontal\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 413,
   "id": "8fa0f8be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x164a3a09300>]"
      ]
     },
     "execution_count": 413,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(T_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ad550cc3",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "21290bbfaef809b5729f03c25a69946f1e8195a209b2e095987c269e3dfe79ea"
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}