The aim of this reposiry

This reposiry is only used for the academic purpose. It implements the direct Eulerian GRP scheme introduced in A direct Eulerian GRP scheme for compressible fluid flows The algorithm only completes the 1D case, and the Strang splitting method should be further implemented based on this version.

Functions that has been implemetned

1. The 1D Riemann solver for the Euler equations.

   Usage. Define the left and right states using vec3d ul; vec3d ur;, where vec3d=Eigen::Vector3d is an alias of the Eigen vector. Define the Riemann solver by auto solver=RPSolver(ul,ur). To solve the Riemman problem, call solver.solve(). The Riemann solution is obtained by calling an overloaded (): vec3d solution=solver(x,t), where x: spatial coordinate and t: time.

   Options. Call solver.setGamma(gamma) to change the value of gamma (default value: 1.4) . Call solver.setTol(tol) to change the tolerance of the error of the Riemann solution, which requires a solution to the nonlinear equation.

2. The 1D direct Eulerian GRP solver for the Euler equations.

   Usage. The class GRPSolver is directly inheritted from RPSolver, which means it preserves the full capability of RPSolver. Define the left and right slopes using vec3d ulSlope; vec3d urSlope;, and define the solver using auto gSolver=GRPSolver(ul,ur,ulSlope,urSlope);. To solve the generalized Riemman problem, call gSolver.solve(). The Riemann solution is obtained by calling an overloaded (): vec3d solution=gSolver(x,t), and the time derivatives is obtained by calling vec3d derivatives=gSolver.timeDerivatives().

   Options. Remains the same as Riemann solver.

3. The 1D finite volume algorithm.

   Usage. Define the initial data auto U0 = vector<vec3d>(n);. Then define the FVM solver by FVM_1D solver(U0, lB, rB);, where lB,rB represent the left/right boundaries of the spatial domain. Set the ending time by calling solver.setEndingTime(T);, and solve with vector<vec3d> result=solver.solve().

   Options. Set the ghost cell strategy by solver.setGhostCellStrategy("reflective"). Available strategies: "flat"(default), "reflective", "periodic". Set $\gamma$ by calling setGamma(gamma). Set CFL by calling setCFL(CFL). Set the parameter in the slope limiter by calling setAlpha(alpha) (1~2). You can set up your own ghost cell strategy by calling setCustomCellTreatment(fun);, where fun is a function that adds values to the ghost cells.

Compile & run

This repo only requires the Eigen library. Install it and the dependency should be OK. On Windows, revise the path to the Eigen in the CMakeLists.txt. The Example__.cpp and TestAccuracy.cpp are both ready to execute.