Comparison of several solution methods for the Euler equations in a finite volume code

Kurzfassung

One of the most popular and simple methods to derive a non-linear equation to steady state is diagonal implicit Runge-Kutta method. This method leads us to get a final linear equation. Then we would like to solve that linear equation with any of the iterative solvers to get efficiently an approximate solution. These solution methods can be often used as smoother in a nonlinear multigrid algorithm. The actual solution depends on the approximation of the derivative of the nonlinear equation and on the iterative method to approximately solve the linear equation. Goal of the Studienarbeit is the implementation of a two dimensional Euler code which approximates solutions on unstructured meshes. Solving the Euler equation with the help of several solution methods such as explicit multi-stage RungeKutta schemes accelerated by local time stepping, implicit scheme based on a derivative corresponding to a discretization of compact stencil, LU-SGS scheme for the given meshes and finally we would like to compare the results. The two dimensional finite volume code, which implements the discretization of the Euler equations in two dimension is developed based on the knowledge acquired from the lecture Algorithmen zur Losung der Euler und Navier-Stokes Gleichungen.