The Application Of The RKDG Method With TVB Limiter And Immersed Boundary Method For Solving The Euler Equations

The Runge-Kutta discontinuous Galerkin (RKDG) method with TVB limiter is used for solvingthe hyperbolic conservation laws on Cartesian meshes in this thesis. The RKDG method with TVBlimiter is a high-order accurate and highly parallelizable method for solving the Euler equations. Forthe purpose of utilizing this method to simulate the problems flowing over a complex body, theimmersed boundary method is applied to deal with the boundary conditions in this thesis. The reasonis the immersed boundary method is a novel and general technique for handling a flow with complexgeometry without any special needs of the computational mesh. For this purpose, we use the RKDGmethod with TVB limiter in conjunction with the immersed boundary method to solve theabove-mentioned problem on Cartesian meshes. Finally, the results of some classical test cases areprovided to verify the efficiency of such methods.