A Simple Weighted Essentially Non-oscillatory Limiter For RKDG Method With Immersed Boundary Method To Solve The Compressible Fluid Problem

In this thesis, a simple weighted essentially non-oscillatory (WENO) limiter for the Runge-Kuttadiscontinuous Galerkin (RKDG) method is applied to solve the compressible fluid on Cartesian grids.This WENO limiter takes full usage of the solutions of the target cell and its neighboring cells, andmakes associated RKDG method to achieve uniformly high order of accuracy both in space and time.Such method which is constructed on Cartesian grids could not solve for the compressible fluidproblem of flowing over a complex geometry body well, yet the immersed boundary method is anovel technique which can deal with this difficulty without any further demanding of the computinggrids. For this purpose, we try to use the RKDG method with the simple WENO limiter inconjunction with the immersed boundary method for solving such compressible fluid problem onCartesian grids. Some classic numerical tests are provided to verify the viability of thesemethodologies.