A Comparison Of Limiters For Runge-Kutta Discontinuous Galerkin Methods

The Runge-Kutta discontinuous Galerkin(RKDG) methods for solving hyperbolic conservation laws are high-order accurate and highly parallelizable methods which can easily handle complicated geometries and boundary conditions. These methods are in the main stream of computational fluid dynamics. Solutions of conservation laws usually have discontinuities, which leads to great difficulty in solving. An important component of RKDG methods for solving conservation laws with strong shocks in the solution is a nonlinear limiter, which is applied to detect discontinuities and control spurious oscillations near such discontinuities. So the study of limters for RKDG methods is necessary, which is our motivation for the work in this dissertation.In this thesis, we study different limiters including TVB, BDF, BSB, MP, MMP, a reconstruction method WENO. We compare these limiters by several test problems, and we make a conclusion of their advantages and disadvantages for helping people to choose a right limiter for certain problem, in order to resolve sharp discontinuities, get better numerical solutions and save the computational cost.