Application of the Local Discontinuous Galerkin Method to the Solution of the Quasi-Gas Dynamic System of Equations

Abstract

The solution of a quasi-gas dynamic (QGD) system of equations using the local discontinuous Galerkin method (LDG) is considered. One-dimensional Riemann discontinuity problems with known exact solutions are solved. Strong discontinuities are present in the solutions of the problems. Therefore, to ensure the monotonicity of the solution obtained by the LDG method, the so-called slope limiters, or limiters, are introduced. A “moment” limiter is chosen that preserves as high an order as possible. The limiter is modified to smooth the oscillations in the areas where the solution is constant.