The Runge-Kutta DG finite element method and the KFVS scheme for compressible flow simulations

Abstract

This article presents a new type of second-order scheme for solving the system of Euler equations, which combines the Runge-Kutta discontinuous Galerkin (DG) finite element method and the kinetic flux vector splitting (KFVS) scheme. We first discretize the Euler equations in space with the DG method and then the resulting system from the method-of-lines approach will be discretized using a Runge-Kutta method. Finally, a second-order KFVS method is used to construct the numerical flux. The proposed scheme preserves the main advantages of the DG finite element method including its flexibility in handling irregular solution domains and in parallelization. The efficiency and effectiveness of the proposed method are illustrated by several numerical examples in one- and two-dimensional spaces. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006