Time step restrictions for Runge–Kutta discontinuous Galerkin methods on triangular grids

✍ Scribed by Ethan J. Kubatko; Clint Dawson; Joannes J. Westerink

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 509 KB
• Volume: 227
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2008.07.026

✦ Synopsis

We derive CFL conditions for the linear stability of the so-called Runge-Kutta discontinuous Galerkin (RKDG) methods on triangular grids. Semidiscrete DG approximations using polynomials spaces of degree p ¼ 0; 1; 2, and 3 are considered and discretized in time using a number of different strong-stability-preserving (SSP) Runge-Kutta time discretization methods. Two structured triangular grid configurations are analyzed for wave propagation in different directions. Approximate relations between the two-dimensional CFL conditions derived here and previously established one-dimensional conditions can be observed after defining an appropriate triangular grid parameter h and a constant that is dependent on the polynomial degree p of the DG spatial approximation. Numerical results verify the CFL conditions that are obtained, and ''optimal", in terms of computational efficiency, two-dimensional RKDG methods of a given order are identified.