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

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 = 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.. (C) 2008 Elsevier Inc. All rights reserved.