Article ID Journal Published Year Pages File Type
520983 Journal of Computational Physics 2008 14 Pages PDF
Abstract

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=0,1,2p=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.

Related Topics
Physical Sciences and Engineering Computer Science Computer Science Applications
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