Taming the CFL Number for Discontinuous Galerkin Methods on Structured Meshes

Authors:
T. Warburton;T. Hagstrom
Affiliations:
timwar@caam.rice.edu;hagstrom@math.unm.edu
Venue:
SIAM Journal on Numerical Analysis
Year:
2008

Citing 0
Cited 2

Nodal discontinuous Galerkin methods on graphics processors

Journal of Computational Physics
An efficient parallel implementation of explicit multirate Runge-Kutta schemes for discontinuous Galerkin computations

Journal of Computational Physics

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Abstract

The upwind discontinuous Galerkin method is an attractive method for solving time-dependent hyperbolic conservation laws. It is possible to use high-order explicit time-stepping methods and high-order spatial approximations without incurring heavy numerical linear algebra overheads. However, the Courant-Friedrichs-Lewy (CFL) condition for these methods depends on the polynomial order used, and there is a somewhat excessive cost for using very high order spatial approximation. We discuss the impact of a covolume mesh based filter on the CFL number for these methods and present an algorithm which has a CFL number independent of the spatial order of approximation. We present computational results for the advection equation and the wave equation on one-dimensional meshes using up to tenth order in space and time.