An Adaptive Discontinuous Galerkin Technique with an Orthogonal Basis Applied to Compressible Flow Problems

Abstract

Abstract. We present a high-order formulation for solving hyperbolic conservation laws using the Discontinuous Galerkin Method (DGM). We introduce an orthogonal basis for the spatial discretization and use explicit Runge-Kutta time discretization. Some results of higher-order adaptive refinement calculations are presented for inviscid Rayleigh Taylor flow instability and shock reflexion problems. The adaptive procedure uses an error indicator that concentrates the computational effort near discontinuities.

DOI: 10.1137/S00361445023830

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@article{Remacle2003AnAD, title={An Adaptive Discontinuous Galerkin Technique with an Orthogonal Basis Applied to Compressible Flow Problems}, author={Jean-François Remacle and Joseph E. Flaherty and Mark S. Shephard}, journal={SIAM Review}, year={2003}, volume={45}, pages={53-72} }