Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws

Authors:
L. Krivodonova;J. Xin;J.-F. Remacle;N. Chevaugeon;J. E. Flaherty
Affiliations:
Courant Institute of Mathematical Sciences, New York University, New York, NY;Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY;Université Catholique de Louvain-la-Neuve, 1348 Louvain-la-Neuve, Belgium;Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, NY;Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, NY
Venue:
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Year:
2004

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Abstract

We describe a strategy for detecting discontinuities and for limiting spurious oscillations near such discontinuities when solving hyperbolic systems of conservation laws by high-order discontinuous Galerkin methods. The approach is based on a strong superconvergence at the outflow boundary of each element in smooth regions of the flow. By detecting discontinuities in such variables as density or entropy, limiting may be applied only in these regions; thereby, preserving a high order of accuracy in regions where solutions are smooth. Several one- and two-dimensional flow problems illustrate the performance of these approaches.