Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 24, Issue 4, Pages 1157-1174Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S1064827501392880
Keywords
hyperbolic conservation laws; nonoscillatory high resolution central schemes; contact discontinuities; artificial compression
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The recently proposed high-order central difference schemes for conservation laws have a tendency of smearing linear discontinuities. In principle, Harten's artificial compression method (ACM) could be used to improve resolution. We analyze why this approach has not yet been used successfully and derive a more powerful version of the ACM based on a rigorous estimate of the total variation. We discuss the potential danger of overcompression and point out directions of future algorithmic development.
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