Discrete shock profiles for systems of conservation laws

Andrew Majda, James Ralston

Research output: Contribution to journalArticlepeer-review

Abstract

The existence of discrete shock profiles for difference schemes approximating a system of conservation laws is the major topic studied in this paper. The basic theorem established here applies to first‐order accurate difference schemes; for weak shocks, this theorem provides necessary and sufficient conditions involving the truncation error of the linearized scheme which guarantee entropy satisfying or entropy violating discrete shock profiles. Several explicit difference schemes are used as examples illustrating the interplay between the entropy condition, monotonicity, and linearized stability. Entropy violating stationary shocks for second‐order accurate Lax‐Wendroff schemes approximating systems are also constructed. The only tools used in the proofs are local analysis and the center manifold theorem.

Original languageEnglish (US)
Pages (from-to)445-482
Number of pages38
JournalCommunications on Pure and Applied Mathematics
Volume32
Issue number4
DOIs
StatePublished - Jul 1979

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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