Fast sweeping methods for hyperbolic systems of conservation laws at steady state

Björn Engquist, Brittany D. Froese, Yen Hsi Richard Tsai

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Fast sweeping methods have become a useful tool for computing the solutions of static Hamilton-Jacobi equations. By adapting the main idea behind these methods, we describe a new approach for computing steady state solutions to systems of conservation laws. By exploiting the flow of information along characteristics, these fast sweeping methods can compute solutions very efficiently. Furthermore, the methods capture shocks sharply by directly imposing the Rankine-Hugoniot shock conditions. We present convergence analysis and numerics for several one- and two-dimensional examples to illustrate the use and advantages of this approach.

Original languageEnglish (US)
Pages (from-to)316-338
Number of pages23
JournalJournal of Computational Physics
Volume255
DOIs
StatePublished - Dec 15 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Conservation laws
  • Fast sweeping methods
  • Hyperbolic equations
  • Numerical analysis

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