Remarks on high-resolution split schemes computation

M. Ben-Artzi*, J. Falcovitz, U. Feldman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The high-resolution generalized Riemann problem (GRP) conservation laws scheme for compressible flows combined with Strang-type operator splitting is applied to computing an initial value problem having a discontinuous initial data. Imperfect representation of the initial data on the Cartesian grid, where the smooth curve of discontinuity is approximated by a jagged line, gives rise to spurious waves when using high-resolution integration with operator splitting. The nature of these waves is clarified by comparison to a one-dimensional model. We demonstrate that it is not the operator splitting that gives rise to these waves, but rather the better quality of the hyperbolic (one-dimensional) solver, which is not degraded by the operator splitting. It is expected that this property of retaining sharp features of initial data will also be produced by other second-order conservation laws schemes.

Original languageEnglish
Pages (from-to)1008-1015
Number of pages8
JournalSIAM Journal on Scientific Computing
Volume22
Issue number3
DOIs
StatePublished - 2001

Keywords

  • Compressible flow
  • Godunov-type scheme
  • GRP method
  • High-resolution computation
  • Irregular cells
  • Shock waves

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