Geometric interpretations and spatial symmetry property of metrics in the conservative form for high-order finite-difference schemes on moving and deforming grids

Yoshiaki Abe, Taku Nonomura, Nobuyuki Iizuka, Kozo Fujii

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

The role of a geometric conservation law (GCL) on a finite-difference scheme is revisited for conservation laws, and the conservative forms of coordinate-transformation metrics are introduced in general dimensions. The sufficient condition of a linear high-order finite-difference scheme is arranged in detail, for which the discretized conservative coordinate-transformation metrics and Jacobian satisfy the GCL identities on three-dimensional moving and deforming grids. Subsequently, the geometric interpretation of the metrics and Jacobian discretized by a linear high-order finite-difference scheme is discussed, and only the symmetric conservative forms of the discretized metrics and Jacobian are shown to have the appropriate geometric structures. The symmetric and asymmetric conservative forms of the metrics and Jacobian are examined by the computation of an inviscid compressible fluid on highly-skewed stationary and deforming grids using sixth-order compact and fourth-order explicit central-difference schemes, respectively. The resolution of the isentropic vortex and the robustness of the computation are improved by employing symmetric conservative forms on the coordinate-transformation metrics and Jacobian that have an appropriate geometry background. An integrated conservation of conservative quantities is also attained on the deforming grid when symmetric conservative forms are adopted to the time metrics and Jacobian.

Original languageEnglish
Pages (from-to)163-203
Number of pages41
JournalJournal of Computational Physics
Volume260
DOIs
Publication statusPublished - 2014 Mar 1
Externally publishedYes

Keywords

  • Body-fitted coordinate
  • Commutativity
  • Conservative metric
  • Freestream preservation
  • Geometric conservation law
  • Geometric interpretation
  • High-order scheme
  • Moving and deforming grids

ASJC Scopus subject areas

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

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