Development of a semi-implicit fluid modeling code using finite-volume method based on Cartesian grids

Matthew R. Smith, Chieh Tsan Hung, Kun Mo Lin, Jong-Shinn Wu, Jen Perng Yu

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Presented is the HLLG (Harten, Lax and van Leer with Gradient inclusion) method for application to the numerical solution of general Partial Differential Equations (PDEs) in conservation form. The HLLG method is based on the traditional HLL method with formal mathematical inclusion of gradients of conserved properties across the control volume employed for flux derivation. The simple extension demonstrates that conventional higher extensions of the HLL method are mathematically inconsistent and produce various numerical instabilities. The HLLG method, with higher order extensions consistent with the flux derivation, is absent of (or less affected by) the said numerical instabilities. The HLLG method is then applied to solutions of the Euler Equations and the simulation of 1D argon RF plasma simulation.

Original languageEnglish
Pages (from-to)170-172
Number of pages3
JournalComputer Physics Communications
Volume182
Issue number1
DOIs
StatePublished - 1 Jan 2011

Keywords

  • Computational Fluid Dynamics (CFD)
  • Finite volume method
  • Flux limiting
  • Total Variable Diminishing (TVD)

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