Supraconservative finite-volume methods for the Euler equations of subsonic compressible flow

Arthur Veldman*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

It has been found advantageous for finite-volume discretizations of flow equations to possess additional (secondary) invariants, next to the (primary) invariants from the constituting conservation laws. The paper presents general (necessary and sufficient) requirements for a method to convectively preserve discrete kinetic energy. The key ingredient is a close discrete consistency between the convective term in the momentum equation and the terms in the other conservation equations (mass, internal energy). As examples, the Euler equations for subsonic (in)compressible flow are discretized with such supra-conservative finite-volume methods on structured as well as unstructured grids.

Original languageEnglish
Pages (from-to)756-779
JournalSiam review
Volume63
Issue number4
DOIs
Publication statusPublished - 4-Nov-2021

Keywords

  • CFD, conservation laws, finite-volume method, supra-conservative discretization

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