An entropy stable, hybridizable discontinuous galerkin method for the compressible Navier-Stokes equations

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Abstract

This article proves that a particular space-time, hybridizable discontinuous Galerkin method is entropy stable for the compressible Navier- Stokes equations. In order to facilitate the proof, 'entropy variables' are utilized to rewrite the compressible Navier-Stokes equations in a symmetric form. The resulting form of the equations is discretized with a hybridizable discontinuous finite element approach in space, and a classical discontinuous finite element approach in time. Thereafter, the initial solution is shown to continually bound the solutions at later times.

Original languageEnglish (US)
Pages (from-to)95-121
Number of pages27
JournalMathematics of Computation
Volume87
Issue number309
DOIs
StatePublished - Jan 1 2018

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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