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Recent advancement of entropy split methods for compressible gas dynamics and MHD

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  • Yee, H.C.
  • Sjögreen, Björn

Abstract

The entropy splitting of the compressible Euler flux derivatives based on Harten’s entropy function Harten (1983), Gerritsen and Olsson (1996), Yee et al. (2000) in conjunction with classical spatial central and DRP (dispersion relation-preserving) finite discretizations with summation-by-parts (SBP) operators Strand (1994) for both periodic and non-periodic boundary conditions is proven to be entropy conservative and stable for a thermally-perfect gas by Sjögreen and Yee (2019), Sjögreen et al. (2020), Sjögreen and Yee (2021). The various high order methods resulting from applying classical spatial central, DRP and Padé (compact) methods to the split form of the Euler flux derivative are referred to as entropy split methods as a function of the splitting parameter β. These entropy split methods are entropy conserving and stable but they are usually not conservative numerical methods without additional reformulation; e.g., those proposed in Sjögreen and Yee (2021).

Suggested Citation

  • Yee, H.C. & Sjögreen, Björn, 2023. "Recent advancement of entropy split methods for compressible gas dynamics and MHD," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    • Handle: RePEc:eee:apmaco:v:439:y:2023:i:c:s0096300322006191
    DOI: 10.1016/j.amc.2022.127545
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