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On Skew-Symmetric Splitting and Entropy Conservation Schemes for the Euler Equations

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Björn Sjögreen

    (Lawrence Livermore National Laboratory)

  • H. C. Yee

    (NASA Ames Research Center)

Abstract

The Tadmor type of entropy conservation formulation for the Euler equations and various skew-symmetric splittings of the inviscid flux derivatives are discussed. Numerical stability of high order central and Padé type (centered compact) spatial discretization is enhanced through the application of these formulations. Numerical test on a 2-D vortex convection problem indicates that the stability and accuracy of these formulations using the same high order central spatial discretization are similar for vortex travel up to a few periods. For two to three times longer time integrations, their corresponding stability and accuracy behaviors are very different. The goal of this work is to improve treatment of nonlinear instabilities and to minimize the use of numerical dissipation in numerical simulations of shock-free compressible turbulence and turbulence with shocks.

Suggested Citation

  • Björn Sjögreen & H. C. Yee, 2010. "On Skew-Symmetric Splitting and Entropy Conservation Schemes for the Euler Equations," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 817-827, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_88
    DOI: 10.1007/978-3-642-11795-4_88
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