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Energy Stability of the MUSCL Scheme

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Qaisar Abbas

    (Uppsala University, Department of Information Technology, Scientific Computing)

  • Edwin van der Weide

    (University of Twente, Faculty of Engineering Technology)

  • Jan Nordström

    (Uppsala University, Department of Information Technology, Scientific Computing
    University of the Witvatersrand, School of Mechanical, Industrial and Aeronautical Engineering
    FOI, The Swedish Defence Research Agency, Department of Aeronautics and Systems Integration)

Abstract

We analyze the energy stability of the standard MUSCL scheme. The analysis is possible by reformulating the MUSCL scheme in the framework of summation-by-parts (SBP) operators including an artificial dissipation. The effect of different slope limiters is studied. It is found that all the slope limiters do not lead to the correct sign of the entries in the dissipation matrix. The implication of that is discussed. The analysis is done for both linear and nonlinear scalar problems.

Suggested Citation

  • Qaisar Abbas & Edwin van der Weide & Jan Nordström, 2010. "Energy Stability of the MUSCL Scheme," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 61-68, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_5
    DOI: 10.1007/978-3-642-11795-4_5
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