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A Space–Time Conservative Method for Hyperbolic Systems of Relaxation Type

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

Listed:
  • S. Qamar

    (Otto-von-Guericke University Magdeburg, Institut für Analysis und Numerik)

  • G. Warnecke

    (Otto-von-Guericke University PSF 4120, Institute for Analysis and Numerics)

Abstract

We propose a higher-order space–time conservative method for hyperbolic systems of relaxation type. In the present model the relaxation time may vary from order of one to a very small value. These small values make the relaxation term stronger and highly stiff. In such situations under-resolved numerical schemes may produce spurious numerical results. However, our present scheme has the capability to correctly capture the behavior of the physical phenomena with high order accuracy even if the initial layer and the small relaxation time are not numerically resolved. The scheme treats the space and time in a unified manner. The flow variables and their slopes are the basic unknowns in the scheme. The source term is treated by its volumetric integration over the space–time control volume and is a direct part of the overall space–time flux balance.

Suggested Citation

  • S. Qamar & G. Warnecke, 2008. "A Space–Time Conservative Method for Hyperbolic Systems of Relaxation Type," Springer Books, in: Sylvie Benzoni-Gavage & Denis Serre (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 865-872, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75712-2_90
    DOI: 10.1007/978-3-540-75712-2_90
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