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

S. Qamar () and G. Warnecke ()
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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

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2008, pp 865-872 from Springer

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.

Keywords: Source Term; Hyperbolic System; Central Scheme; Direct Part; Relaxation Type (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-75712-2_90

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DOI: 10.1007/978-3-540-75712-2_90

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