The GRP Treatment of 2-D Complex Wave Structures

M. Ben-Artzi () and J. Falcovitz ()
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M. Ben-Artzi: Hebrew University of Jerusalem, Institute of Mathematics
J. Falcovitz: Hebrew University of Jerusalem, Institute of Mathematics

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2003, pp 125-134 from Springer

Abstract: Abstract Solutions to initial value problems of hyperbolic conservations laws often involve discontinuities satisfying appropriate jump conditions. In the case of fluid dynamics, the 1-D equations admit two types of discontinuous waves — a shock discontinuity and a contact discontinuity. When fluid dynamics in two space dimensions is considered, even for the simplified “Riemann-type” problems (where the data are piecewise constant in sectors of the plane), a surprisingly rich variety of wave structure may evolve. Generally speaking, exact solutions of such fluid dynamical wave structures are not available and one must resort to approximations, such as those obtained by the high-resolution GRP scheme for hyperbolic conservation laws.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55711-8_10

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DOI: 10.1007/978-3-642-55711-8_10

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