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Efficient implementation of essentially nonoscillatory shock-capturing schemes. II. (English) Zbl 0674.65061
This paper presents simplifications and improvements to the essentially nonoscillatory schemes for conservation laws developed in an earlier work by the same authors [ibid. 77, 439-471 (1988; Zbl 0653.65072)]. The method is applicable to systems of equations in several spatial dimensions. The simplifications involve the use of numerical fluxes instead of cell averages in the approximation of spatial derivatives. Better shock capturing methods are developed. Improved methods for sharpening contact discontinuities are also incorporated. The results of many computations are presented, and they are impressive.
Reviewer: G.Hedstrom

MSC:
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
76N15 Gas dynamics (general theory)
35L65 Hyperbolic conservation laws
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