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A Second-Order Accurate, Component-Wise TVD Scheme for Nonlinear, Hyperbolic Conservation Laws

✍ Scribed by Heng Yu; Yu-Ping Liu

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 130 KB
Volume: 173
Category: Article
ISSN: 0021-9991
DOI: 10.1006/jcph.2001.6834

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✦ Synopsis

In this paper, we present a two-step, component-wise TVD scheme for nonlinear, hyperbolic conservation laws, which is obtained by combining the schemes of Mac Cormack and Warming-Beam. The scheme does not necessitate the characteristic decompositions of the usual TVD schemes. It employs component-wise limiting; hence the programming is much simpler, especially for complicated coupled systems. For Euler systems of conservation laws, we found the scheme is two times faster in computation than the usual TVD schemes based on field-by-field decomposition limiting. A lot of numerical results show primarily the value of the new method.

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