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FULLY DISCRETE HIGH-ORDER SHOCK-CAPTURING NUMERICAL SCHEMES

✍ Scribed by J. SHI; E. F. TORO

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 754 KB
Volume: 23
Category: Article
ISSN: 0271-2091
DOI: 10.1002/(sici)1097-0363(19960815)23:3<241::aid-fld421>3.0.co;2-l

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✦ Synopsis

The present paper is a sequel to a previous one by the same authors in which a family of up to fourth-order fully discrete (FD) upwind numerical schemes was presented. In this paper we extend those high-order FD schemes to solutions with discontinuities, e.g. shocks. A rigorous anlaysis of the total variation diminishing (TVD) constraint for the high-order FD schemes is carried out. For non-linear systems the TVD constraint is, as usual, applied empirically. These schemes are validated by solving a test problem for the time-dependent shallow water equations.

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