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High Resolution Schemes for Hyperbolic Conservation Laws

โœ Scribed by Ami Harten

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
604 KB
Volume
135
Category
Article
ISSN
0021-9991

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โœฆ Synopsis

A class of new explicit second order accurate finite difference schemes for the computation of weak solutions of hyperbolic conwhere F is some other function called entropy flux.

servation laws is presented. These highly nonlinear schemes are Admissible weak solutions of (1.1) satisfy, in the weak obtained by applying a nonoscillatory first order accurate scheme sense, the inequality to an appropriately modified flux function. The so-derived second order accurate schemes achieve high resolution while preserving the robustness of the original nonoscillatory first order accurate U(u) t ฯฉ F(u) x ั€ 0

(1.3b) scheme. Numerical experiments are presented to demonstrate the performance of these new schemes. แฎŠ 1983 Academic Press

(see [12]). The inequality (1.3b) is called an entropy condition.

We shall discuss numerical approximations to weak solu-

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