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Entropy satisfying schemes for shallow water systems
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Entropy inequalities play an essential role in the election of a unique solution among all possible weak solutions for a system of conservation laws. Existence of an entropy will also allow to study the stability of numerical schemes for such equations and the main ideas can be easily extended to the more general case of quasi-linear systems. Nevertheless, developing numerical schemes that agree to this notion of entropy and at the same time grant some other "good" properties is not an easy task. Here we study the case of shallow water systems. In particular, the classical one-layer and two-layer shallow water systems and a generalized Savage-Hutter model are considered. Each particular case is studied and some schemes that agree to an entropy inequality are presented. We seek that these schemes will also satisfy properties like steady-states preservation and positiviy of water heights.
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