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How to find a discrete entropy inequality when you don’t know if it exists

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Abstract

The solutions of hyperbolic systems contain discontinuities. These weak solutions verify not only the original PDEs, but also an entropy inequality that acts as a selection criterion determining whether a discontinuity is physical or not. Obtaining a discrete version of these entropy inequalities when approximating the solutions numerically is crucial to avoid convergence to unphysical solutions or even unstability. In this paper, we introduce an optimization framework that enable to quantify a posteriori entropy. We use it to obtain maps of numerical diffusion and to prove that some schemes do not have a discrete entropy inequality.
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Dates and versions

hal-03881570 , version 1 (02-12-2022)

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  • HAL Id : hal-03881570 , version 1

Cite

Nina Aguillon, Emmanuel Audusse, Vivien Desveaux, Julien Salomon. How to find a discrete entropy inequality when you don’t know if it exists. 2022. ⟨hal-03881570⟩
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