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Pré-Publication, Document De Travail Année : 2024

An entropy-stable and fully well-balanced scheme for the Euler equations with gravity

Résumé

The present work concerns the derivation of a numerical scheme to approximate weak solutions of the Euler equations with a gravitational source term. The designed scheme is proved to be fully well-balanced since it is able to exactly preserve all moving equilibrium solutions, as well as the corresponding steady solutions at rest obtained when the velocity vanishes. Moreover, the proposed scheme is entropy-preserving since it satisfies all fully discrete entropy inequalities. In addition, in order to satisfy the required admissibility of the approximate solutions, the positivity of both approximate density and pressure is established. Several numerical experiments attest the relevance of the developed numerical method.
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Dates et versions

hal-04620125 , version 1 (21-06-2024)

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  • HAL Id : hal-04620125 , version 1

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Christophe Berthon, Victor Michel-Dansac, Andrea Thomann. An entropy-stable and fully well-balanced scheme for the Euler equations with gravity. 2024. ⟨hal-04620125⟩
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