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arXiv · 2310.01713

First-order greedy invariant-domain preserving approximation for hyperbolic problems: scalar conservation laws, and p-system

Jean-Luc Guermond·Matthias Maier·Bojan Popov·Laura Saavedra·Ignacio Tomas
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Abstract

The paper focuses on first-order invariant-domain preserving approximations of hyperbolic systems. We propose a new way to estimate the artificial viscosity that has to be added to make explicit, conservative, consistent numerical methods invariant-domain preserving and entropy inequality compliant. Instead of computing an upper bound on the maximum wave speed in Riemann problems, we estimate a minimum wave speed in the said Riemann problems such that the approximation satisfies predefined invariant-domain properties and predefined entropy inequalities. This technique eliminates non-essential fast waves from the construction of the artificial viscosity, while preserving pre-assigned invariant-domain properties and entropy inequalities.

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Jean-Luc Guermond, Matthias Maier, Bojan Popov, Laura Saavedra, Ignacio Tomas. 2023-10-03. First-order greedy invariant-domain preserving approximation for hyperbolic problems: scalar conservation laws, and p-system. https://arxiv.org/abs/2310.01713

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