Greedy invariant-domain preserving approximation for hyperbolic systems

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

Published 2023-10-03Version 1

The paper focuses on 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.