  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.
