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.

翻译：本文聚焦于双曲系统的不变域保持逼近问题。我们提出一种新方法，用于估计为使显式、守恒、相容的数值方法满足不变域保持和熵不等式所需添加的人工粘性。与计算黎曼问题中最大波速的上界不同，我们估计该黎曼问题中的最小波速，使得逼近满足预设的不变域性质和熵不等式。该技术消除了人工粘性构造中非必要的快波，同时保留了预设的不变域性质和熵不等式。