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.

翻译：本文聚焦于双曲系统的一阶不变域保持近似方法。我们提出了一种估计人工粘性的新方法，该方法可使显式、守恒且相容的数值方法同时满足不变域保持特性与熵不等式。不同于计算黎曼问题中最大波速的上界，我们通过估计黎曼问题中的最小波速，使得近似解满足预设的不变域性质与熵不等式。该技术能在保持预设不变域性质与熵不等式的前提下，在人工粘性构造中消除非本质的快波干扰。