Title: Greedy invariant-domain preserving approximation for hyperbolic systems Show Chinese title

Title: 贪婪不变域保持近似用于双曲系统

Abstract: 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. Show Chinese abstract

Abstract: 本文专注于双曲系统的不变域保持近似。 我们提出了一种新的方法来估计必须添加的人工粘性，以使显式、保守、一致的数值方法保持不变域并符合熵不等式。 而不是计算黎曼问题中最大波速的上界，我们估计了所述黎曼问题中的最小波速，使得近似满足预定义的不变域性质和预定义的熵不等式。 该技术消除了构造人工粘性中的非必要快波，同时保持预设的不变域性质和熵不等式。