混合Riemann求解器用于大系统守恒律
Hybrid Riemann Solvers for Large Systems of Conservation Laws
AI总结：
本文提出了一种新的近似Riemann求解器家族，用于超保守律的数值解近似。该方法通过估计全局最快波速来避免特征分解，特别适用于大系统和无显式特征系统的情况，具有比HLL更少的耗散性。
摘要：
本文介绍了用于超保守律数值解近似的新型近似Riemann求解器家族。这些求解器是近似的，即不计算通量雅可比矩阵的特征分解，而是仅需估计全局最快波速的估计值。因此，这种求解器家族特别适用于具有许多不同传播速度的大系统，且在没有显式特征系统表达式时。尽管仅需最快波速作为输入值，新的Riemann求解器族能以比HLL更少的耗散性重现所有波，HLL具有相同的前提条件，仅需额外一个通量评估。
英文摘要：
In this paper we present a new family of approximate Riemann solvers for the numerical approximation of solutions of hyperbolic conservation laws. They are approximate, also referred to as incomplete, in the sense that the solvers avoid computing the characteristic decomposition of the flux Jacobian. Instead, they require only an estimate of the globally fastest wave speeds in both directions. Thus, this family of solvers is particularly efficient for large systems of conservation laws, i.e. with many different propagation speeds, and when no explicit expression for the eigensystem is available. Even though only fastest wave speeds are needed as input values, the new family of Riemann solvers reproduces all waves with less dissipation than HLL, which has the same prerequisites, requiring only one additional flux evaluation.
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