The HLLC (Harten–Lax–van Leer contact) approximate Riemann solver for computing solutions to hyperbolic systems by means of finite volume and discontinuous Galerkin methods is reviewed. HLLC was designed, as early as 1992, as an improvement to the classical HLL (Harten–Lax–van Leer) Riemann solver of Harten, Lax, and van Leer to solve systems with three or more characteristic fields, in order to avoid the excessive numerical dissipation of HLL for intermediate characteristic fields. Such numerical dissipation is particularly evident for slowly moving intermediate linear waves and for long evolution times. High-order accurate numerical methods can, to some extent, compensate for this shortcoming of HLL, but it is a costly remedy and for stationary or nearly stationary intermediate waves such compensation is very difficult to achieve in practice. It is therefore best to resolve the problem radically, at the first-order level, by choosing an appropriate numerical flux. The present paper is a review of the HLLC scheme, starting from some historical notes, going on to a description of the algorithm as applied to some typical hyperbolic systems, and ending with an overview of some of the most significant developments and applications in the last 25 years.

中文翻译：

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HLLC 黎曼求解器

回顾了 HLLC（Harten-Lax-van Leer 接触）近似黎曼求解器，用于通过有限体积和不连续伽辽金方法计算双曲系统的解。HLLC 早在 1992 年就被设计为对 Harten、Lax 和 van Leer 的经典 HLL（Harten-Lax-van Leer）黎曼求解器的改进，用于求解具有三个或更多特征场的系统，以避免过度中间特征场的 HLL 数值耗散。这种数值耗散对于缓慢移动的中间线性波和长演化时间尤为明显。高阶精确数值方法可以在一定程度上弥补 HLL 的这个缺点，但它是一种昂贵的补救措施，而且对于平稳或接近平稳的中间波，这种补偿在实践中很难实现。因此，最好通过选择合适的数值通量在一阶水平上从根本上解决问题。本文是对 HLLC 方案的回顾，从一些历史记录开始，继续描述应用于一些典型双曲线系统的算法，最后概述一些最重要的发展和应用。 25年。