The wave structure of approximate Riemann solvers has a significant impact on the accuracy and computational requirements of finite volume codes. We propose a class of structurally complete approximate Riemann solvers (StARS) and provide an efficient means for analytically restoring the expansion wave to pre-existing three-wave solvers. The method analytically restores the expansion, is valid for arbitrary thermodynamics, and has comparable complexity to the popular Harten-Hyman entropy fix. The StARS modification is applied to a Roe scheme, resulting in Roe-StARS with noticeable improvements in unsteady transcritical and supercritical conditions with large flow gradients. A novel scaling analysis is performed on the flow conditions that cause rarefaction fluxes and the magnitude of errors if the rarefaction is omitted. Four test cases are examined: a transcritical shock tube, a shock tube with periodic bounds resulting in interfering shocks and rarefactions, a two-dimensional Riemann problem, and a “gradient” Riemann problem—a variant on the traditional Riemann problem featuring an initial gradient of varying slope rather than an initial step function. The results highlight the complex causes and effects of entropy violations, and encourage further study of StARS-type solvers for modern flow problems in which high flow speeds, large gradients, and non-ideal thermodynamics are increasingly common.

近似黎曼求解器的波结构对有限体积码的精度和计算要求有重大影响。我们提出了一类结构完整的近似黎曼求解器（StARS），并提供了一种有效的方法，用于将膨胀波解析恢复为预先存在的三波求解器。该方法在分析上恢复了膨胀，适用于任意热力学，并且具有与流行的 Harten-Hyman 熵修正相当的复杂性。将 StARS 修改应用于 Roe 方案，导致 Roe-StARS 在具有大流动梯度的非稳态跨临界和超临界条件下具有显着改进。对导致稀疏通量的流动条件和忽略稀疏的误差大小进行了新的缩放分析。检查了四个测试案例：跨临界激波管、具有周期性边界的激波管导致干扰激波和稀疏、二维黎曼问题和“梯度”黎曼问题——传统黎曼问题的变体，具有初始梯度变化斜率而不是初始阶跃函数。结果突出了熵违反的复杂原因和影响，并鼓励进一步研究 StARS 型求解器，以解决高流速、大梯度和非理想热力学越来越普遍的现代流动问题。和一个“梯度”黎曼问题——传统黎曼问题的一个变体，其特征是具有变化斜率的初始梯度，而不是初始阶跃函数。结果突出了熵违反的复杂原因和影响，并鼓励进一步研究 StARS 型求解器，以解决高流速、大梯度和非理想热力学越来越普遍的现代流动问题。和一个“梯度”黎曼问题——传统黎曼问题的一个变体，其特征是具有变化斜率的初始梯度，而不是初始阶跃函数。结果突出了熵违反的复杂原因和影响，并鼓励进一步研究 StARS 型求解器，以解决高流速、大梯度和非理想热力学越来越普遍的现代流动问题。