The Finite Volume Method in Computational Fluid Dynamics to numerically model a fluid flow problem involves the process of formulating the numerical flux at the faces of the control volume. This process is important in deciding the resolution of the numerical solution, thus its quality. In the current work, the performance of different flux construction methods when solving the one-dimensional Euler equations for an inviscid flow is analyzed through a test problem in the literature having an exact (analytical) solution, which is the Sod problem. The work considered twenty two flux methods, which are: exact Riemann solver (Godunov), Roe, Kurganov-Noelle-Petrova, Kurganov-Tadmor, Steger-Warming Flux Vector Splitting, van Leer Flux Vector Splitting, AUSM, AUSM+, AUSM+-up, AUFS, five variants of the Harten-Lax-van Leer (HLL) family, and their corresponding five variants of the Harten-Lax-van Leer-Contact (HLLC) family, Lax-Friedrichs (Lax), and Rusanov. The methods of exact Riemann solver and van Leer showed excellent performance. The Riemann exact method took the longest runtime, but there was no significant difference in the runtime among all methods.

中文翻译：

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Sod 气体动力学问题作为有限体积法中工作面通量构建的基准工具

计算流体动力学中用于对流体流动问题进行数值模拟的有限体积方法涉及制定控制体积面处的数值通量的过程。这个过程对于决定数值解的分辨率很重要，因此它的质量。在当前的工作中，通过文献中具有精确（解析）解的测试问题，即 Sod 问题，分析了求解无粘性流动的一维欧拉方程时不同通量构造方法的性能。该工作考虑了 22 种通量方法，它们是：精确黎曼求解器 (Godunov)、Roe、Kurganov-Noelle-Petrova、Kurganov-Tadmor、Steger-Warming Flux Vector Splitting、van Leer Flux Vector Splitting、AUSM、AUSM+、AUSM+-up , AUFS, Harten-Lax-van Leer (HLL) 家族的五个变体，及其相应的 Harten-Lax-van Leer-Contact (HLLC) 家族、Lax-Friedrichs (Lax) 和 Rusanov 的五个变体。精确黎曼求解器和van Leer方法表现出优异的性能。黎曼精确方法的运行时间最长，但所有方法的运行时间没有显着差异。