有限体积法中作为基准面通量构造工具的Sod气体动力学问题
The Sod gasdynamics problem as a tool for benchmarking face flux construction in the finite volume method
摘要：
计算流体动力学中的有限体积法对流体流动问题进行数值建模，涉及在控制体积的表面处制定数值通量的过程。这一过程对决定数值解的分辨率和质量是很重要的。在目前的工作中，不同的通量建设方法的性能时，求解一维欧拉方程的无粘流进行了分析，通过在文献中的测试问题具有精确（解析）的解决方案，这是Sod问题。这项工作考虑了22个通量方法，它们是：精确的黎曼解算子（Goddern），Roe，Kurganov-Noelle-Petrova，Kurganov-Tadmor，Steger-Warming通量矢量分裂，van Leer通量矢量分裂，AUSM，AUSM+，AUSM+-up，AUFS，Harten-Lax-van Leer（HLL）族的五个变体，以及Harten-Lax-van Leer-Contact（HLLC）族的它们相应的五个变体，Lax-Friedrichs（Lax），还有鲁萨诺夫精确的黎曼解算子和van Leer方法表现出优良的性能。Riemann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。
英文摘要：
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.
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