A space-time conservation element and solution element method for solving the two- and three-dimensional unsteady euler equations using quadrilateral and hexahedral meshes
A space-time conservation element and solution element method for solving the two- and three-dimensional unsteady euler equations using quadrilateral and hexahedral meshes
复制标题
DOI：
10.1006/jcph.2001.6934
复制
发表时间：
2002
影响因子：
4.1
通讯作者：
Z. Zhang;S. Yu;Sin-Chung Chang
中科院分区：
文献类型：
--
作者：
Z. Zhang;S. Yu;Sin-Chung Chang
本文报道了一种时空守恒元和解元（CE/SE）方法，该方法分别采用结构化或非结构化四边形和六面体网格模拟二维和三维非定常欧拉方程。该方法将流动变量的网格值及其空间导数作为独立的未知量进行求解。在每个网格点上，通过施加通量守恒条件获得流量变量的值。另一方面，利用有限差分/加权平均方法对空间导数进行评估。请注意，目前的扩展保留了原始CE/SE方法的许多关键优点，该方法分别使用三角形和四面体网格用于其2D和3D应用。这些优点包括高效的并行计算，易于实现非反射边界条件，高保真的冲击和波分辨率，以及真正的多维公式，而不需要使用维度分裂方法。特别是，由于黎曼解算器（godunov型迎风方案的基石）不需要捕获冲击，因此本方法的计算逻辑要简单得多。为了证明该方法的能力，给出了几个基准问题的数值结果，包括斜激波反射、超音速流过楔形和三维爆轰流动。
In this paper, we report a version of the space-time conservation element and solution element (CE/SE) method in which the 2D and 3D unsteady Euler equations are simulated using structured or unstructured quadrilateral and hexahedral meshes, respectively. In the present method, mesh values of flow variables and their spatial derivatives are treated as independent unknowns to be solved for. At each mesh point, the value of a flow variable is obtained by imposing a flux conservation condition. On the other hand, the spatial derivatives are evaluated using a finite-difference/weighted-average procedure. Note that the present extension retains many key advantages of the original CE/SE method which uses triangular and tetrahedral meshes, respectively, for its 2D and 3D applications. These advantages include efficient parallel computing, ease of implementing nonreflecting boundary conditions, high-fidelity resolution of shocks and waves, and a genuinely multidimensional formulation without the need to use a dimensional-splitting approach. In particular, because Riemann solvers-- the cornerstones of the Godunov-type upwind schemes--are not needed to capture shocks, the computational logic of the present method is considerably simpler. To demonstrate the capability of the present method, numerical results are presented for several benchmark problems including oblique shock reflection, supersonic flow over a wedge, and a 3D detonation flow.