Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations
Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations
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DOI：
10.1007/s10915-006-9113-9
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发表时间：
2007-07
影响因子：
2.5
通讯作者：
Z. Wang;Yen Liu;G. May;A. Jameson
中科院分区：
文献类型：
--
作者：
Z. Wang;Yen Liu;G. May;A. Jameson
谱差分法是近年来发展起来的一种求解非结构网格上守恒律方程的高效、高阶、守恒的方法。它结合了结构化和非结构化网格方法的最佳特性，以实现高计算效率和几何灵活性;它利用不连续和高阶局部表示的概念，以实现守恒和高精度;为了简单起见，它基于有限差分公式。该方法不涉及曲面积分和体积积分，易于实现。通用的重建得到的解决方案和通量点分布在一个几何相似的方式为单纯形细胞。本文将该方法进一步推广到非线性守恒律方程组，即欧拉方程组。进行准确度研究，以数值验证准确度的顺序。为了捕捉光滑的功能和不连续性，单调性限制器的实施，并在一个和两个维度的几个问题进行测试。在非结构网格上，该方法比间断Galerkin法和谱体积法更有效。
An efficient, high-order, conservative method named the spectral difference method has been developed recently for conservation laws on unstructured grids. It combines the best features of structured and unstructured grid methods to achieve high-computational efficiency and geometric flexibility; it utilizes the concept of discontinuous and high-order local representations to achieve conservation and high accuracy; and it is based on the finite-difference formulation for simplicity. The method is easy to implement since it does not involve surface or volume integrals. Universal reconstructions are obtained by distributing solution and flux points in a geometrically similar manner for simplex cells. In this paper, the method is further extended to nonlinear systems of conservation laws, the Euler equations. Accuracy studies are performed to numerically verify the order of accuracy. In order to capture both smooth feature and discontinuities, monotonicity limiters are implemented, and tested for several problems in one and two dimensions. The method is more efficient than the discontinuous Galerkin and spectral volume methods for unstructured grids.