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首页> 外文期刊>Journal of Computational Physics >Efficient quadrature-free high-order spectral volume method on unstructured grids: Theory and 2D implementation
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Efficient quadrature-free high-order spectral volume method on unstructured grids: Theory and 2D implementation

机译：非结构化网格上的高效无正交高阶频谱体积方法：理论和二维实现

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An efficient implementation of the high-order spectral volume (SV) method is presented for multi-dimensional conservation laws on unstructured grids. In the SV method, each simplex cell is called a spectral volume (SV), and the SV is further subdivided into polygonal (2D), or polyhedral (3D) control volumes (CVs) to support high-order data reconstructions. In the traditional implementation, Gauss quadrature formulas are used to approximate the flux integrals on all faces. In the new approach, a nodal set is selected and used to reconstruct a high-order polynomial approximation for the flux vector, and then the flux integrals on the internal faces are computed analytically, without the need for Gauss quadrature formulas. This gives a significant advantage over the traditional SV method in efficiency and ease of implementation. For SV interfaces, a quadrature-free approach is compared with the Gauss quadrature approach to further evaluate the accuracy and efficiency. A simplified treatment of curved boundaries is also presented that avoids the need to store a separate reconstruction for each boundary cell. Fundamental properties of the new SV implementation are studied and high-order accuracy is demonstrated for linear and non-linear advection equations, and the Euler equations. Several well known inviscid flow test cases are utilized to show the effectiveness of the simplified curved boundary representation. (C) 2007 Elsevier Inc. All rights reserved.
机译：针对非结构化网格上的多维守恒律，提出了高阶频谱量（SV）方法的有效实现。在SV方法中，每个单纯形单元称为频谱量（SV），并且SV进一步细分为多边形（2D）或多面体（3D）控制量（CV）以支持高阶数据重建。在传统实现中，使用高斯正交公式来近似所有面上的通量积分。在新方法中，选择一个节点集并将其用于重构通量矢量的高阶多项式逼近，然后无需高斯正交公式即可对内面的通量积分进行解析计算。与传统的SV方法相比，这在效率和易于实现方面具有明显优势。对于SV接口，将无正交方法与高斯正交方法进行了比较，以进一步评估准确性和效率。还提出了对弯曲边界的简化处理，从而避免了为每个边界单元存储单独的重构的需要。研究了新的SV实现的基本特性，并证明了线性和非线性对流方程以及Euler方程的高阶精度。利用几个众所周知的无粘性流测试案例来展示简化的弯曲边界表示的有效性。 （C）2007 Elsevier Inc.保留所有权利。

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