A quadrature simplification method for fast implicit discontinuous Galerkin schemes
A quadrature simplification method for fast implicit discontinuous Galerkin schemes
复制标题
快速隐式间断伽辽金格式的求积化简方法
DOI：
10.1016/j.compfluid.2018.03.035
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Sawada Keisuke
中科院分区：
文献类型：
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作者：
Asada Hiroyuki;Kawai Soshi;Sawada Keisuke
本文描述了一种用高阶不连续伽辽金方法进行快速隐式时间积分的方法。该方法假定每个单元的雅可比矩阵是恒定通量的，并利用基函数的正交特性来简化隐式时间积分方案中的正交问题。QSO可以实现更快的隐式时间积分，而不会导致计算结果的严重恶化。在计算成本、数值稳定性和收敛性方面，首先通过使用二维结构网格的激波和边界层问题来评估QSO的性能。本文还研究了量子粒子群对时间演化的影响。然后通过边界层计算研究了所提出的QSO在三维非结构化网格中的应用。最后，通过一个更复杂的三角翼流场问题的实例应用，证明了高阶DG方法与QSO的能力。
This paper describes a methodology for fast implicit time integrations with high-order discontinuous Galerkin (DG) methods. The proposed approach, named quadrature simplification by orthogonality (QSO), assumes constant-flux Jacobians in each cell and utilizes the orthogonal properties of basis functions to simplify the quadrature involved in implicit time integration schemes. QSO enables substantially faster implicit time integration without any major deterioration in the computed results. In terms of the computational cost, numerical stability, and convergence property, the performance of QSO is first assessed through shock wave and boundary layer problems using 2D structured meshes. Effects of QSO on time evolutions are also examined. The application of the proposed QSO to 3D unstructured meshes is then investigated through boundary layer computations. Finally, an illustrative application to the more complex problem of the flowfield over a delta wing is used to demonstrate the capability of high-order DG methods with QSO.