Weighted essentially non-oscillatory scheme on unstructured quadrilateral and triangular meshes for hyperbolic conservation laws
Weighted essentially non-oscillatory scheme on unstructured quadrilateral and triangular meshes for hyperbolic conservation laws
复制标题
双曲守恒定律的非结构化四边形和三角形网格的加权基本非振荡方案
DOI：
10.1016/j.jcp.2018.08.008
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发表时间：
2018
影响因子：
4.1
通讯作者：
Shuanghu Wang
中科院分区：
文献类型：
--
作者：
Fengxiang Zhao;Liang Pan;Shuanghu Wang
本文针对非结构四边形和三角形网格上的双曲型守恒律方程，提出了一种三阶加权基本无振荡（韦诺）格式。作为一个出发点，一个通用的模板被选择为具有任何局部拓扑结构的单元，并可以构造一个统一的线性格式。然而，传统的非结构网格韦诺格式在局部网格质量较低的情况下会出现很大的权值和负值，这使得韦诺格式在光滑条件下也不稳定。该方案给出了一种处理极大线性权值的优化方法，并采用分裂技术处理由优化方法得到的负权值。提出了一种同时考虑局部网格质量和解的不连续性的非线性权值和新的光滑指标。数值试验验证了该方法的有效性。得到了期望的精度收敛速度，且误差绝对值不受网格质量的影响。强间断条件下的数值试验验证了当前韦诺格式的鲁棒性。
In this paper, a third-order weighted essentially non-oscillatory (WENO) scheme is developed for the hyperbolic conservation laws on unstructured quadrilateral and triangular meshes. As a starting point, a general stencil is selected for the cell with any local topology, and a unified linear scheme can be constructed. However, in the traditional WENO scheme on unstructured meshes, the very large and negative weights may appear for the mesh with lower local mesh quality, which make the WENO scheme unstable even for the smooth tests. In the current scheme, an optimization approach is given to deal with the very large linear weights, and the splitting technique is considered to deal with the negative weights obtained by the optimization approach. The non-linear weights with the new smooth indicator are proposed as well, in which the local mesh quality and discontinuities of solutions are taken into account simultaneously. Numerical tests are presented to validate the current scheme. The expected convergence rate of accuracy is obtained, and the absolute value of error is not affected by mesh quality. The numerical tests with strong discontinuities validate the robustness of current WENO scheme.