A Moving Mesh WENO Method for One-Dimensional Conservation Laws
A Moving Mesh WENO Method for One-Dimensional Conservation Laws
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DOI：
10.1137/110856381
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发表时间：
2012-08
期刊：
影响因子：
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通讯作者：
Xiaobo Yang;Weizhang Huang;J. Qiu
中科院分区：
文献类型：
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作者：
Xiaobo Yang;Weizhang Huang;J. Qiu
本文对一维双曲型守恒律方程发展了一种有效的移动网格加权本质无振荡（韦诺）方法。该方法是基于准拉格朗日方法的移动网格的策略，其中网格被认为是在时间上连续移动。解决了该方案实施过程中出现的几个问题，包括网格平滑度、网格移动限制和变换关系的计算，以及它们对底层方案准确性的影响。特别地，它被发现，最小二乘平滑可以用来有效地平滑网格，和转换关系可以使用高阶有限差分或韦诺应用于一些几何守恒律计算。此外，网格移动会导致韦诺格式变得无条件不稳定。采用一种简单的策略来限制网格的运动，恢复网格的稳定性。数值结果验证了该方法的准确性和激波捕捉能力。
In this paper, we develop an efficient moving mesh weighted essentially nonoscillatory (WENO) method for one-dimensional hyperbolic conservation laws. The method is based on the quasi-Lagrange approach of the moving mesh strategy in which the mesh is considered to move continuously in time. Several issues arising from the implementation of the scheme, including mesh smoothness, mesh movement restriction, and computation of transformation relations, and their effects on the accuracy of the underlying scheme have been addressed. Particularly, it is found that a least squares smoothing can be used to effectively smooth the mesh, and the transformation relations can be computed using either high order finite differences or WENO applied to some geometric conservation laws. Moreover, mesh movement can cause WENO schemes to become unconditionally unstable. A simple strategy is used to restrict the mesh movement and recover the stability. Numerical results are presented to demonstrate the accuracy and shock-captu...