A high order positivity-preserving conservative WENO remapping method based on a moving mesh solver
A high order positivity-preserving conservative WENO remapping method based on a moving mesh solver
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DOI：
10.1016/j.jcp.2022.111754
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发表时间：
2022-11
期刊：
影响因子：
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通讯作者：
Xiaolu Gu;Juan Cheng;Yue Li;Chi-Wang Shu
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文献类型：
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作者：
Xiaolu Gu;Juan Cheng;Yue Li;Chi-Wang Shu
本文提出了一种高阶高精度保正保守重映射算法。以二维四边形网格为例。这种重映射方法是基于运动网格上的平凡方程∂u∂t= 0的数值解，运动网格是t= 0重映射前的旧网格，是t= t重映射后的新网格。在运动网格上使用高阶有限体积方案来解决这个问题。具体来说，我们采用多分辨率加权基本非振荡（WENO）方法进行空间离散，采用强稳定保持（SSP）龙格-库塔方法进行时间离散。重映射算法在对网格运动速度的平滑要求（Lipschitz连续性）非常温和的情况下具有高阶精度，只要选择合适的最终伪时间t就能满足这一要求。我们利用线性尺度保正限制器设计了具有保正性的重映射算法，从而保证了相关物理变量的保正性，并保持了精度的守恒性和原阶性。通过一系列数值实验证明了该算法具有高阶精度、基本无振荡、保持正性和计算效率高等特点。
In this paper, a high order accurate positivity-preserving conservative remapping algorithm is developed. Quadrilateral meshes in two dimensions are used as examples. This remapping method is based on the numerical solution of the trivial equation∂ u∂ t= 0 on a moving mesh, which is the old mesh before remapping at t= 0 and is the new mesh after remapping at t= T. A high order finite volume scheme on the moving mesh is used to solve this problem. Specifically, we adopt the multi-resolution weighted essentially non-oscillatory (WENO) method for the spatial discretization and a strong stability preserving (SSP) Runge-Kutta method for the temporal discretization. The remapping algorithm is high order accurate under very mild smoothness requirement (Lipschitz continuity) on the mesh movement velocity, which can always be satisfied with a suitable choice of the final pseudo-time T. Furthermore, we design our remapping algorithm to have positivity-preserving property by using the linear scaling positivity-preserving limiter so that the algorithm could ensure the positivity-preserving property of relevant physical variables and maintain conservation and original order of accuracy. A series of numerical experiments are given to demonstrate the properties of our remapping algorithm such as high order accuracy, essentially non-oscillatory performance, positivity-preserving and high computational efficiency.