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A cell-centered indirect Arbitrary-Lagrangian-Eulerian discontinuous Galerkin scheme on moving unstructured triangular meshes with topological adaptability
Journal of Computational Physics ( IF 4.1 ) Pub Date : 2021-04-21 , DOI: 10.1016/j.jcp.2021.110368
Wenbin Wu , A-Man Zhang , Moubin Liu

In this paper, we present a novel cell-centered indirect Arbitrary-Lagrangian-Eulerian (ALE) discontinuous Galerkin (DG) scheme on moving unstructured triangular meshes with mesh topological adaptability, aiming to deal with the strong distortions and large deformation flow problems. The scheme combines the explicit time marching Lagrangian DG methodology with the adaptive mesh topology optimization technique. The scheme consists of the following three steps. Firstly, we utilize the Runge-Kutta DG method to solve the compressible Euler equation in Lagrangian framework, and employ a nodal solver to obtain the nodal velocity and numerical fluxes across element boundaries. The physical variable and nodal position are updated in this step. Secondly, the adaptive mesh topology optimization technique, which includes the mesh refinement, edge collapse operation and mesh regularization, is implemented to eliminate the highly distorted elements and improve the mesh quality. Thirdly, the conservative remapping algorithm is employed, which can maintain the conservative interpolation of the Lagrangian solution onto the remeshed grid. The present indirect ALE DG scheme can ensure the high quality of the mesh by optimizing the topology connectivity, so that the present scheme can successfully simulate complex vortical flow problems for a sufficient simulation time. Due to the inherent Lagrangian nature, the present scheme can naturally track the multi-material flow interface, rather than using algorithms with interface reconstruction or diffuse interfaces. The scheme is validated with several benchmark flow problems. It is demonstrated that the present indirect ALE DG scheme with topological adaptability can accurately simulate flow problems with large fluid deformations and distortions. It can achieve remarkable improvements compared with the conventional Lagrangian DG method with fixed topological connectivity.



中文翻译:

具有拓扑适应性的运动非结构三角形网格上以细胞为中心的间接拉格朗日-欧拉不连续Galerkin不连续Galerkin格式

在本文中,我们提出了一种新颖的以单元为中心的间接任意Lagrangian-Eulerian(ALE)不连续Galerkin(DG)方案,该方案以具有网格拓扑适应性的移动非结构三角网格为目标,以解决强变形和大变形流动问题。该方案将显式的时间行进拉格朗日DG方法与自适应网格拓扑优化技术相结合。该方案包括以下三个步骤。首先,我们利用Runge-Kutta DG方法在拉格朗日框架中求解可压缩的Euler方程,并采用节点解算器来获得节点速度和跨单元边界的数值通量。在此步骤中,将更新物理变量和节点位置。其次,自适应网格拓扑优化技术,包括网格细化,实施边缘折叠操作和网格正则化,以消除高度变形的元素并提高网格质量。第三,采用保守的重映射算法,该算法可以保持拉格朗日解在修正网格上的保守插值。本发明的间接ALE DG方案可以通过优化拓扑连通性来确保网格的高质量,从而本方案可以在足够的仿真时间内成功地模拟复杂的涡流问题。由于固有的拉格朗日性质,本方案可以自然地跟踪多材料流界面,而不是使用具有界面重构或扩散界面的算法。该方案已通过几个基准流量问题进行了验证。结果表明,目前具有拓扑适应性的间接ALE DG方案可以准确地模拟具有大的流体变形和变形的流动问题。与具有固定拓扑连接性的常规Lagrangian DG方法相比,它可以实现显着的改进。

更新日期:2021-04-21
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