A cell-centered indirect Arbitrary-Lagrangian-Eulerian discontinuous Galerkin scheme on moving unstructured triangular meshes with topological adaptability
A cell-centered indirect Arbitrary-Lagrangian-Eulerian discontinuous Galerkin scheme on moving unstructured triangular meshes with topological adaptability
复制标题
DOI：
10.1016/j.jcp.2021.110368
复制
发表时间：
2021-04
期刊：
影响因子：
--
通讯作者：
Wenbin Wu;A. Zhang;Moubin Liu
中科院分区：
文献类型：
--
作者：
Wenbin Wu;A. Zhang;Moubin Liu
针对强畸变和大变形流动问题，提出了一种新的移动非结构三角形网格上的基于网格拓扑自适应的单元中心间接拉格朗日欧拉（ALE）间断Galerkin（DG）格式.该方案结合了显式时间推进拉格朗日DG方法与自适应网格拓扑优化技术。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下求解可压缩欧拉方程，并采用节点求解器来获得节点速度和跨单元边界的数值通量。物理变量和节点位置在此步骤中更新。其次，采用自适应网格拓扑优化技术，包括网格加密、边折叠操作和网格正则化，以消除高度畸变的单元，提高网格质量。第三，采用守恒重映算法，保持拉格朗日解在重网格上的守恒插值。本文提出的间接ALE DG格式通过优化拓扑结构的连通性，保证了网格的高质量，从而可以在足够的时间内成功地模拟复杂的旋涡流动问题。由于固有的拉格朗日性质，本方案可以自然地跟踪多物质流界面，而不是使用具有界面重建或扩散界面的算法。该计划是验证与几个基准流问题。结果表明，本文提出的具有拓扑自适应性的间接ALE DG格式能够准确地模拟具有大变形和畸变的流动问题。与传统的具有固定拓扑连通度的拉格朗日DG方法相比，该方法具有显著的改进效果。
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.