High-order ALE gas-kinetic scheme with WENO reconstruction
High-order ALE gas-kinetic scheme with WENO reconstruction
复制标题
具有 WENO 重建的高阶 ALE 气体动力学方案
DOI：
10.1016/j.jcp.2020.109558
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发表时间：
2020
影响因子：
4.1
通讯作者：
Kun Xu
中科院分区：
文献类型：
--
作者：
Liang Pan;Fengxiang Zhao;Kun Xu
本文提出了一种适用于无粘和粘性流动的任意拉格朗日-欧拉（ALE）格式的高阶多维气体动力学格式。与传统的ALE方法相比，该方法在有限体积框架内对流动变量进行更新，不需要重新分区和重新映射。两阶段的四阶方法用于时间离散，和二阶气体动力学求解器应用于通量评估。在两阶段方法中，空间重建在初始和中间阶段进行，计算网格由网格速度确定。在移动网格过程中，网格可能会严重变形，降低网格质量。为了实现准确性和提高鲁棒性，在每个阶段都采用新开发的四边形网格韦诺方法[40]。高斯求积用于通量计算。对于每个高斯点，在局部移动坐标系下进行韦诺重建，其中考虑了网格速度沿沿着细胞界面的变化。数值算例验证了该方法的有效性，其中网格自适应方法和单元中心拉格朗日方法被用来提供网格速度。
In this paper, a high-order multi-dimensional gas-kinetic scheme is presented for both inviscid and viscous flows in arbitrary Lagrangian-Eulerian (ALE) formulation. Compared with the traditional ALE method, the flow variables are updated in the finite volume framework, and the rezoning and remapping steps are not required. The two-stage fourth-order method is used for the temporal discretization, and the second-order gas-kinetic solver is applied for the flux evaluation. In the two-stage method, the spatial reconstruction is performed at the initial and intermediate stages, and the computational meshes are determined by the mesh velocity. In the moving mesh procedure, the mesh may distort severely and the mesh quality is reduced. To achieve the accuracy and improve the robustness, the newly developed WENO method [40] on quadrilateral meshes is adopted at each stage. The Gaussian quadrature is used for flux calculation. For each Gaussian point, the WENO reconstruction is performed in local moving coordinate, where the variation of mesh velocity along cell interface is taken into account. Numerical examples are presented to validate the performance of current scheme, where the mesh adaptation method and the cell centered Lagrangian method are used to provide mesh velocities.