In the previous study [J. Comput. Phys. 417 (2020) 109558], under arbitrary-Lagrangian-Eulerian (ALE) formulation a high-order gas-kinetic scheme has been developed for the computation of two-dimensional flows. For the three-dimensional flows, due to the distorted mesh, it becomes more difficult to develop robust high-order ALE methods with the precise preservation of geometric conservation law. In this paper, the high-order gas-kinetic ALE scheme will be constructed for three-dimensional flows. The key ingredients of the scheme are the use of weighted essentially non-oscillatory (WENO) scheme for spatial reconstruction and the two-stage fourth-order discretization for temporal evolution. In the ALE formulation, in order to release the problems associated with mesh distortion and non-coplanar vertexes of a control volume, in the spatial reconstruction the selection of candidate stencils and the topologically independent linear weights have to be carefully designed. In the surface integrals for the flux transport, a bilinear interpolation is used to parameterize both grid coordinates and grid moving velocity with the preservation of the geometric conservation law. In the computation, the grid velocity is determined by the variational formulation based Lagrangian nodal solver. Numerical examples are presented to evaluate the accuracy, robustness, and the preservation of geometric conservation law of the current scheme.

在先前的研究中[J. 计算 物理 417（2020）109558]，在任意拉格朗日-欧拉（ALE）公式下，已开发出一种高阶气体动力学方案来计算二维流。对于三维流动，由于网格变形，要开发出精确保留几何守恒定律的鲁棒高阶ALE方法变得更加困难。在本文中，将针对三维流动构造高阶气体动力学ALE方案。该方案的关键要素是使用加权的基本非振荡（WENO）方案进行空间重建，并采用两阶段的四阶离散化进行时间演化。在ALE公式中，为了消除与网格变形和控制体积的非共面顶点相关的问题，在空间重建中，必须仔细设计候选模板的选择和拓扑独立的线性权重。在用于通量传输的表面积分中，使用双线性插值来参数化栅格坐标和栅格移动速度，同时保留了几何守恒定律。在计算中，网格速度由基于变分公式的拉格朗日节点求解器确定。数值例子被提出来评估当前方案的准确性，鲁棒性和几何守恒律的保存。在保留几何守恒定律的情况下，使用双线性插值对网格坐标和网格移动速度进行参数化。在计算中，网格速度由基于变分公式的拉格朗日节点求解器确定。数值例子被提出来评估当前方案的准确性，鲁棒性和几何守恒律的保存。在保留几何守恒定律的情况下，使用双线性插值对网格坐标和网格移动速度进行参数化。在计算中，网格速度由基于变分公式的拉格朗日节点求解器确定。数值例子被提出来评估当前方案的准确性，鲁棒性和几何守恒律的保存。