An Arbitrary-Lagrangian-Eulerian High-Order Gas-Kinetic Scheme for Three-Dimensional Computations

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.