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A fully discrete ALE method over untwisted time–space control volumes
Authors:Jin Qi  Jiequan Li
Institution:1. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, China;2. School of Mathematical Sciences, Beijing Normal University, Beijing, China
Abstract:In this paper, a fully discrete high‐resolution arbitrary Lagrangian–Eulerian (ALE) method is developed over untwisted time–space control volumes. In the framework of the finite volume method, 2D Euler equations are discretized over untwisted moving control volumes, and the resulting numerical flux is computed using the generalized Riemann problem solver. Then, the fluid flows between meshes at two successive time steps can be updated without a remapping process in the classic ALE method. This remapping‐free ALE method directly couples the mesh motion into a physical variable update to reflect the temporal evolution in the whole process. An untwisted moving mesh is generated in terms of the vorticity‐free part of the fluid velocity according to the Helmholtz theorem. Some typical numerical tests show the competitive performance of the current method. Copyright © 2016 John Wiley & Sons, Ltd.
Keywords:2D Euler equations  remapping‐free ALE method  generalized Riemann problem solver  Helmholtz theorem  untwisted time–  space control volume
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