| In the research of simulation for problems with large distortion in fluid dynamics, one of the most popular numerical algorithms is so called ALE (Arbitrary Lagrangian-Eulerian) method. For the reason of concerning with large mesh distortion, the research of this kind of methods mainly focuses on constructing of finite volume schemes in Lagrangian coordination , mesh redistribution and remapping of physical quantities between mesh systems. In this paper, a new kind of ALE method is investigated , mainly including : constructing of finite volume schemes on structure grids in Lagrangian coordination; constructing of a new kind of high order accurate conservative remapping algorithm; generation of a kind of structured grids. It primarily concerns three following aspects:Firstly, a class of three cell-centered high order finite volume schemes is developed on structured grids in Lagrangian formulism. By using high order WENO reconstruction and RBF reconstruction on structured grids, a high order WENO or RBF Lagrangian finite volume scheme both on space and time is developed.Secondly, a new kind of high order conservative remapping algorithm is constructed. Through researching the problem of finding cell intersections, a new kind of conservative remapping algorithm has been constructed by using high order RBF,WENO,ENO reconstruction.Thirdly, a kind of approximate integration conservative remapping algorithm is constructed. Through analyzing a second order sign preserving conservative remapping method, two conservative remapping algorithms have been constructed by using the WENO reconstruction and RBF method to take the place of the positivity preserving error compensation algorithm.At last, combining the high order finite volume schemes and the efficient remapping algorithms, we succeed to develop ALE method for numerical computations. Testing with a set of reliable numerical examples, it is shown that the ALE algorithm proposed presently be effective.
|
PDF Full Text Request