Research On Arbitrary Lagrangian-Eulerian Method And Its Key Technology

In the research of simulation for problems with large distortion in fluid dynamics, one of popular numerical algorithms is so called Arbitrary Lagrangian-Eulerian (ALE) method. For the reason of concerning with large mesh distortion, the research of this kind of method mainly focuses on constructing high order schemes in Lagrangian formulism, meshes regenerate for grid distortion and conservative remapping algorithms for transferring physical quantities between two computational meshes. In this paper, a class of high order ENO Lagrangian finite volume schemes on the staggered and a class of two cell-centered high order Lagrangian finite volume schemes have been developed. Combining with the ENO interpolation, two kinds of conservative remapping algorithms have been developed for arbitrary mesh systems based on computing intersections of two polygons and cell donor method. It primarily concerns five following aspects:Firstly, a class of two cell-centered high order finite volume schemes is developed on structured grids in Lagrangian formulism. By using high order ENO reconstruction with Roe - type characteristic decomposition of Least Squares method (LSM) on structured grids, a high order ENO of LSM Lagrangian finite volume scheme both on space and time is developed .Secondly, a high order finite volume scheme is developed on the staggered mesh in Lagrangian formulism. By using ENO interpolating polynomials, a high order ENO finite volume scheme has been constructed through modifying a first order finite volume scheme on rectangular mesh.Thirdly, 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 ENO reconstruction.Fourthly, 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 ENO reconstruction and Least Squares 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. Furthermore, coupling adaptive mesh generation method with our ALE method, a new kind of adaptive ALE method is developed. One and two dimensional numerical examples are presented to demonstrate the performance of the schemes in terms of accuracy and resolution for contact discontinuities and shock regions.