Arbitrary Lagrangian-Eulerian Method and Remapping Technique

Abstract: In the research of simulation for problems with large distortion in fluid dynamics, one of 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 and remapping of physical quantities between mesh systems. In this paper, by use of the idea of constructing of high accurate ENO (Essentially Non-oscillatory) schemes applied successfully in the simulation of Euler equations, a new kind of high accurate finite volume schemes have been constructed in Lagrangian coordination. Combining with the ENO interpolation, two kinds of conservative remapping algorithms have been developed for arbitrary mesh systems. It primarily concerns four following aspects: i) Constructing of finite volume schemes on structure grids in Lagrangian coordination. By use of ENO interpolating polynomials on structure grids, a high accurate finite volume scheme has been constructed through modifying a first order finite volume scheme on rectangular mesh.ii) Constructing of finite volume schemes on unstructured grids in Lagrangian coordination. By use of ENO interpolating polynomials on unstructured grids, a high accurate finite volume scheme has been constructed through combining the idea of constructing of high order accurate finite volume schemes on structured grids.iii) Constructing of a new kind of high order accurate conservative remapping algorithm. It is based on the technique transferring physical quantities between the two computational meshes, known as remapping. Through researching the problem of finding cell intersections, a new kind of conservative remapping algorithm has been constructing by use of ENO interpolation.iv) Constructing of a kind of approximate integration conservative remapping algorithm. Through analyzing a second order sign-preserving conservative remapping method, two conservative remapping algorithms have been constructed by using the reconstruction method to take the place of the positivity-preserving error compensation algorithm.Subsequently, combining the high order accurate finite volume schemes and the efficient remapping algorithms, we write ALE method computational code. Testing with a set of reliable numerical examples, it is shown that the new algorithm proposed presently be effective…
Key words: ALE method; finite volume scheme; rezoning (remapping) technique; ENO interpolation

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