Arbitrary Lagrangian-Eulerian Method Based on Adaptive Structure Grids

Abstract: In the research of numerical simulation for front tracking problems in computational 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 adaptive grids. It primarily concerns three following aspects:(ⅰ)By use of ENO(Essentially Non-oscillatory) 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)Two kinds of integration conservative remapping algorithms are introduced, one is based on cell intersections and another is based on interface flux. Then the author constructs a new kind of integration conservative remapping algorithm through a kind of WENO(Weighted Essentially Non-oscillatory) interpolating polynomials reconstruction .At last the author tests the efficiency of the scheme with a set of reliable numerical examples.(ⅲ)Proposing a kind of structure grid generation method and two kinds of adaptive grids strategies: AMR(Adapative Mesh Refinement) and MMM(Moving Mesh Method). As the physical quantities are required to update in the adaptive grids, which needs to satisfy the requirement of conservation and monotonicity for physical quantities, the author applies the conservative remapping algorithm to the solution updating and tests the efficiency of the method at last.The author compiles three computational program modules according to the work above .Subsequently, assembling them into a whole, we gain a new kind of method. At last, testing with a set of reliable numerical examples, it is shown that the new algorithm proposed presently be effective…
Key words: Front tracking technique; ALE method; finite volume scheme; rezoning (remapping) technique; ENO interpolation; WENO interpolation; Adaptive grids strategy

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