A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction

JOURNAL OF COMPUTATIONAL PHYSICS

卷:229

Article

Galera, Stephane²  Maire, Pierre-Henri¹  Breil, Jerome² 

[1] CEA, CESTA, DSGA, F-33114 Le Barp, France

[2] Univ Bordeaux 1, UMR CELIA, F-33405 Talence, France

关键词: Lagrangian hydrodynamics;    Cell-centered scheme;    Godunov-type method;    Compressible flow;    High-order finite volume methods;    Multi-dimensional unstructured mesh;    Arbitrary Lagrangian-Eulerian methodology;    Interface reconstruction;   

DOI  :  10.1016/j.jcp.2010.04.019

来源: Elsevier

【 摘 要 】

We present a new cell-centered multi-material arbitrary Lagrangian-Eulerian (ALE) scheme to solve the compressible gas dynamics equations on two-dimensional unstructured grid. Our ALE method is of the explicit time-marching Lagrange plus remap type. Namely, it involves the following three phases: a Lagrangian phase wherein the flow is advanced using a cell-centered scheme; a rezone phase in which the nodes of the computational grid are moved to more optimal positions; a cell-centered remap phase which consists of interpolating conservatively the Lagrangian solution onto the rezoned grid. The multi-material modeling utilizes either concentration equations for miscible fluids or the Volume Of Fluid (VOF) capability with interface reconstruction for immiscible fluids. The main original feature of this ALE scheme lies in the introduction of a new mesh relaxation procedure which keeps the rezoned grid as close as possible to the Lagrangian one. In this formalism, the rezoned grid is defined as a convex combination between the Lagrangian grid and the grid resulting from condition number smoothing. This convex combination is constructed through the use of a scalar parameter which is a scalar function of the invariants of the Cauchy-Green tensor over the Lagrangian phase. Regarding the cell-centered remap phase, we employ two classical methods based on a partition of the rezoned cell in terms of its overlap with the Lagrangian cells. The first one is a simplified swept face-based method whereas the second one is a cell-intersection-based method. Our multi-material ALE methodology is assessed through several demanding two-dimensional tests. The corresponding numerical results provide a clear evidence of the robustness and the accuracy of this new scheme. (C) 2010 Elsevier Inc. All rights reserved.

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