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An effective second-order three-dimensional unstructured multimaterial arbitrary Lagrangian–Eulerian (MMALE) method was presented for compressible fluid dynamics, which uses  Moment of Fluid (MOF) method to reconstruct material interface for immiscible fluids. It is of the explicit time-marching Lagrange plus remap type. Comparing with traditional ALE method, MMALE method permits multimaterials in a singel cell, thus has the extra advantage of accurately modeling problems involving severe mesh distortion as well as interface fragmentations and coalitions induced by strong shearing deformation. Because the stencil used in the staggered compatible discretization involves only the nearest neighbouring cells and the MOF algorithm does not need information from the neighboring cells, the MMALE method in this paper is suitable for parallel computation while keeps second-order accurate. Several numerical tests on three-dimensional structured and unstructured meshes have proved the accuracy and robustness of the present method.

MMALE method, MOF method, compatible Lagrangian method, multimaterial fluid dynamics