Numerical Simulation Technique Research For Multi-Material Flows On Unstructural Moving Grids

Numerical methods based on unstructural moving grids are developed to solve compressible multi-material flows where an arbitrarily moving interface exists between two immiscible fluids.Unstructural 2D triangle and 3D tetrahedron grids are generated using advancing front technology. The bidirectional chains are applied to accelerate some operations such as inserting, deleting and searching. A simple rule is proposed to judge the intersection of segment, facet and volume during generating tetrahedron grids. Besides, edge swaping and face swaping methods are also applied to improve the quality of tetrahedron grids.Arbiratry Lagrangian-Eulerial (ALE) formulation based on unstructual moving grids is used to solve multi-material flows. The material interface is looked upon as a lagrangian interface which can move freely and is composed of a number of edges of the unstructured grids. The state vectors of the points on the interface have two different definitions corresponding to the two different fluids. Then, Riemann problem is solved to track the interface accurately and the grids are moving automatically with the motion of the interface. The analytic solution of Riemann problem for stiffened gas equation of state (EOS) is deduced in this article. And two-shock approximation method is implemented for general EOS. Two different methods, Lagrange methods and ghost fluid method (GFM) are discussed here to compute the numeical flux through the material interface. 1D double-material shock tube problems are solved to indicate that GFM still work well when large pressure grads exists near the interface.Spring analogy and local remeshing technology is respectively applied to deal with small and large deforming grids. At the same time, points at the material interface may slip in tangent direction of the interface resulting in negative volume grids. To resolve this problem, the material interface is defined as deforming boundary where the points and grids can adaptively adjust their positions.Underwater explosion model, shock bubble model and supersonic aerofoil over water model are computed using ALE method, which indicates that ALE method is feasible in the computing of multi-material flows and holds these advantages comparing with Euler mehods: (1) real-time tracking of the material interface; (2) ability of capturing mirco-deforming interface.