An ALE method for compressible multi-material flows on unstructured grids

Abstract

Multi-material flows, where a moving interface exists between two immiscible fluids, can be found in a variety of engineering problems. Development of numerically accurate and computationally efficient algorithms for multi-material flow simulations remains one of the unresolved issues in computational fluid dynamics. These flow problems are characterized by the existence of material interfaces. The modeling of these complicated free boundaries poses a difficult numerical challenge, as they are either time dependent or unknown a priori and determined as part of the solution. A number of numerical methods exist for solving the interface problems: interface capturing methods (mixed cell methods), level set methods, volume of fluid and interface reconstruction methods, interface tracking methods, free-Lagrange methods. Unfortunately, there are still limitations and shortcomings attached to each of them. In general, for all these methods that allow mixed cells, the computation of thermodynamical variables such as pressure, speed of sound, and temperature on mixed cells is difficult to achieve correctly. In particular, when the equations of state for different materials are drastically different, a small error on the thermodynamical variables can lead to collapse or meaningless of the computation. For all these methods where the interface is represented and tracked explicitly either by marking it with special marker points, or by treating it like a boundary, it is difficulty to handle very complex free surface problems, especially those involving interface topological changes such as merging or breakup of the interface.