A Conservative Interface Treating Method For Multi-medium Flow

In the simulation of the multi-medium flow, The Ghost Fluid Methods (GFMs) have been shown to be a simple method and are easy to be extended to multi-dimensions. In GFMs, the states at the ghost nodes are defined for each medium so as to the multi-medium flow can be computed as single medium flow, this lead to the numerical flux at the cell boundary near the interface is defined non-unique. Thus the scheme is not conservative in the computational domain and the conservative errors are incurred. Those errors may result in the nonphysical oscillation and inaccuracy of the solution. In this paper a conservative interface treating method is presented to simulate the multi-medium flow. The interface is tracked by solving the level set equation, The Riemann problems can be defined and solved to give the fluid states at the interface, those states are employed to define the numerical flux at the interface and the interfacial boundary condition, the solution can be obtained by using the method as that for single medium flow. In this method the numerical flux is defined uniquely and the conservative errors are avoided. For two-dimensional problems, new cells are generated by cutting the cells which crossing the interface, the Heaviside function is employed to compute the area of the new cells. To improve the accuracy of the solution and save computational cost, the new obtained small cells are detected and mixed with their neighboring cells which stay in the same medium with the small cells. The numerical tests for one- and two-dimensional cases show that this method can capture the interface and discontinuities accurately.