Our goal is to present a simple volume-of-fluid type interface-tracking algorithm to compressible two-phase flow in two space dimensions. The algorithm uses a uniform underlying Cartesian grid with some cells cut by the tracked interfaces into two subcells. A volume-moving procedure that consists of two basic steps: (1) the update of volume fractions in each grid cell at the end of the time step, and (2) the reconstruction of interfaces from discrete set of volume fractions, is employed to follow the dynamical behavior of the interface motion. As in the previous work with a surface-tracking procedure for general front tracking (LeVeque & Shyue 1995, 1996), a high resolution finite volume method is then applied on the resulting slightly nonuniform grid to update all the cell values, while the stability of the method is maintained by using a large time step wave propagation approach even in the presence of small cells and the use of a time step with respect to the uniform grid cells. A sample preliminary numerical result for an underwater explosion problem is shown to demonstrate the feasibility of the algorithm for practical problems.

• KEH-MING SHYUE(Department of Mathematics, National Taiwan University)