A moving interface reconstructing algorithm keeping volumed fraction of fluid in the volume of fluids (VOF) method is presented. The moving interface is approximated by a diagonal line of a grid, and two diagonal lines located in adjacent grids intersect on a public side. By keeping constant volume fraction of fluid in each grid, nonlinear equations are built on boundary grids, location of intersecting points of moving-interfaces with grid sides are decided by solving equations. The shape of moving-interfaces is reconstructed. The method simulates accurately moving interfaces with fewer cusps. Its availability and efficiency are demonstrated.

A numerical method is presented for solving the shallow water equation with TVD scheme. Comparison of the numerical solution with analytic solution shows that the method can well specity situation and shape of discontinuous surface. Further, numerical simulating studies about the interaction of a dam breaking long wave with an obstacle have also been done with reasonable results.

In this paper, we design a kind of two levels five points explicit difference scheme for no initial condition diffusion problem. This kind of scheme not only allows the greater time step length, but also has the greater precision.