We present simulation of two typical free surface flows using Smoothed Particle Hydrodynamics-Arbitrary Lagrangian Eulerian(SPH-ALE) method basd on Rimann-solver. A first order kernel correction pressure integral method is presented, which was used to estimate pressure of boundary by integrating water particles within the kernel radius influence. Distribution of pressure field and evolution of free surface are given, and compared with experimental data and numerical solutions. It shows that SPH-ALE method is more accurate and reliable than traditional SPH in pressure calculation of flow field. It has a higher precision in solving strong nonlinear free surface flows.

With electric potential of three electrodes, discrete equations of surface electric charge density was founded with boundary element integral equations. The distribution of surface electric charge on the electrodes was calculated by solving a linear equation group. Then the spatial distribution of the potential and the electric field are obtained. In vacuum, the edge effect of a double glow discharge was analysed.