Application of normalized SPH method to inviscid fluid flows with large deformation of free surface

Abstract

A new normalized smoothed particle hydrodynamics (SPH) method has been presented recently and applied to transient solid mechanics problems of small deformation. The method can overcome boundary deficiency of the conventional SPH method without troublesome inversion of corrective matrix and provide convenience for treating boundary conditions. In this paper, a formulation of the normalized SPH method is derived for modeling inviscid fluid flows with large deformation of free surface. The treatment of dynamic free surface boundary conditions in the present method is addressed and theoretically compared with that in the conventional SPH method. A method based on kernel estimation is proposed for calculation of boundary summation and compared with the method based on α-shape. The normalized SPH method is applied to modeling inviscid free surface flows. Numerical results demonstrate that the present method is capable of modeling large deformation of free surface and can produce higher accuracy than the conventional SPH method, especially at boundary regions. The newly developed kernel estimation method for the calculation of boundary summation is more efficient than the α-shape-based method, and makes the computational efficiency of the normalized SPH method close to the conventional SPH method. To simulate violent free surface flows, a particle shifting technique is introduced in the present method. With this technique, the method is applied to simulating extremely large deformation, fragmentation and reconnection of free surface.