We introduce several improvements on key numerical techniques,especially for free surface identification and solid boundary handling method.They make K2_SPH simulating breaking waves successfully.It includes running-up,over-turning and breaking processes.Numerical test of violent tank sloshing shows that K2_SPH method is more accurate and reliable than traditional smoothed particle hydrodynamics(SPH) method for wave profile and pressure distribution.

Smoothed particle hydrodynamics is a Lagrangian meshless partilcle method.It gets superiority in simulation of free surface flow and large deformation problems. But low accuracy of kernel approximation becomes an obstacle for widely applications as particles are distributed disorderly or near a boundary.Adopting Taylor expansion and solving integral equation matrix.a second order kernel approximation method,namely K2_SPH is obtained and discussed.With improvement of kernel approximation,improved numedcal techniques are adopted.such as free surface boundary and solid boundary.They are very important for K2_SPH method.With comparison of standard SPH for nonlinear water wave simulation,K2_SPH improves obviously in free surface simulation and distribution of some variables in total particle system.

A method for simulation of a sway tank is presented,in which phase interface is treated as a physical discontinuity.The discontinuity is captured by a well-designed high order scheme.A numerical method for free surface flow on a fixed grid is established.This method is implemented in an in house code GTEA(General Transport Equation Analyzer) which is an unstructured grids finite volume solver.A classical dam break case and a two-dimensional rectangular sway tank at different excitation frequency are used to validate the method.The sloshing load on monitor points agrees well with experimental data.The method gives better results on the secondary peak compared with a commericial software CFX.It shows that the method simulates free surface overturning and breakup well.