Research On Improved Kernel Function Of SPH Method And Numerical Simulation

Smoothed Particle Hydrodynamics(SPH)method is a meshless method,which has certain advantages in the simulation of large deformation problems such as dam breaks,surge waves and underwater explosions.For this reason,an ever-increasing number of scholars study various large deformation problems using the SPH method.However,the current SPH method is not mature enough,and there are still problems such as stress instability between particles,low computational efficiency,and difficulty in applying boundary conditions.Among them,the consequences of stress instability in the actual simulation are relatively serious,which can bring about the non-physical aggregation of the particles,and even bring about the computation to crash.Due to the fact that fluids can only withstand pression and cannot withstand tension,stress instability in fluids becomes pression instability.To solve this problem,an improved SPH method is proposed in this article,which can improve the pression instability of fluids.The improved method is applied to the simulation of the wave pool and the interaction between a floating body and waves.The experimental results show that the improved SPH method in this article is theoretically feasible.Firstly,in response to the phenomenon of pression instability,a new kernel function is proposed in this article to aligns the trend of the first derivative of the kernel function with the trend of pression variation.In theory,the improved kernel function can improve the phenomenon of pression instability.Secondly,in order to verify the effectiveness of the improved kernel function proposed in this article,numerical simulations are conducted on waves using the traditional kernel functions and the improved kernel function respectively.The simulation results show that the improved kernel function makes the particle distribution more regular compared with the traditional kernel functions,verifying the effectiveness of the improved kernel function in improving the phenomenon of instability of pression.Finally,the improved SPH method is used to simulate the motion of a floating body in waves,and hydrodynamic analysis is conducted on the experimental results to verify the feasibility of applying the improved kernel function SPH method to simulate the interaction between a floating body and waves.