Research On Improved Kernel Approximation Form Of SPH Method And Wave Building Simulation

Smooth particle hydrodynamics(SPH)is a meshless computing method,which has attracted extensive attention in recent years,especially in the field of computational fluid dynamics.This method completely avoids mesh division and reconstruction,and it has many advantages in dealing with large deformation fluid,free-surface fluid,multiphase flow and has a broad application prospect.However,the SPH method is not mature enough.Compared with the mesh method,there are still some problems,such as insufficient computation accuracy,difficulty imposing boundary conditions directly,large amounts of computation and so on.The SPH method relies on the kernel function to establish the interaction relationship between particles.Since the support domain of the kernel function of the particle near the boundary is truncated,the kernel function no longer satisfies the normalization,and the accuracy of the particle’s kernel approximation cannot be guaranteed.The usual processing method is to arrange extra ghost particles outside the boundary to participate in the calculation,which undoubtedly increases the amount of calculation,and it is difficult to arrange multi-layer ghost particles for the complex boundary.The corrective smooth particle hydrodynamics(CSPH)method avoids placing virtual particles outside the boundary.By improving the kernel approximation form of the particles,the effect of the truncation of the kernel function is considered,and the approximation accuracy of the particles near the boundary is improved.Similarly,the modified smooth particle hydrodynamics(MSPH)method further improves the approximation accuracy of boundary particles and internal irregularly distributed particles by solving the field function and the approximation of the first and second derivatives simultaneously,but the computational amount is also much larger.In this paper,the problem of particle approximation precision decreasing near the boundary is studied.Based on the CSPH method and the MSPH method,a SPH method with improved kernel approximation is proposed.This method is similar to the MSPH method.Firstly,the field function and the approximation value of the first derivative are solved simultaneously,and then the obtained result is used to solve the approximate value of the second derivative.At the same time,the number of unknown elements of the second derivative to be solved is reduced.Compared with the MSPH method,the calculation is reduced.Finally,the paper establishes a two-dimensional numerical wave tank to carry out the numerical simulation of push plate wave-making,and preliminarily verifies the feasibility of the SPH method for simulating solitary waves and linear waves.It provides a reference value for the subsequent use of the SPH method to establish a general high-precision numerical wave-making tank,and to study the complex dynamic behavior of nonlinear waves and irregular waves.