Research And Application Of SPH-ALE Method Based On Riemann-Solver In Free Surface Flow

Free surface flow problem exist widely in nature and practical engineering applications,it has been a hot topic in hydrodynamics research for many years.The grid-based numerical methods applied in the problem with large deformation will encounter mesh distortion technology difficulties.Smoothed particle hydrodynamics(SPH)is a meshless Lagrangian method,it has aroused widespread attention in academic circle since 1977.This method is not constrained by the grid,particularly suitable for dealing with the problem involving highly impact and large deformation.However,with deepening of SPH research,many inherent problems discovered by scholars,such as non-physical pressure oscillation、kernel truncated by boundary、tensile instability and so on,these issues has seriously hindered SPH apply in parctical engineering.In order to expand the scope of application of SPH,many optimize methods has been invented,the SPH-ALE method based on Riemann-Solver is one of them.The basic theory of traditional SPH and some related numerical methods has been study deeply,including kernel approximation 、 artificial compressibility 、 artificial viscosity 、boundary treament、nearest neighboring particle search、time integration,and thus developed two-dimensional calculation code.A classica model “dam-break” is simulated,comparison and analyzation of each parameters’ effect on the calculation result is done.Two classical models Lennard-Jones and normal repulsive model are used to simulate the two-dimensional dam break,and a correction term is added to the normal repulsive model to prevent singularity occur in the calculation causing compute crash,the result show that normal repulsive model gives a lower diturbance to the fluid particles near boundary,which is more suitable for SPH calculation.On the basis of previous work,SPH-ALE method has been deeply studied.The physical quantity of each particles in this method does not directly take into the governing equation,but at first use the MUSCL algorithm with high order accuracy for variable reconstruction,and then input into HLLC Riemann Solver to get Riemann approximation variable,finally take into the governing equation to calculate.Through a number of numerical examples,confirmed that the SPH-ALE method compared to the traditional SPH method has higher numerical stability,the oscillation of pressure field can be effectively suppressed.First-order kernel correction method was presented,which was used to estimate the pressure of boundary particles.Dam break water impact on the vertical wall has been simulated in order to verify the feasibility and accuracy of this method,meanwhile clearly the MUSCL algorithm slope-limiter factor effect during the simulation processing.A two-dimensional numerical wave tank based on SPH-ALE is estabished,in the process of study found that “Predictor-Corrector” time stepping method is not suitable for SPH-ALE,when after a long time of calculation,a “low-pressure penetration” numerical phenomenon will be occurred,and then cause calculation crash,while the “Symplectic” time stepping method is a better choice.In order to verify the validation of SPH-ALE,which was applied to several piston wave making problems: weak nonlinear regular wave propagates、solitary wave generation and breaking on the slope,the numerical results show that SPH-ALE can achieve higher precision in wave making problem,and the wave height loss in the process of propagation is very limited.The problem of wave height loss in the traditional SPH has been studied,the result shows that “tensile instability” is the main reason of pressure oscillation and wave height loss,the use of artificial stress correction can effectively improve it.In addition,when using the Quadratic smoothing kernel in the treatment of wave making problem,will appear the obvious wave height loss phenomenon,and the Cubic smoothing kernel is a better choice.The numerical model of fluid、floating body interaction numerical model based on SPH-ALE is established.A boundary treatment of normal repulsive model combined with kernel correction were presented,which can prevent particles from peneration during the simulation,and the boundary pressure value was obtained by integrating the pressure of water particles within the kernel radius influence.By simulating uniform and non uniform box floating cases,initially to verify the feasibility and accuracy of this method.Then a two-dimensional wedge entry water was simulated,the pressure on wedge boundary at initial impact phase 、 free surface deformation during whole water entry and the cavitation development were both given respectively,and compared with the analytical solution and experimental data.Finally,by using this model for green water on deck,gives a tentative study.All of these results show that SPH-ALE method is suitable for dealing with this kind of problems.But,in order to obtain accurate free surface pattern,need to adopt a more precise computational domain divided,at this time a huge number of patricles will cause the efficiency of calculation fallen sharply.