Study Of Fluid Stress Instability,Surface Tension And Boundary Treatment Based On SPH Method

Fluid simulation,as an important branch of computer graphics,is widely used in many fields such as special effects of film and television,military simulation,animation and medicine.The Smooth Particle Hydrodynamics(SPH)model is one of the main models for fluid simulation,especially for liquid simulation.In SPH mode,the study of the fluid simulation stress instability,liquid surface tension and solid boundary treatment is an important subject in fluid simulation research.It is of great practical application value to study the above problems.In this thesis,we first introduce the historical background and significance of fluid simulation stress instability,liquid surface tension and solid boundary treatment research,as well as the history and present situation of related research at home and abroad.Then the following three areas of work have been done:In view of the problem of stress instability in fluid simulation,the causes of the problem are studied,the existing research results are analyzed carefully,and an improved kernel function is proposed,which can not only solve the instability of compressive stress,but also improve the computational efficiency.However,the instability of compressive stress and tensile stress can not be improved simultaneously by the improved kernel function.Therefore,the discrete form of momentum equation is improved,and the instability of tensile stress is effectively improved.By combining the improved kernel function with the discrete form of the modified momentum equation,a method is proposed to improve the instability of compressive stress and tensile stress at the same time.There are two main methods to simulate surface tension,one is continuous surface force(CSF)method,the other is interparticle interaction force(IIF)method.The traditional CSF method applies the force to the SPH particles in an asymmetric form,which causes the momentum of the fluid to be no longer conserved and the effect of the liquid surface can not be simulated stably and accurately.When simulating the liquid surface tension,the traditional IIF surface tension treatment algorithm can not minimize the surface curvature,resulting in the liquid surface is not smooth enough.Therefore,according to the physical properties of fluid surface tension,an intermolecular force model which accords with the physical law is constructed.Combining with the modified momentum equation introduced above,the method effectively overcomes the numerical instability in the simulation of liquid surface tension.Compared with the traditional CSF method and IFF method,the liquid surface simulated by this method is smoother and more realistic,and the distribution between particles is more uniform and the calculation is more stable.Solid-wall boundary treatment is always the focus and difficulty in fluid simulation.The common methods of solid-wall boundary treatment are boundary force method and virtual particle method.The boundary force method can prevent the fluid particles from penetrating the boundary by applying force on the fluid particles near the boundary,but there are many parameters of the boundary force model,the force size is difficult to adjust,and the boundary truncation error will occur in the calculation process.Virtual particle method solves the problem of boundary truncation error by generating virtual particles outside the boundary.However,when dealing with the complex boundary,the generation of the virtual particles outside the boundary is difficult,and the distribution of the virtual particles is uneven,the calculation accuracy is affected,and the particle dispersion occurs.In order to solve the problems of the two methods mentioned above,this thesis proposes a velocity correction based solid boundary processing method,which does not need to solve the boundary force or generate virtual particles outside the boundary.The rebound velocity of the fluid particles after touching the boundary is calculated directly by using momentum equation and calculated velocity consumption,which greatly reduces the complexity of dealing with the boundary.It also overcomes the problem that the boundary force method and the virtual particle method lead to the instability of the algorithm caused by the uneven sampling of particles at the corner of the boundary.Simulation results show that the proposed method is better than the traditional methods in stability and computational efficiency.With the increase of particle number,the time-consuming growth of the proposed method is slower than that of the above two methods,and the advantages of high computational efficiency are more obvious,so the proposed method is more suitable for simulating complex boundary processing.