A Study Of Fluid Simulation Based On SPH

Flow simulation is one of the most important parts of computer simulation.With the development of the hardware the results of computer simulation become more and more realistic.However,how to get a faster and more realistic simulating result is the goal of researchers.Smoothed Particle Hydrodynamics(SPH)is one kind of Lagrangian meshfree methods,and usually used for liquid simulation.Compared to mesh methods,the SPH metnod is simple and easy to implement.The key of this method is the kernel function,which affects the accuracy of the SPH method.However,the SPH method has two shortcoming:(1)it is not accuract enough for treating particles near the boundary;(2)it needs too many particles during the simulation of spectacle scenery and is more time consuming.This thesis does some work for above two problems.One of kernel function's properties is symmetry,but the symmetry can't be satisfied at boundaries because that the support radius of kernel function is truncated by boundaries.It results in low computing accuracy at boundaries.Base on that,this thesis proposes an asymmetrical kernel function applied at boundaries.This kernel function can effectively reduce numerical dissipation at boundaries.The construction of the asymmetrical kernel function in one dimensional space is described in detail,and an example is given to verify its effectiveness.Because the SPH method can't keep enough accuracy at boundaries,serious numerical dissipation occurs at boundaries,which affects the calculating accuracy of particle's density and pressure and leads to incorrect change of the volume of fluid,and then causes unrealistic result.This thesis gives a method to solve the problem aforementioned using the combination of the SPH method and physical collision: the properties of particles far from the boundary will be calculated by the SPH method,and particles near the boundary will be given a static density,and their velocities and positions will be calculated by physical collision.During this process,this thesis proposes a good method to distinguish particles near or far from the boundary;this thesis proposes a method for coupling the two kinds of force from physical collision and SPH,which decreases the errors during the process of coupling,and reduces numerical dissipation.Compar to the simulation results,the method of this thesis gives more accurate values of density and pressure,which makes the volume of fluid get closer to exact value.Surface reconstructing is another time-consuming operation.The traditional method of surface reconstructing is marching cubes,which wastes a lot of time in traversing the area without particles.This thesis proposes a new method of surface reconstruction based on the SPH method.The surface reconstruction is divided into two parts: one is the continuous fluid surface,the other is the spray.The first part is simulated by the improved height field method,using adaptive grids in place of uniform grids,which can reduce the count of triangles.Instead of traditional particles,the second part is simulated by waterdrop-like particles that are constructed by third-order Bézier curve and simulate spray better.The two parts reduce the compution of triangles and the time of computing grid data and rendering,which accelerate simulation process.Besides,compared with traditional methods,only one iteration is applied to compute the support radius of each particle,which smoothes the change of density,and therefore improve the accuracy of pressure with less computation.