Adaptive SPH Method Based On The Weighted Average Of Neighbor Particle Density

In the field of graphics fluid simulation,the SPH method has gradually become the mainstream method for simulating fluids.The basic idea of the SPH method is to discretize the fluid computing space into particles,analyze the force of each particle by means of kernel function estimation,and move the particles under the action of the force to form a flowing liquid.Among them,the size of the smooth length is very important and determines the accuracy of the kernel estimation to a large extent.If the smoothing length is too small,there are not enough particles in the support domain,and the kernel estimation will bring many errors,which will seriously reduce the calculation accuracy.If the smoothing length is too large,there are too many particles in the support domain,which weakens the specificity between particles,causes numerical dissipation,and also reduces the calculation accuracy.In graphic fluid simulation,the method of fixed smooth length is usually used,which will cause low accuracy of kernel estimation in some areas of the fluid.For example,at the surface of the fluid and where the water splashes,the use of a fixed smooth length will cause too few particles in the support domain,thereby reducing the accuracy of the calculation.To this end,this paper proposes an adaptive SPH method for smooth length,which assigns a unique smooth length to each particle,and each particle dynamically adjusts the smooth length according to the density of its surrounding particles.The main research work of this paper is as follows:(1)Research the relationship between smooth length and density,and design an adaptive SPH algorithm for smooth length.Through research,it is found that the change rule of the smooth length of a particle has a corresponding relationship with the weighted average density of the surrounding particles.If the weighted average density of the surrounding particles is larger,it means that the surrounding particles are denser,and the smaller smooth length can be calculated by formula.On the contrary,a larger smooth length can be obtained by formula calculation.(2)In order to solve the problem of asymmetry of neighbor particles and improve the efficiency of neighbor search,a set of neighbor search schemes based on adaptive smooth length is designed.First of all,the use of adaptive smoothing length algorithm will cause the neighbor particles to be asymmetric.For this reason,this paper designs a new neighbor particle judgment standard to solve this problem.Secondly,in order to improve the efficiency of neighbor search,this paper proposes a neighbor search algorithm based on the maximum smooth length,which can better realize high-performance computing.(3)In order to solve the problem of asymmetry of force,a symmetric kernel function algorithm is designed.After adopting the adaptive smoothing length algorithm,the phenomenon of asymmetric force on the particles will appear.Therefore,the symmetric kernel function algorithm is designed in this paper,which can be conveniently applied to various force equations,and at the same time,it satisfies Newton's third law and improves the simulation reality.(4)Through programming,the adaptive SPH method in this paper is successfully implemented,and the effectiveness of the algorithm is verified through experiments.Firstly,through C++ programming and continuously optimizing the algorithm,the adaptive SPH method of this article is successfully realized.The experimental results show that the method in this paper is feasible,and the smooth length of each particle can be adjusted adaptively.At the same time,the adaptive method can effectively improve the uniformity of neighbor particles,obtain a uniform density field,and improve the accuracy of calculation.Compared with the commonly used fixed smooth length algorithm,the adaptive SPH method has a better improvement in simulation quality.In addition,it has higher simulation stability and a further improvement in calculation efficiency.