On Precision,Efficiency,and Stability Of The Smoothed Particle Hydrodynamics Algorithm

Smooth particle hydrodynamics(SPH)was originally invented to solve astrophysical phenomena,and then was applied to high-energy nuclear physics and other aspects.Numerical simulation based on SPH algorithm can give a reasonable description of various experimental observation results.The Smooth particle hydrodynamics is a mash-free and Lagrangian method for solving particle differential equations.It’s different form traditional methods such as the finite difference method(FDM)and the finite element method,The SPH approximates a partial differential equation in terms of ordinary differential equations of freely moving interpolation points,known as SPH particles.Subsequently,the original system with infinite degrees of freedom is represented by a finite number of SPH particles,in order to describe any arbitrary configuration of the continuum medium.The SPH has been modified many times since its invention.For example,correct smoothing particle method(CSPM),Finite particle method(FPM)and so on.These methods more or less improve some problems that are difficult to solve in traditional,such as the numerical results instability problem or boundary particle processing problem in the SPH method.until now,there have been no articles comparing these methods or exploring their optimality.Therefore,this paper mainly studies the stability,accuracy and efficiency of different methods in smooth particle hydrodynamics,and we will discuss the influence of various aspects of these algorithms(such as particle motion form,boundary conditions,etc.)on the results.According to the fluid motion equation(burger equation),the calculation is carried out in two different situations,where the particles are either stationary or dynamically evolving over time.1.The results show that CSPM and SFPM have better efficiency.2.A difference value method,namely symmetric finite particle generator SFPM,is proposed.The main advantage of this method is that its implementation does not involve any derivatives of the kernel function,which improves the numerical result deviation caused by the derivative of the kernel function.3.Different boundary treatment methods are used to improve the boundary instability,and the mirror particle boundary method has the most obvious improvement on the boundary instability.4.The boundary problem at x=1 is studied in detail,and it is found that instability can be observed when particles cross each other.