Shock Wave Simulation Based On Meshless Particle Method

With the development of science,the research and application of fluid dynamics has become a hot spot of concern.In fluid mechanics,the shock tube problem is one of the classic problems.It is abstracted from many kinds of gas shocks in real life.The main physical conditions including gas shock in the pipeline,explosion in the cylinder and explosion in the open space.In the past few decades,various numerical calculation methods have been applied to this problem.The modified smooth particle method(CSPM)has been considered to be incapable of solving the shock tube problem.In response to this statement,this paper will mainly explore the reasons why the CSPM method can not be used to solve the shock tube problem,and how to solve it.And prove the superiority of the CSPM method itself.At the same time,due to the energy conversion and the overheating effect in the shock tube problem,the shock wave will have a serious numerical oscillation at the contact discontinuity surface,so it is particularly important to explore how to effectively eliminate the oscillation at the contact discontinuity,so as to improve the accuracy of the numerical results.In order to study and solve the problems in the numerical simulation of shock tube,the mathematical model of the shock tube problem is firstly introduced in this paper.Then the CSPM and SPH methods are described in detail,and the mathematical model is discretized by using these two methods to obtain the semi-discrete form of the governing equation.At the same time,in order to obtain better results,variable smooth length and boundary processing techniques were used in the experiment.In this paper,density summation and discrete continuity equation are respectively used to calculate the fluid density,and the modified values of these two formats are compared and analyzed,so as to explore the feasibility of CSPM method to solve the shock tube problem.Then the advantages of the CSPM scheme are studied by using the two-dimensional shock wave problem solved by the CSPM and MPM schemes and the blast wave problem solved by the CSPM and SPH schemes.Finally,in view of the shock phenomenon of shock wave at the contact discontinuity,two different artificial viscosity schemes are introduced in the paper,and an adaptive heat term is added to the energy equation to study how to effectively eliminate the oscillation phenomenon.Through the analysis of the experimental results,it is found that whether CSPM can be used to solve the shock tube problem depends on how to select the density solution format,and it is proved that CSPM method has certain accuracy advantages over SPH and MPM method in solving shock wave problems.Finally,experiments show that the numerical oscillation at the contact discontinuity can be effectively eliminated by introducing artificial viscosity and artificial heat into the control equation.