Research On The Pseudo Compressibility Method-Flux Vector Splitting(PCM-FVS) For Solution Of Incompressible Flow

In fluid mechanics,the problem of incompressible flow occupies a large proportion,and it is of great significance to study these problems.In computational fluid dynamics,many numerical algorithms for incompressible flows have been developed,each with its own advantages and disadvantages.In this paper,the virtual compression method and the vector flux splitting method are combined to form a new method.The virtual compression method is used to solve the coupling problem of pressure and velocity in the incompressible flow,and the vector flux splitting method is used to deal with the convection term.The new method is applied to the numerical calculation of incompressible flow,and the feasibility of the method is verified.Firstly,the theoretical formulas of the virtual compression-vector flux splitting method in two dimensional generalized coordinate system and three dimensional generalized coordinate system are derived in detail.The virtual compression method and Steger-Warming vector flux splitting method are introduced in detail.Based on the Navier-Stox equation of incompressible flow,a virtual compression method is introduced to solve the coupling problem of pressure and velocity in incompressible flow.The vector flux splitting method is used for the convection term and the central difference is used for the viscous term.The theoretical basis of the virtual compression-vector flux splitting method is formed.Then a CFD program for calculating incompressible flow is designed and developed according to the theoretical formula of virtual compression-vector flux splitting method.Several parts of the program,including computational grid generation,convection term discretization,viscous term discretization and time advance,are introduced.In the program,matrix is used to organize the data,and the flow parameters on the grid points of the flow field are put into the matrix for calculation,which greatly saves the calculation time,and the setting of boundary conditions is also very convenient.Finally,three classical examples of incompressible flow are numerically calculated by using the program to verify the feasibility of the proposed method and the correctness of the program.In the two-dimensional driving square cavity,four sets of grids are divided and densified for calculation,and the results show that the calculation accuracy of encrypted grids is higher.When different time steps are set for calculation,there is no difference in the calculation results under the case of convergence,which shows that this method is insensitive to time step.Different difference templates are used for the convection term,and the result is that the calculation accuracy gradually increases with the increase of template points in the difference template.By changing the value of the virtual compressibility coefficient,the result is that the calculation accuracy increases with the increase of the value.The flow conditions of the square cavity at different Reynolds numbers are calculated,and the results are in good agreement with those in the literature.In the example of laminar boundary layer,the influence of mesh partition on the calculation results was investigated.Compared with the standard values,the calculated results meet the requirements.It is also found that the convergence rate of this method is a little slower.In the example of two-dimensional Poiseuille flow,the results of the program are compared with the analytical solution,and the accuracy is satisfactory.Three examples are given to prove the feasibility of the proposed method,which can be used to calculate incompressible flow effectively.