EFG Numerical Simulation Of Tow-dimensional N-S Equations And Its Application Research

The feature of high nonlinearity of Navier-Stokes equations(N-S equations) makes it impossible to get an exact solution. Hence, the numerical methods which are used to solve the N-S equations became the hot research spot. At present, the main numerical methods are: the Finite element method(FEM), Finite volume method(FVM), Finite difference method(FDM), etc. But the problems of mesh distortion, calculation of instability, and numerical oscillation, etc. are likely to happen due to the occurrence of gridding of the calculation process of iterative computations causing the limitation on its calculation accuracy and efficiency improvement. Therefore, it is necessary to provide a stable and efficient numerical method to solve the N-S equations. Element-free Galerkin(EFG) method is a new numerical method that requires only nodes information. It can construct higher order field function. This method can get rid of the constraints of the discontinuity problem, and it has the advantage of higher smoothness, etc. In this paper, the split of EFG method is used to solve the N-S equations, and conducts study on engineering application. The main research contents are summarized as follows:(1) The penalty function method is used to deal with pressure items of N-S equations, the discrete matrix of EFG method of the 2-D N-S equation is obtained. Feasibility of the proposed algorithm was put forward by the verification of analysis examples. The influential rules for the number of Gaussian points, the scale parameter, and Reynolds number on the calculation were discussed. Comparison and analysis were made with the result of FEM. The results showed the EFG method has better convergence speed and computational accuracy.(2) In the EFG method, the Lagrange multiplier method(LMM), the penalty function method(PM) and the meshless and coupled finite element method(FEM-EFG) have been utilized to enforce the boundary conditions, and its influence on the results is discussed, and by comparing the EFG results with the FEM result, it shows that the relative error of the result of LMM method and FEM method is minimum, the relative error of the result of PM method and FEM method is maximum. The result of LMM method and FEM-EFG method is approximated. The influence of selection of penalty parameter on calculation accuracy when the PM method has been utilized to enforce the boundary conditions is discussed. The results show that the adjusted the penalty parameter values can effectively improve the simulation accuracy.(3) Concerning the numerical instability problems caused by convective term in the airfoil and projectile flow field. The advantage of EFG method which only needs nodes information is combined with the wind stabilization algorithm, to construct an off-center compact support of calculation point. It was applied to the analog computation for the problems of the NACA0012 airfoil and projectile flow field so as to effectively avoid the phenomenon of numerical oscillation, and improved the calculation accuracy.In this paper, the EFG method and an off-center compact support EFG method are used to solve the problem of 2-D N-S equations, and the results are analyzed. The results show that the EFG method possesses the characteristics of calculation stability, high precision and better convergence greatly, etc. The conclusions have certain theoretical reference and application value for research on the fluid and engineering application.