Numerical Analysis Of 2-D Incompressible Laminar Flow Problems Based On EFG Method

Element Free Galerkin(EFG) method is a kind of excellent new numerical algorithm, it needs only the information of nodes, and it can still be calculated in the case of nodes are deformed and even coincidently distributed. Moreover, EFG method is well known for the characteristics of higher precision, faster convergence. So it also has great developmental potential in the field of computational fluid dynamics.Currently, the application of EFG method in fluid mechanics problems is still in the exploratory stage. There are still many problems can’t be well solved in the numerical calculation, such as: the false numerical oscillation of pressure and velocity、the free surface is difficult to track, etc. In this paper, the numerical method of fluid dynamics based on EFG is studied to solve the problems of two-dimensional incompressible and viscous flow. The main contents and conclusions in this paper are introduced as follows:(1) The direct coupling solving method based on EFG method is developed in order to solve Stokes approximation equations(completely neglected the convection term) which are used to describe two-dimensional laminar flow. The influence on the calculative accuracy which is exerted by several related parameters is discussed, and effective range of all the parameters are given respectively. In order to deal with the numerical oscillation when incompressibility condition is loaded in the numerical simulation process, a simple feasible numerical stabilizing program is introduced, which used two sets of nodes to represent pressure and velocity respectively.(2) Using direct derivation to deal with the convection term in Navier-Stokes equations,a stable velocity-pressure EFG formulation is established, which is then solved by the linear iteration method. Numerical experiments show that the velocity-pressure EFG column which needs two sets of nodes possesses the characteristics of high precision and fast convergence. And the solution in this paper does not need to introduce the redundant artificial stabilization parameters when dealing with the higher Reynolds number flow problems, thus avoiding the error of artificial introduction.(3) EFG formulations about explicit Euler method and implicit difference method are derived to solve the unsteady problems which are associated with the time. And the numerical experiments show that the EFG method for solving the incompressible viscous flow problems is feasible.(4) The heat fluid flow problem between the concave wall is well simulated by the program, and the value of velocity、pressure and viscosity of the fluid in the wall are obtained. In addition, the energy equation of fluid mechanics is solved numerically based on the EFG method, and the temperature distribution in the flow field is obtained.In this paper, numerical studies about two-dimensional Stokes flow、Navier- Stokes flow and two-dimensional heat flow problems are performed based on EFG method, EFG method is successfully introduced to the field of computational fluid dynamics, Numerical experiments show that EFG method is an effective high-precision numerical methods for incompressible flow problems.