The Applied Research Of Element-free Galerkin Method In Flow Field Analysis

As a main branch of the family of meshless methods, Element-Free Galerkinmethod is deeply developed because of its better precision and faster convergence.while, EFG method is usually used in solid mechanics area more than computationalfluid dynamics, so this article is focus on the use of EFG method on the solve of flowfield. The main work are summarized as follows:1. EFG method is extended to solve two-dimensional potential flow problems.Results of different boundary conditions in rectangular computation domain which aresolved by EFG method are obtained, so do the solve programs, and the results arecompared with those obtained by other numerical methods. The results show that EFGmethod is more accurate and has a fast convergence than finite difference method; tocompared with the PDE tool solution, EFG solution has a better answer away from theboundary while which is not satisfactory near the boundary.2. To deal with the oscillation phenomena which was introduced by solve theconvection dominate question in standard EFG method, here improve the traditionalmethod by use the ideal of upwind of FD method and stabilization of FE method.Results show that the upwind method can deal with the oscillation which is occurredby high Reynolds number well, but it brings other error in diffusion dominate; thestabilization method can do well in both diffusion and convection. Meanwhile, theimproved method can solve the convection diffusion equation which contains anonlinear term as well.3. According the question of hard to confirm the layout of Gauss points intwo-dimensional complex flow field, finite element grid is put forward to instead ofthe traditional integral grid. Three examples are given to test the difference betweenthe new grid and the old one. The results confirm that the improved method is notonly reduce the calculation time and progress but also do no effort on the calculationaccuracy for the complex flow field, moreover, the new method can also improve theaccuracy of solution near the boundary.