Analysis Of Incompressible Flow Problems At Low Reynolds Numbers By Three-dimensional EFG Method

At present,all kinds of numerical methods are applied to solve the nonlinear partial differential equations in fluid mechanics.It is difficult for solution and application that numerical methods based on element need to use elements to discrete the computational domain when solving the problems of fluid mechanics.As a numerical method that has great study and application value,Element-free Galerkin(EFG)method is based on the approximation of discrete nodes and doesn't need the information of elements.It is not only easy to deal with the complex boundary,but also can calculate accurately,therefore many researchers applied EFG method to solve the fluid mechanics problems.In recent years,the application of EFG method in the field of fluid mechanics is still in the developmental stage,and the EFG method is mainly applied to solve two-dimensional fluid field problems,however,many actual flow problems usually can't be analyzed by simplifying to two-dimensional fluid field problems.Thus this paper presented here studies the flow of three-dimensional incompressible viscous fluid at low Reynolds numbers based on the theories of EFG method and computational fluid dynamics,and numerical studies the flow by writing computational programs.The main research contents and conclusions for the present study are listed as follows:(1)The discrete control equations of three-dimensional Stokes flow based on the EFG method was deduced,and the computational programs on the basis of the derived discrete equations and the theory of EFG method are complied,then the three-dimensional Stokes equations with exact solutions were solved,the programs and the algorithms proved to be effective and reliable.We applied EFG method to solve the three-dimensional cavity Stokes flow problem,focused on the effects of different speed ratio and height to width ratio on the flow.The numerical results show that with the increase of speed ratio S value,the form of internal flow was divided into five different stages at four critical values.In addition,the process of the interior vortex expanding also experienced from one vortex becomes two,and then only one vortex,and finally become multiple vortices as the height to width ratio A value changes.(2)Considering the effect of inertia item,the discrete formulation of three-dimensional steady Navier-Stokes(it is called for short N-S)equation based on the EFG method was deduced.The characteristics of flow in 180-degree circular cross-section bend pipe are studied numerically by writing the computational programs,mainly analyzed the effects of curvature and Re number on flow field and vortex generation.Results indicate that under the same curvature-diameter ratio,the value of the inlet Reynolds number affects the structure and strength of the Dean vortex in bend pipe.Under the same Reynolds number,the position of Lyne vortex is close to the frontier of the bending section in small curvature-diameter ratio of bend pipe and the back of the bending section in large curvature-diameter ratio of bend pipe.Moreover,the curvature-diameter ratio of bend pipe has a more obvious effect on the distributions of velocity and pressure in the bend pipe.(3)Considering the flow situation related to time,the discrete of the time item was obtained by the ? weighted method,the discrete formulation of three-dimensional unsteady N-S equation based on the EFG method was deduced,the flow around of side-by-side circular cylinders at low Reynolds numbers was analyzed by writing solving program.The results show that the flow of side-by-side circular cylinders obviously appears three-dimensional characteristic,the form of wake flow is different in side-by-side circular cylinders under the different Reynolds number.In this paper,the EFG method was used to simulate the three-dimensional steady Stokes flow,the steady flow of curved pipe considering the inertia item and the unsteady flow of side-by-side circular cylinders considering the time item.The computation results reflect the situation of the three-dimensional flow field accurately and provide some effective guidance for engineering application.