Research On The Mold Filling Simulation With The Stream Function-Vorticity Method

Foundry simulation is an important tool of optimizing the technics of foundry. Mold filling simulation is an important part of foundry simulation. Contemporary, there are two arithmetics used in foundry filling simulation: the prototype method and the stream function-vorticity method. Most researchs adopt the prototype method. In the method the velocity and the pressure are the variables. There are few research adopts the stream function-vorticity method. In the method the stream function and the vorticity are the variables, the pressure is connotative variable, conservation of mass is satisfied automatically, and it needn't revise the velocity and the pressure, uses one suit of gridding. The stream function-vorticity method conquers the disadvantage of the prototype method which must use interlaced gridding. It debases the possibility of radiation in the simulation, it's astringency is better, calculates faster. Therefore it is a significative job to research foundry flowing simulation which adopts the stream function-vorticity method.Conventional iterative arithmetic of elliptoid equation usually be used in flowing simulation, it's astringency is bad, and it has long runtime. These disadvantages restrict the application of computational fluid dynamics, the reformative methods are using different iterative methods. Conventional iterative arithmetic such as Jacobi and Gauss-Seidel, even SOR or Conjugate Grads Method aren't satisfied. Multigrid method has already been approved a classic numerical method to elliptoid equation, the task of calculation is smaller and astringency is better. Accordingly Multigrid method is widely used in various subjects and technical problems, especially computational fluid dynamics.Base on background above, researching simple and convenient arithmetics, developing new program to simulate foundry flowing is a significative job. Therefore the stream function-vorticity method and Multigrid method are researched in this paper, and programs used in flowing simulation are developed. Firstly, in this paper equations used in flowing simulation are researched, according to the concept of the stream function and the vorticity, constitutes the equation of the stream function-vorticity method, studies the boundary conditions of the stream function and the vorticity. Then meshes grids with finite difference method and solves the equation, develops program to simulate flowing area which have inlet and export.Secondly, the theory and calculation steps of multigrid method have been researched. FAS scheme and V circulation also have been studied.At last, solve the stream function with Two-Grid Algorithm. Program of simulating driving cavity flow have been developed.