The Research Of Euler Equations' Solution Using Cartesian Grid And Multi-grid Methods And It's Applications

To simulate complex flow field more accurately ,a method for 2-d of an cartesian mesh is presented for the solution of the steady Euler equations .And the multigrid is used to accelerate the convergence. Firstly ,a new method for cartesian mesh Generation is developed. The background grid is used to provide the information for refining the Cartesian mesh.By quantitative comparison between mesh scale and calculated parameters,the mesh is decided whether to refine or not.Then every effective edges of cells is numbered for the subsequent algorithm based on edge. Secondly,2-d Euler equations based on Cartesian mesh are solved using the cell-centred Jameson's finite volume spatial discretization and four-stage Runge-Kutta time-stepping scheme.At the same time,local time step and residual smoothing are introduced to accelerate the convergence. Lastly ,to speed up the convergence,the multigrid method is presented.Based on space-filling curves,the agglomeration method is used in the solution on the cartesian grids. The solution of coarse grids is driven by the fine grids' residue,and the solution on the coarse grids is used to correct the solution on the fine grids,which can eliminate all parts of frequency errors on the fine grids. A series of numerical studies have been made with the method mentioned above.The results demonstrate that the method can simulate 2-d complex flow field satisfactorily.