The Research Of N-S Equations' Solution Using Hybrid Grids And Multi-grid Methods And It's Applications

The present thesis deals with the solutions of N-S equations on hybrid grids. It includes three parts: the grid generation, the numerical scheme and the acceleration techniques. Hybrid grids are adopted: structured or semi-structured grids near the wall and unstructured grids in the other field. A finite volume hybrid solver which is based on Jamson's Finite-Volume scheme is developed, and it can be used by arbitrary grids. The agglomeration multigrid method is used. The agglomeration method is different in different fields in the turbulence flow simulation. Extensive numerical studies have been performed in order to access the accuracy of the present approach. All of results demonstrate the capability of simulating complex flow fields efficiently and robustly.The hybrid grids include two parts: structured or semi-structured grids near the wall and unstructured grids in the other field. The magnified methods and the layer advancing methods are adapted for generating the grids near the wall, while the advancing front methods and Delaunay methods are adapted for generating the grids in the other fields. Joining the grids near the wall and in the other fields into hybrid grids is the final step for generating hybrid grids. One of the hybrid grids' advantages is easy to control the number of mesh layers and can decrease the number of grids, which make the numerical process require less computer resources and reduce the computation time. So the hybrid grids are involved in improving the computation efficiency.A finite volume hybrid solver which is based on Jamson's scheme is developed. The flow algorithm solves the time-depended integral form of the equations by means of a cell-centred, symmetric finite volume spatial discretisation. The integration in time, to a steady-state solution, is performed using an explicit multi-stage procedure. The algorithm works in terms of cell faces, rather than the cells themselves, and the cells can be polygons of an arbitrary number of faces. Numerical modeling of flows by solution of Reynolds averaged Navier-stokes equations with Baldwin-Lomax algebraic turbulence model is presented as well. A turbulence reference grid is used to supply the necessary length scale for each cell.The multigrid method is presented to speed up the convergence. The agglomeration method is used in the solution on the unstructured grids. The coarse grids are obtained by agglomerating the fine 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 eliminated all parts of frequency errors on the fine grids. In order to obtain more efficiency, the agglomeration method is different in different fields, especially for the solution of N-S equations.Extensive numerical studies have been performed in order to access the accuracy of the present approach, for example, the supersonic flow over the shuttle, and so on. Allof results demonstrate the capability of simulating complex flow fields efficiently and robustly.