Development Of Numerical Simulation Program Of Fluid Flow And Heat Transfer Based On The Polygonal Mesh

With the development of the Computational Fluid Dynamics, the study of the flow and heat transfer in abnormity domain is more and more popular. The traditional structured grids have not adapted this development tendency, so, the unstructured grids obtained widespread application. But the computational capability of the triangular meshes, which are widely used, are not good. In this paper, in order to solve this problem, the corresponding polygonal mesh was constructed based on the basic triangular mesh. The conversion from triangular mesh to polygonal mesh can be done by connecting the centroids or the circumcenters of the triangular meshes. In this way, not only can the difficulty of the generation of the non-simplest shape's grid unit be avoided, but also the flexibility of the unstructured grid can be retained. Firstly, two different methods were used to converse the grid unit from triangular mesh to polygonal mesh in this paper. Then the governing equation was discretized by using the edge-based method. And the calculating program was developed according to the complete pressure correction algorithm. Then some classic problems for numerical heat transfer such as lid-driven cavity flow, natural convection flow of square cavity and so on were simulated to testify the program. From the comparative results which were gained by using different grid systems, it was shown that the polygonal mesh converged faster, and the computation precision didn't have obvious variations. The polygonal mesh which was converted by the circumcenter method had higher computation precision than that of the centroid method. But the circumcenter method may cause the situation that the new node is out of the current unit, so its universality was inferior to the centroid method. In the end, the computation precisions of the different discretization schemes were compared by using the polygonal mesh. It was shown that the computation precision would reduce when the interpolation algorithm was used to compute the value of the interface in the dicretization.