A new finite volume difference method for solving 2-D diffusion equation isconstructcd in this paper. The choice of computational nodes is studied on thegross distortion concave quadrilateral grid. We choose the midpoint of a diagonalline of the mesh cells as the calculation nodes because it can assure the cells con-tain the calculation nodes and reduce the total calculation. In order to keep theconservation, we use the conditions of flux conservation to compute the values ofthe central of the boundary. Lagrange multiplier method is used to get the valuesof grid points. With the consideration of the relative position of the grid points,the method is more suitable for nonorthogonal grids. We make experiments onconcave grids and "Z" grids. The numerical results show that the new arithmeticis feasible and effective, especially for highly distortional meshes.
Based on the second-order compact upwind scheme, a group explicit method for solving the two-dimensional time-independent convection-dominated diffusion problem is developed. The stability of the group explicit method is proven strictly. The method has second-order accuracy and good stability. This explicit scheme can be used to solve all Reynolds number convection-dominated diffusion problems. A numerical test using a parallel computer shows high efficiency. The numerical results conform closely to the analytic solution.
