A parallel algorithm is developed for the two-dimensional time-dependent convective dominant-diffusion problem. An explicit alternating direction (EAD) method, which is based on the second-order compact upwind finite difference scheme, is studied. The algorithm is tested on a linear and a nonlinear differential equation using a parallel computer. Some numerical results show that the method has high accuracy and is ideally suitable for massively parallel computers.
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.
