Simulation of incompressible flow with alternate pressure Dirichlet and Neumann conditions

The convergence rate of a methodology for solving incompressible flow in general curvilinear co-ordinates is analyzed. Double-staggered grids (DSG), each defined by the same boundaries of the physical domain are used for discretization. The use of the extended semi-implicit method for pressure linked equations (SIMPLE), in combination with domain discretization by means of the marker and cell (MAC) mesh enables the computation of the first grid pressure without requiring the explicit specification of boundary conditions (Neumann boundary conditions). Calculation algorithm at the second grid includes the approximation of Dirichlet pressure boundary conditions which were obtained from the differential form of the first grid momentum equation. Calculation process on the DSG comprises sequences of alternate pressure Dirichlet and Neumann boundary conditions and calculated domains (first grid, second grid); these switches, lead to a higher convergence rate with the DSG. The convergence rate was demonstrated with the calculation of natural convection heat transfer in concentric horizontal cylindrical annuli. Calculation times when DSG are used 6–10 times shorter those achieved by interpolation. With the DSG method calculation time slightly increases with increasing non-orthogonally of the grids whereas an interpolation method calls for very small iteration parameters that lead to unrealistic calculation time.