MULTIGRID ACCELERATION OF A FRACTIONAL-STEP SOLVER IN GENERALIZED CURVILINEAR COORDINATE SYSTEMS

A fractional-step (FS) solver of the three-dimensional time-dependent incompressible Navier-Stokes equations in generalized curvilinear coor dinate systems, previously developed by the present authors, has been significantly enhanced by accelerating the Poisson solver with multigr id (MG) procedures. The most CPU time-consuming part of fractional-ste p methods is the solution of a discrete Poisson-like equation with Neu mann-type boundary conditions formulated to satisfy the continuity equ ation. Usually, more than 80% of the total computational time of FS me thods is consumed by the iterative solution of the Poisson equation. I n the present study, multigrid techniques have been employed for accel erating the convergence rate of the Poisson solver in nonorthogonal co ordinate systems. Various MG strategies have been tested in numerous n umerical experiments. The total computational time required for solvin g the Poisson equation was reduced by an order of magnitude, whereas t he overall computational time of the flow solver was reduced by a fact or of 3-4. The MG Poisson solver consumes less than 25% of the total C PU time. The computational work has been found to be of order O(N), wh ere N is the total number of mesh points, whereas the CPU time on a ve ctor computer (CRAY Y-MP) is of O(N0.75). Consequently, the present me thod is a viable alternative for solving complex flowfields with a ver y large number of mesh points.