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 coordinate systems, previously developed by the present authors, has been significantly enhanced by accelerating the Poisson solver with multigrid (MG) procedures. The most CPU time-consuming part of fractional-step methods is the solution of a discrete Poisson-like equation with Neumann-type boundary conditions formulated to satisfy the continuity equation. Usually, more than 80% of the total computational time of FS methods is consumed by the iterative solution of the Poisson equation. In the present study, multigrid techniques have been employed for accelerating the convergence rate of the Poisson solver in nonorthogonal coordinate systems. Various MG strategies have been tested in numerous numerical experiments. The total computational time required for solving the Poisson equation was reduced by an order of magnitude, whereas the overall computational time of the flow solver was reduced by a factor of 3-4. The MG Poisson solver consumes less than 25% of the total CPU time. The computational work has been found to be of order O(N), where N is the total number of mesh points, whereas the CPU time on a vector computer (CRAY Y-MP) is of O(N0.75). Consequently, the present method is a viable alternative for solving complex flowfields with a very large number of mesh points.