Preconditioned Multigrid Methods for Unsteady Incompressible Flows

Abstract

A highly efficient numerical approach based on multigrid and preconditioning methods is developed for modeling 3D steady and time-dependent incompressible flows. Thek-ω turbulence model is used to estimate the effects of turbulence. The model equations are solved together with the N-S equations in a strongly coupled way, and acceleration techniques like the multigrid method are also used for the turbulence model equations. For unsteady problems, a dual-time stepping procedure is adopted to satisfy the divergence-free constraint and to obtain a time-accurate solution. To improve the performance of this approach for small physical time steps, a modification to residual smoothing parameters is proposed. The numerical algorithm and the turbulence model are validated first by calculating unsteady inviscid flow around an oscillating cylinder, unsteady laminar flow past a circular cylinder, and steady high-Reynolds number turbulent flow over a 6:1, prolate spheroid. Then the three-dimensional time-dependent turbulent flow over a spheroid when it is undergoing a pitch-up maneuver is calculated and compared with experimental data.