A highly efficient numerical approach based on multigrid and preconditioning methods is developed for modeling 3-D steady and time-dependent incompressible flows. The k-omega turbulence model is used to estimate the effects of turbulence. The model equations are solved together with the Navier-Stokes equations in a strongly coupled way, and acceleration techniques like multigrid methods 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 time-accurate solutions. To improve the performance of this approach for a small physical time step, a modification to residual smoothing parameters is proposed. After the validation of the numerical algorithm and the turbulence model 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, a three-dimensional time-dependent turbulent flow over a spheroid when it is undergoing a pitch-up maneuver is calculated and compared with experimental data.
AbstractA highly efficient numerical approach based on multigrid and preconditioning methods is developed for modeling 3-D steady and time-dependent incompressible flows. The k-u 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 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 timeaccurate solution. To improve the performance of this approach for small physical time step, a modification to residual smoothing parameters is proposed.After the validation of the numerical algorithm and the turbulence model 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, a three dimensional timedependent turbulent flow over a spheroid when it is undergoing a pitch-up maneuver is calculated and compared with experimental data.