Three-dimensional unsteady incompressible flow computations using multigrid

We apply a robust and computationally efficient multigrid-driven algorithm for the simulation of time-dependent three-dimensional incompressible bluff body wakes at low Reynolds numbers (Re less than or equal to 350). The computational algorithm combines a generalized time-accurate artificial compressibility approach, a finite-volume discretization in space, and an implicit backward discretization in time. The solution is advanced in time by performing iterative ‘pseudo-transient’ steady-state calculations at each time step. The key to the algorithm’s efficiency is a powerful multigrid scheme that is employed to accelerate the rate of convergence of the pseudo-transient iteration. The computational efficiency is improved even further by the application of residual smoothing and local pseudo time-stepping techniques, and by using a point-implicit discretization of the unsteady terms. The solver is implemented on a multiprocessor IBM SP2 computer by using the MPI Standard, and a high parallel scalability is demonstrated. The low Reynolds number regime (Re less than or equal to 500) encompasses flow transitions to unsteadiness and to three-dimensionality and attracts considerable attention as an important step on the road to turbulence. In this regime, the slow asymptotics of the wake provide a challenging test for numerical methods since long integration times are necessary to resolve the flow evolution toward a limiting cycle. Our method is extended to three dimensions and applied for low Reynolds number flows over a circular cylinder (Re less than or equal to 250) and a circular semi-cylinder (Re = 350). The computational results are found to be in close agreement with the available experimental and computational data.