Unsteady flow calculations with a multigrid Navier-Stokes method

A multigrid Navier-Stokes method with a two-equation k-u> turbulence model is developed for calculating unsteady flows. The method uses a staggered finite volume scheme to discretize the Navier-Stokes and the turbulence model equations in space. A fully implicit time-accurate scheme is reformulated so that an efficient explicit multistage method with local time stepping, residual smoothing, and multigrid can be used to accelerate convergence within each unsteady time step. The method combines the advantages of implicit and explicit schemes for unsteady flow calculations. Solutions for the forced oscillation of an airfoil are obtained with the Euler and the Navier-Stokes equations. Results are compared with experimental data.