Multigrid Acceleration of Time-Accurate Navier-Stokes Calculations

A numerical scheme to solve the unsteady Navier-Stokes equations is described. The scheme is fully implicit in time and is unconditionally stable (at least for first- and second-order discretizations of the physical time derivatives). With unconditional stability, the choice of the time step is based on the physical phenomena to be resolved rather than limited by numerical stability. This is especially important for high Reynolds number viscous flows, where the spatial variation of grid cell size can be as much as six orders of magnitude. A multigrid-multiblock, steady-state, three-dimensional Navier-Stokes solver, TLNS3D, was modified to iteratively invert the equations at each physical time step. The implementation of this procedure in TLNS3D is discussed. The implications of applying several popular turbulence models to unsteady flow are also considered. Numerical results are presented to show the application of the scheme to various two-dimensional turbulent flows. The results of a three-dimensional laminar flow calculation are also given.