over an obstacle is the production of lee waves, which can persist for long distances downstream, making the use of A robust multigrid method for the incompressible Navier-Stokes equations is presented and applied to the computation of viscous stretched grids unavoidable. When lee wave amplitudes flow over obstacles in a bounded domain under conditions of neuare large, wave-breaking can occur, and under these cirtral stability and stable density stratification. Two obstacle shapes cumstances streamline reversal leads to a local region of have been used, namely a vertical barrier, for which the grid is statically unstable flow where mixing occurs. Adequate Cartesian, and a smooth cosine-shaped obstacle, for which a boundmodeling of such processes, as well as lee-side separation, ary-conforming transformation is incorporated. Results are given for laminar flows at low Reynolds numbers and turbulent flows at requires the use of viscous equations with, preferably, a a high Reynolds number, when a simple mixing length turbulence high Reynolds number and the use of a turbulence model. model is included. The multigrid algorithm is used to compute When lee waves are present, wave propagation (upstream steady flows for each obstacle at low and high Reynolds numbers as well as downstream) means that time dependence should in conditions of weak static stability, defined by K ฯญ ND/ศU ี
ี
1, where U, N, and D are the upstream velocity, bouyancy frequency, also be included. The range of phenomena is thus wide in and domain height respectively. Results are also presented for the two dimensions, and even wider in three, with additional vertical barrier at low and high Reynolds number in conditions of questions concerning the passage of fluid over or around strong static stability, K ฯพ 1, when lee wave motions ensure that isolated obstacles. Such flows present a challenge to the the flow is unsteady, and the multigrid algorithm is used to compute techniques of computational fluid dynamics, and computthe flow at each timestep. แฎ 1997 Academic Press ing times for single grid solution algorithms for the incompressible Navier-Stokes equations are exceedingly long,