Abstract
In this paper we describe a second-order projection method for the time-dependent, incompressible Navier-Stokes equations. The method is a second-order fractional step scheme in which one first solves diffusion-convection equations to determine intermediate velocities which are then projected onto the space of divergence-free vector fields. The diffusion-convection step uses a specialized second-order Godunov method for differencing the nonlinear convective terms that is conservative and free-stream preserving and provides a robust treatment of the nonlinearities at high Reynolds number. The projection is based on cell-centered centered difference approximations to divergence and gradient operators with the resulting linear system solved using a multigrid relaxation scheme. We apply the method to vortex spindown in a box to validate the numerical convergence of the method and to measure its overall performance. 13 refs., 2 figs.
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