Numerical solution of the Navier-Stokes equations for three-dimensional incompressible flows with open boundaries

Numerical modeling of the transient, nonisothermal, three-dimensional, incompressible Navier-Stokes equations imposes extreme demands on computational resources. For incompressible flow the Navier-Stokes equations form a coupled parabolic-elliptic set, with the elliptic nature caused by the incompressibility constraint. The elliptic nature of the incompressibility constraint forces some portion of the solution algorithm to be implicit, with the attendant computational costs. In addition, in regions of the computational domain where advective effects overwhelm viscous effects, the Navier-Stokes equations exhibit behavior which is similar to the hyperbolic nature of the Euler (inviscid) equations. In such regions many numerical methods which are suitable for parabolic equations will be dispersive, causing oscillations to appear in the solution. If accurate long-time solutions are required, dispersion must be avoided, as well as excessive numerical diffusion, which can result from attempts to control dispersion. The numerical algorithm presented here attempts to address these issues. 10 refs., 4 figs.