Conditions at the Downstream Boundary for Simulations of Viscous, Incompressible Flow

The proper specification of boundary conditions at artificial boundaries for the simulation of time-dependent fluid flows has long been a matter of controversy. In this work, the general theory of asymptotic boundary conditions for dissipative waves, developed in [T. Hagstrom, Math. Comp., submitted],is applied to the design of simple, accurate conditions at a downstream boundary for incompressible flows. For Reynolds numbers far enough below the critical value for linear stability, a scaling is introduced which greatly simplifies the construction of the asymptotic conditions. Numerical experiments with the nonlinear dynamics of vortical disturbances to plane Poiseuille flow are presented which illustrate the accuracy of our approach for low to moderate Reynolds numbers. The consequences of directly applying the scalings to the equations are also considered.