EFFECTS OF OPEN BOUNDARY ON INCOMPRESSIBLE NAVIER-STOKES FLOW COMPUTATION: NUMERICAL EXPERIMENTS

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Abstract
The issue of the acceptable numerical treatment along downstream open boundaries for incompressible flow calculations is investigated. The conventional viewpoint holds that the flow problem is not well posed when both inflow and outflow appear on open boundaries. To test this point, a series of Navier-Stokes flow calculations have been conducted for both a planar channel with a one-sided asymmetric expansion and a planar channel with a two-sided symmetric expansion with varying Reynolds numbers and grid densities. Several interesting results have been observed that are not consistent with the conventional viewpoint. The numerical experiments indicate that even with inflow across some portions of an open boundary, the numerical procedure can be well posed by adopting the straightforward extrapolation formula on the open boundary. Overall, it appears that the numerical stability of the computation is related to the Reynolds number, especially for flows with multiple recirculating eddies across the open boundary. For channel flows with expansion and moderate Reynolds numbers, converged steady-state solutions can be obtained regardless of the position of the open boundary and the number of recirculating eddies. However, for higher Reynolds numbers, large sensitivity of the nonlinear responses to the small disturbances is observable if the open boundary contains multiple recirculating eddies and numerical oscillations can result fram those interactions. On the other hand, for an open boundary containing only one recirculating eddy, the steady-state solution appears to exist and the numerical algorithm converges even with very high Reynolds numbers.