On boundary conditions for inner incompressible flows

Abstract

We consider the flow of viscous incompressible fluids in confined two dimensional regions. The flow field is determined not only by the geometry and the properties of the fluid but largely by the conditions that are imposed at the inflow and the outflow boundaries. These conditions are usually not known explicitly. Often, one extends the physical domain so that analytically known free-stream conditions can be applied at 'infinity'. For numerical simulation the computational domain is redefined and in most cases in an arbitrary manner. The application of free-stream conditions, at finite distance, for channel and duct flows have been considered in [I] and [2]. It has been shown that by applying the free-stream velocity profile at some finite distance, errors appeared close to the outflow boundary. In several papers somewhat 'less restrictive' ([3], p.154) conditions were defined by assuming that the variations in the main flow directions are small. For both boundary conditions the computed flow approximates the physical one except in a thin region near the outflow boundary. ]o obtain uniform accuracy, parabolic boundary conditions have been developed [1,2]. These conditions assume that the flow has a main direction and that no separation occurs near the outflow boundary. Thunell [4] studied some of the effects of using free-stream velocity values (Dirichlet conditions) at the outflow boundary even when separation occurred. It was found that when such outflow boundary conditions were applied at a place where separation should take place, a distorted flow field, with most errors near the outflow boundary was obtained.