ABSTRACT
For incompressible flows there are several possibilities for the formula tion of the problem. These include primitive variables, stream-function vorticity, and vorticity velocity formulations. The primitive variable approach offers the fewest complications in extending two-dimensional schemes to three dimensions. The primary difficulty with this approach is the specifi cation of boundary conditions on pressure. See Peyret and Taylor (1983) and Anderson et al. (1984) for ways to overcome this problem. The streamfunction vorticity formulation is best suited for two-dimensional flows, though it has been applied to three-dimensional incompressible flows as well [see, for example, Aziz and Heliums (1967), and Mallinson and De Vahl Davis (1973, 1977) for application details, and Hirasaki and Heliums (1970) and Richardson and Cornish (1977) for boundary condition considerations]. The difficulty with such methods is primarily associated with determination of vorticity at a boundary. A number of ways to over come this difficulty are available (Peyret and Taylor, 1983; Anderson et al., 1984). An inconvenience of this formulation is that the pressure is not directly available, and additional computation is required for its determi nation. We may point out that for two-dimensional flows, the streamfunction-only formulation can also be utilized. The interested reader is referred to Bourcier and Francois (1969), Roache and Ellis (1975), Morchoisne (1979), Cebeci et al. (1981), and Jaluria and Torrance (1986)
for the details. The vorticity velocity formulation requires the vorticity equation, the continuity equation, and the equations that define vorticity in terms of velocity gradients. A combination of the continuity equation and the definition of vorticity yields elliptic equations for the velocity com ponents. The interested reader is referred to Fasel (1976) and Dennis et al. (1979) for details.
