Grid, faces centered between nodes

The discretization stencil (Fig. 17.14) uses a staggered grid in which the axial velocities are represented on the control-volume faces and all other variables are represented at the control-volume centers (nodes) [307], The nodes are separated by Az, which is variable on a nonuniform mesh. The inlet at the top and the solid surface at the bottom correspond to nodes and the faces are halfway between nodes. The first axial velocity (face 1) is evaluated just above the surface at z — Az/2. The inlet velocity, however, is taken at the top node,... 

Some commonly used interpolation practices are discussed here. A simple and straightforward approximation to the value at the CV face center is linear interpolation between the two nearest nodes. At location e on a Cartesian grid (Fig. 6.2), general interpolation coefficients (yS) for such a scheme can be written ... 

Another classical approximation for the value at GCV face center is obtained by linear interpolation between the two nearest nodes. The linear interpolation corresponds to the central difference approximation of the first derivative in FDMs. At location e on a non-uniform Cartesian grid we have [49, 202] ... 

---