Three-dimensional distribution mass weighting for noninverted convection skew upwinding

Numerical studies of skew upstream differencing are presented for three-dimensional convective heat transfer problems. Two new types of noninverted skew upwind schemes are developed and compared, so that local inversion of influence coefficient matrices is not required. Unlike previous schemes, skew upwind values of temperature are expressed explicitly in terms of surrounding nodal variables. Different mass weighting alternatives, including 3-node/3-point and 4-node/8-point formulations are developed and evaluated. Results are presented for three application problems, that is, convective step change of temperature, tank inflow/outflow, and radial heat flow in a rotating hollow sphere. Although the effects of upwind nodal asymmetry appear minor in the first and second problems, noticeable improvement with 4-node/8-point interpolation is observed in the rotating sphere problem. Additional reduction of CPU time due to noninverted convective upwinding is reported.