Higher-Order Upwind Differencing
More accurate solutions are obtained if the convective terms are discretized by higher-order schemes. Davis and Moore (1982) use the MAC method with a multidimensional third-order upwinding scheme. Needless to mention that their marching algorithm for the momentum equation is explicit and the stability restriction concerning the CFL condition  and  is satisfied. The multidimensional third-order upwinding is in principle similar to one dimensional quadratic upstream interpolation scheme introduced by Leonard (1979).
Figure 35.1: Dependent variables  and  on a rectangular grid
Consider Fig. 35.1, let  be any property which can be convected and diffused. The convective term  may be represented as
where the variable  and  are defined as
 or  |
(35.6) |
and
 for  |
(35.7) |
The parameter  can be chosen to increase the accuracy or to alter the diffusion like characteristics. It may be pointed out  corresponds to the QUICK scheme of Leonard (1979). |
