A central difference type approximation of convection in fluid flow

In fluid flow and heat transfer problems, to eliminate instability and oscillations resulting from the numerical approximation of the convection term, it is common practice to use first order upwind differencing. For example, first order upwind differencing is used in codes like COMMIX and PHOENICS. However, in problems characterized by high Peclet numbers, this approach is highly inaccurate unless an excessive number of nodes is used. To eliminate this difficulty, a method of grid adaptation using central differencing in one-dimensional problems was presented. In the effort to extend this approach to 2-D and 3-D problems a new method was developed for multidimensional problems that is superior to first order upwind differencing even for a few non-adaptive grid points. This method is presented in this work.