Skew upstream differencing schemes for problems involving fluid flow

When the convection terms in the conservation equations are approximated using upstream or upwind differences, a large error may result in the regions of the flow where the grid line and velocity directions are not closely aligned. Two schemes are introduced which reduce this error but retain the advantages of upstream differencing. The schemes are particularly accurate in problems where diffusion and convection play dominant roles in establishing the distribution of the dependent variable. Solutions to two example problems illustrate the substantial improvement in accuracy resulting from those schemes.