A Study of Finite Difference Approximations to Steady-State, Convection-Dominated Flow Problems

Five different finite difference schemes, first-order upwind, skew upwind, second-order upwind, second order central differencing, and QUICK, approximating the convection terms in the transport equation with fluid motion, have been studied. Three simple test problems are used to compare the performances by the five schemes for high cell Peclet number flows; they are also used to demonstrate the restraints on the accuracy of the numerical approximations set by the types of the boundary conditions, by the presence of the source term in the flow region, and by the skewness of the numerical grid lines. The basic reasons behind the spurious oscillations in a numerical solution are studied. Among all five schemes studied, the second-order upwind is found to be, in general, the most satisfactory.