THE COMPACT SECOND-ORDER UPWIND FINITE DIFFERENCE SCHEMES FOR THE CONVECTION-DIFFUSION EQUATIONS

The compact second-order upwind finite difference schemes free of ceil Reynoldsnumber limitation are developed in this paper for the one-to three-dimensional steady convection-diffusion equations,using a perturbational technique applied to the classical first-order upwindschemes.The present second-order schemes take essentially the same form as those of the first-order schemes,but involve a simple modification to the diffusive coefficients.Numerical exam-ples including one-to three-dimensional model equations of fluid flow and a problem of naturalconvection with boundary-layer effect are given to illustrate the excellent behavior of the presentschemes.

THE COMPACT SECOND-ORDER UPWIND FINITE DIFFERENCE SCHEMES FOR THE CONVECTION-DIFFUSION EQUATIONS

The compact second-order upwind finite difference schemes free of ceil Reynolds number limitation are developed in this paper for the one-to three-dimensional steady convection- diffusion equations,using a perturbational technique applied to the classical first-order upwind schemes.The present second-order schemes take essentially the same form as those of the first- order schemes,but involve a simple modification to the diffusive coefficients.Numerical exam- ples including one-to three-dimensional model equations of fluid flow and a problem of natural convection with boundary-layer effect are given to illustrate the excellent behavior of the present schemes.