Abstract: With the varieties of the cell Reynolds number,We analyse the properties of the upwind scheme, the Samarskii Scheme and the modified Dennis scheme for convection-diffusion equations. Three semi-implicit schemes which are unconditionally stable and monotonic are present by those schemes. Numerical tests have shown these semi-implicit can be applied to solve for the steady fluid flow problems of high Reynolds.

Key words: convection-diffusion equation, finite difference scheme, stability, monotonicity