Abstract: The perturbational fourth-order finite difference scheme of exponential type proposed by the authors is improved, by replacing the exponential coefficients in the source term perturbation with rational expressions, and is applied, aimed at the basic difficulties in computational fluid mechanics, to one-to three-dimensional model equations and a problem of natural convection with large Rayleigh-numbers, turning out the outstanding advantages of the perturbational scheme in such aspects as adaptability to flows with large Reynolds-numbers, resolution to ‘shock wave’-and ‘viscous boundary layer’-like effects, and saving computing CPU time.

Key words: fluid mechanics, convection-diffusion equation, finite difference scheme, model equation, natural convection