Abstract: A kind of exponential finite difference schemes with h⁴ consistency are developed in this study. The h⁴ scheme is obtained from a second-order modification of the convective coefficients and the source term in an h² scheme, and the modification could be determined once and for all from computational information of the h² scheme, which bring great convenience to the h⁴ scheme. The proposed exponential scheme are unconditionally stable, and show a excellent accuracy and adaptability to great gradient variation when applicated in illustrative computations of 1D to 3D fluid flow model problems.

Key words: fluid mechanics, convective diffusion equation, exponential finite difference scheme