Abbas Dashtimanesh

This paper describes the general convection-diffusion equation in 2D domain based on a particular fourth order finite difference method. The current fourth-order compact formulation is implemented for the first time, which offers a semi-explicit method of solution for the resulting equations. A nine point finite difference scheme with uniform grid spacing is also put into action for discretization purpose. The proposed numerical model is based on the Navier–Stokes equations in a stream function-vorticity formulation. The fast convergence characteristic can be mentioned as an advantage of this scheme. It combines the enhanced Fournie´’s fourth order scheme and the expanded fourth order boundary conditions, while offering a semi-explicit formulation. To accomplish this, some coefficients which do not influence the solutions are also omitted from Fournie´’s formulation. Consequently, very accurate results can be acquired with a relatively coarse mesh in a short time. The robustness and accuracy of the proposed scheme is proved using the benchmark problems of flow in a driven square cavity at medium and relatively high Reynolds numbers, flow over a backward-facing step, and flow in an L-shaped cavity.