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Abstract
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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.
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