CONDIF: A MODIFIED CENTRAL-DIFFERENCE SCHEME WITH UNCONDITIONAL STABILITY AND VERY LOW NUMERICAL DIFFUSION

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Abstract
This paper describes a method, called CONDIF, which retains the essential nature of the central difference scheme (CDS) but eliminates the over-and under- shoots. It modifies the CDS by introducing a controlled amount of numerical diffusion based on local gradients. The results obtained for a number of test problems show that the CONDIF is significantly more accurate than the hybrid scheme when the Peclet number is very high and the flow is at large angles to the grid. In the worst case, it yields results similar to those of the hybrid scheme. Though the CONDIF is unconditionally stable, under some conditions the rate of convergence deteriorates as the grid Peclet number is increased. Efforts are currently underway to develop a faster converging variation of CONDIF.

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