CONDIF: A modified central-difference scheme for convective flows

For most practical purposes, the central-difference scheme (CDS) would be ideal only if it were unconditionally stable. It is a simple and second-order scheme which is easy to implement. It does not introduce any second-order ‘diffusion’ like truncation error. However, for grid Peclet numbers larger than 2, the CDS leads to over- and under-shoots and is unstable. This paper presents a method, called CONDIF, which eliminates this undesirable feature of the CDS. It modifies the CDS by introducing a controlled amount of numerical diffusion based on the local gradients. The numerical diffusion can be adjusted to be negligibly low for most problems. CONDIF has been used to solve a number of test problems which have been widely used for comparative study of numerical schemes in the published literature. For all these problems the CONDIF results are significantly more accurate than those obtained from the hybrid scheme when the Peclet number is very high (∞) and the flow is at large angles (45 degrees) to the grid. In general the computational effort for CONDIF is comparable (within 20 per cent) to that for the hybrid scheme. However, in one instance the rate of convergence was found to be significantly slower.