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In the last few decades, the Higher Order Compact (HOC) finite difference schemes are gaining momentum in the fluid dynamics community because of their high accuracy and advantages associated with compact difference stencils. However, in most of the cases, their application is seen to be limited solely to the computation of fluid flows and in some cases to problems of heat transfer only. The present work is perhaps first in the direction where an HOC algorithm has been extended to a problem of combined heat and mass transfer. A recently developed higher-order compact (HOC) scheme of fourth order spatial and second order temporal accuracy is employed to carry out simulation of double-diffusive natural convection in a vertical porous annulus between two concentric cylinders maintained at constant temperatures and concentrations. Flow is investigated in the regime -50≤N≤50, 1 ≤A≤10, 1≤κ≤50, 0≤Ra≤1000 and 1≤Le≤500, where N, A, κ, Ra and Le are the buoyancy ratio, aspect ratio, radius ratio, thermal Rayleigh number and the Lewis number respectively. Comparison is made with established numerical results and very good comparison is obtained on relatively coarser grids.
Kalita et al. (Sat,) studied this question.