Comparative study of the unified finite approach exponential-type scheme (UNIFAES) and its application to natural convection in a porous cavity

This article describes the UNIFAES, Unified Finite Approach Exponential-typ e Scheme for convective-diffusive fluid transport equations, including the treatment of Neumann boundary conditions. To reduce the computing time, UNI FRES allows the use of Patankar's power-law approximation rule. The scheme is subjected to the Smith and Hutton test problem, where it is compared to central differencing, the exponential scheme, and the locally analytic diff erencing scheme (LORDS). Finally, the scheme is applied to the problem of n atural convection within a square porous cavity heated from below, consider ing single-cell and multiple-cell solutions of this porous Benard-like conv ection problem.