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-type Scheme for convective-diffusive fluid transport equations, including the treatment of Neumann boundary conditions. To reduce the computing time, UNIFRES 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 differencing scheme (LORDS). Finally, the scheme is applied to the problem of natural convection within a square porous cavity heated from below, considering single-cell and multiple-cell solutions of this porous Benard-like convection problem.