A stable explicit fractional step procedure for the solution of heat and fluid flow through interfaces between saturated porous media and free fluids in presence of high source terms

In this paper, porous medium-free fluid interface problems in the presence of high source terms are studied for the first time by using a stable, accurate and efficient Artificial Compressibility (AC) Characteristic- Based Split (CBS) algorithm. The interest in the AC-CBS scheme has increased, as its matrix-inversion free procedure offers the possibility of an easy and efficient parallelization. The present algorithm, recently introduced for the solution of porous media flows, presented some difficulties in solving complex interface problems. In this paper, the AC-CBS scheme has been specifically developed to overcome such difficulties and produce an accurate, stable, and efficient solution for the generalized porous medium flow equations for forced, free, and mixed convection through interfaces. In order to obtain the present results, a stability analysis for the AC-CBS scheme for the solution of problems with high source terms is carried out for the first time. The efficiency and the accuracy of the AC-CBS algorithm are verified through comparison with analytical, numerical, and experimental data available in the literature. The authors consider three different types of interface benchmark problems: (i) forced convection in a horizontal channel; (ii) mixed convection in a vertical channel; and (iii) natural convection in a vertically divided cavity.