High Rayleigh number natural convection in rectangular cavities with different aspect ratios solved by using a stabilized finite element algorithm

In this work, high Rayleigh number natural convection has been solved for the first time by using a stabilized Artificial Compressibility (AC) Characteristic Based Split (CBS) algorithm. The authors have carried out a stability analysis, based on the order of magnitude analysis of all the terms present in the conservation equations, in order to solve problems in presence of very large source terms. A new benchmark problem for high Rayleigh number natural convection in rectangular cavities with different aspect ratios has been detected by the authors. This new benchmark case is the only one for which experimental data are available. The stabilized AC-CBS scheme is successfully used to solve the present benchmark problem. The efficiency and the accuracy of the AC-CBS algorithm are verified through comparison with the experimental data for the new benchmark problem and with the numerical solutions available in the literature for well known problems. The interest in the AC-CBS scheme has increased since it offers the possibility of an easy and efficient parallelization procedure.