Artificial compressibility based CBS solutions for double diffusive natural convection in cavities

Abstract

Purpose

The purpose of the paper is to numerically simulate steady‐state thermo‐solutal convection in rectangular cavities with different aspect ratios, subject to horizontal temperature and concentration gradients, and validate the results against numerical and experimental data available from literature.

Design/methodology/approach

The fully explicit Artificial Compressibility (AC) version of the Characteristic Based Split (CBS) scheme is adopted to solve double diffusion (DD) problems. A stabilization analysis is carried out to efficiently solve the problems considered in the present work. The thermal and solutal buoyancy forces acting on the fluid have been taken into account in case of aiding and opposing flow conditions.

Findings

The stability limits derived by the authors for the thermo‐solutal convection assume a fundamental role to efficiently solve the DD problems considered. In the cases characterized by higher Rayleigh number the convergent solution is obtained only by employing the new stability conditions. The efficient matrix free procedure employed is a powerful tool to study complex DD problems.

Originality/value

In this paper, the authors extend the stabilization analysis for the AC‐CBS scheme to the solution of DD, fundamental to efficiently solve the present problems, and apply the present fully explicit matrix free scheme, based on finite elements, to the solution of DD natural convection in cavities.

Citation

Arpino, F., Massarotti, N., Mauro, A. and Nithiarasu, P. (2013), "Artificial compressibility based CBS solutions for double diffusive natural convection in cavities", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 23 No. 1, pp. 205-225. https://doi.org/10.1108/09615531311289196