Buoyancy-driven flows beyond the Boussinesq approximation: a brief review

The well-known Boussinesq (also known as Oberbeck—Boussinesq) approximation is still the most common approach for the numerical simulation of natural convection problems. However, the accurate performance of this approximation is mainly restricted by small temperature differences. This encourages researchers and engineers to use other approaches beyond the range of validity of the Boussinesq approximation, especially when buoyancy-driven flows are generated by large temperature differences. This paper assembles and classifies the various approaches for numerical simulation of laminar natural convection, including Boussinesq and non-Boussinesq approximations for Newtonian fluids. These classifications reside under two overarching classes capturing compressible and incompressible approaches, respectively. This review elaborates on the different approaches and formulations adopted within each category.