We offer a synthetic exposition on the state of the art for Computational Fluid Dynamics (CFD) relevant to the Navier–Stokes equations with the Boussinesq approximation, smoothly blending a history of the field with an accessible exposition of the underlying mathematical rationale, supporting theorems and a survey of the landmark results on the subject. Attention is paid to those efforts which have opened up new paradigms in modern CFD, the techniques that have emerged as leading candidates as well as their diverse reverberations in producing advancements in our understanding of thermal buoyancy convection (especially Rayleigh–Bénard convection and the so-called Hadley Flow) in both laminar and turbulent conditions.

Revised:

Accepted:

Online First:

Marcello Lappa ^{1}

@article{CRMECA_2022__350_S1_A6_0, author = {Marcello Lappa}, title = {Incompressible flows and the {Boussinesq} approximation: 50 years of {CFD}}, journal = {Comptes Rendus. M\'ecanique}, publisher = {Acad\'emie des sciences, Paris}, year = {2022}, doi = {10.5802/crmeca.134}, language = {en}, note = {Online first}, }

Marcello Lappa. Incompressible flows and the Boussinesq approximation: 50 years of CFD. Comptes Rendus. Mécanique, Online first (2022), pp. 1-22. doi : 10.5802/crmeca.134.

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