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La mecanique des fluides est abordee sous deux points de vue, physique et mathematique. Les bases de la mecanique des milieux continus sont d'abord presentees en detail en precisant les hypotheses et approximations qui conduisent aux lois de conservation. Les outils d'analyse des equations generales, etude en ordres de grandeurs, analyse adimensionnelle et similitude, permettent ensuite d'introduire les approximations de fluide parfait d'Euler, de fluides visqueux en regime de Stokes et de la couche limite de Prandtl. Les notions de stabilite des ecoulements, de turbulence et les ecoulements compressibles sont ensuite presentes. Les ecoulements multiphysiques ouvrent des perspectives pour la recherche et le traitement d'applications complexes.
In this book, fluid mechanics is addressed from both physical and mathematical perspectives. As a first step, the basic theory of continuum mechanics is detailed, pointing out the different assumptions and approximations that lead to conservation laws. As a second step, scaling studies, dimensional analysis and similitude of the general equations help to introduce the inviscid Euler fluid approximation, the Stokes approximation of viscous flow and Prandtl’s boundary layer approximation. Lastly, the concepts of stability, turbulence and compressible flows are presented. Multiphysics approach of flows will provide readers with deeper insights into basic and applied research on complex processing.
