A primitive formulation (v, ψ) for incompressible flows based on velocity and vector potential of the acceleration
Résumé
An original primitive formulation of the equation of motion for viscous flows, based on two variables, the velocity and the vector potential of the acceleration, ensures the strict incompressibility of the flow. This equation, which reflects the conservation of the total energy, states that the intrinsic acceleration of the material medium is equal to the sum of the two terms of a Helmholtz-Hodge decomposition, one divergence-free and the second curl-free; the velocity field is itself decomposed into a solenoidal and an irrotational part. The incompressibility approximation of a flow leads to retain only the solenoidal components of all the terms of the equation of motion, viscous, inertial and vector potential of the acceleration; thus, all the terms which are expressed in the form of a dual curl are free of divergence. If, at a given moment, the velocity field is solenoidal, it will remain so both on a trajectory and in the whole domain. This decomposition allows us to state dual Bernoulli's theorem which applies to rotational flows as the equivalent of Bernoulli's theorem associated to irrotational flows.
Origine : Fichiers produits par l'(les) auteur(s)