A particle-in-Burgers model: theory and numerics - Laboratoire de ...

Model and motivation Auxiliary steps Results h = 0: coupling h = 0: definition, uniqueness h = 0: numerics, existence The coupled problem
Model and motivation...
D’Alembert paradox : a solid immersed in an inviscid fluid is not
submitted to any resultant force ; in other words, birds (and planes...)
could not fly with a model where viscosity is neglected ! Yet, inviscid
(hyperbolic !) models are ok for some fluids...
Answer 1 to the d’Alembert paradox: use viscous models of
fluid-solid interaction (see e.g. M. Hillairet , for a recent review).
Answer 2 (when the Reynolds number is large): it is reasonable to
neglect the viscous effects in the model that governs the fluid ;
but we have to conserve information from the vanishing viscosity
in a DRAG FORCE .
The drag force takes the form of a source term which takes into
account the difference between the velocity of the fluid and the
velocity of the solid.