A coupling of stationary navier-stokes equations for two fluids with non-linear interface condition

Francois Legeais (1, 2)

1 ODYSSEY - Océan Dynamique Observations Analyse
2 IRMAR - Institut de Recherche Mathématique de Rennes

We study a coupled system of two Navier-Stokes equations with a non-linear friction condition at the interface between the two fluids. In a first part, we prove the existence of weak solutions in the proper functional spaces. To do that, we use a potential vector method to get the pressure as a function of the velocity, which allows us to obtain error estimates and to conclude using a fixed point argument. In a second part we develop a numerical finite elements iterative method which leads us to error estimates and numerical simulations with Freefem++ for different sets of data.

Mots clés: Fluid mechanics; Turbulence models; singular perturbations

Domaines: Mathématiques [math]

Francois Legeais. A coupling of stationary navier-stokes equations for two fluids with non-linear interface condition. 2024. ⟨hal-04551843⟩