Asymptotic study for Stokes-Brinkman model with jump embedded transmission conditions

Philippe Angot (1) , Gilles Carbou (2) , Victor Péron (3, 2)

1 I2M - Institut de Mathématiques de Marseille
2 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
3 Magique 3D - Advanced 3D Numerical Modeling in Geophysics

In this paper, one considers the coupling of a Brinkman model and Stokes equations with jump embedded transmission conditions. In this model, one assumes that the viscosity in the porous region is very small. Then we derive a Wentzel–Kramers–Brillouin (WKB) expansion in power series of the square root of this small parameter for the velocity and the pressure which are solution of the transmission problem. This WKB expansion is justified rigorously by proving uniform errors estimates.

Domains: Mathematics [math]

Philippe Angot, Gilles Carbou, Victor Péron. Asymptotic study for Stokes-Brinkman model with jump embedded transmission conditions. Asymptotic Analysis, 2016, 96 (3-4), pp.223-249. ⟨10.3233/ASY-151336⟩. ⟨hal-01184429⟩