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

TL;DR

This paper analyzes the asymptotic behavior of a coupled Stokes-Brinkman model with jump conditions, deriving a WKB expansion for small viscosity and rigorously proving error estimates.

Contribution

It introduces a novel asymptotic analysis using WKB expansion for the coupled model with jump conditions, including rigorous error bounds.

Findings

WKB expansion derived for velocity and pressure in the small viscosity limit

Uniform error estimates established for the asymptotic approximation

Insights into the behavior of the coupled system as viscosity approaches zero

Abstract

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.