Continuous boundary condition at the interface for two coupled fluids

TL;DR

This paper studies the coupling of two laminar incompressible flows at an interface, demonstrating convergence of solutions as friction increases and validating results with numerical simulations.

Contribution

It introduces a friction Navier law for coupled flows and proves convergence to the original system as friction tends to infinity, supported by 2D numerical simulations.

Findings

Solutions converge as friction coefficient increases

Numerical simulations confirm theoretical convergence

Proposed coupling algorithm is effective in 2D simulations

Abstract

We consider two laminar incompressible flows coupled by the continuous law at a fixed interface. We approach the system by one that satisfies a friction Navier law, and we show that when the friction coefficient goes to infinity, the solutions converges to a solution of the initial system. We then write a numerical Schwarz-like coupling algorithm and run 2D-simulations, that yields same convergence result.