Asymptotics of solutions for a basic case of fluid structure interaction

TL;DR

This paper derives universal asymptotic expansions for the velocity and vorticity in a fluid flow governed by Navier-Stokes equations in a half-plane with a small source, aiding numerical simulations.

Contribution

It provides detailed asymptotic behavior of solutions for a basic fluid-structure interaction model, linking it to exterior flow problems and numerical boundary conditions.

Findings

Asymptotic expansion depends only on source constants.

Expansion matches exterior flow around a moving body.

Useful for artificial boundary conditions in simulations.

Abstract

We consider the Navier--Stokes equations in a half-plane with a drift term parallel to the boundary and a small source term of compact support. We provide detailed information on the behavior of the velocity and the vorticity at infinity in terms of an asymptotic expansion at large distances from the boundary. The expansion is universal in the sense that it only depends on the source term through some multiplicative constants. This expansion is identical to the one for the problem of an exterior flow around a small body moving at constant velocity parallel to the boundary, and can be used as an artificial boundary condition on the edges of truncated domains for numerical simulations.