Asymptotics of solutions and artificial boundary conditions for a basic case of fluid-structure interaction

We investigate in detail a simple flow with fluid-structure interaction, namely the case of a small rigid body moving parallel to a wall at constant velocity in a quiescent, incompressible and viscous fluid. We concentrate mainly on stationary flows by describing the problem in an adequately chosen reference frame. We prove detailed information on the solution in a specially adapted functional framework and extract an explicit asymptotic expansion to the solution. This is then used to define boundary conditions for the artificial boundaries that appear when truncating the domain in numerical simulations, which are validated against traditional choices of boundary conditions

Numerical Aspects of the Implementation of Artificial Boundary Conditions for Laminar Fluid-Structure Interactions

We discuss the implementation of artificial boundary conditions for stationary Navier-Stokes flows past bodies in the half-plane, for a range of low Reynolds numbers. When truncating the half-plane to a finite domain for numerical purposes, artificial boundaries appear. We present an explicit Dirichlet condition for the velocity at these boundaries in terms of an asymptotic expansion for the solution to the problem. We show a substantial increase in accuracy of the computed values for drag and lift when compared with results for traditional boundary conditions. We also analyze the qualitative behavior of the solutions in terms of the streamlines of the flow

Asymptotics of solutions for a basic case of fluid–structure interaction

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 constants. The expansion also applies to the problem of an exterior flow past 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

Decay Estimates for Steady Solutions of the Navier--Stokes Equations in Two Dimensions in the Presence of a Wall

Let w be the vorticity of a stationary solution of the two-dimensional Navier-Stokes equations with a drift term parallel to the boundary in the half-plane -infty1, with zero Dirichlet boundary conditions at y=1 and at infinity, and with a small force term of compact support. Then, |xyw(x,y)| is uniformly bounded in the half-plane. The proof is given in a specially adapted functional framework and complements previous work