Artificial boundary conditions for stationary Navier-Stokes flows past bodies in the half-plane

TL;DR

This paper introduces an explicit Dirichlet boundary condition for stationary Navier-Stokes flows in the half-plane, significantly improving numerical accuracy for drag and lift calculations by incorporating asymptotic flow behavior.

Contribution

It presents a universal artificial boundary condition based on asymptotic expansion, enhancing numerical simulations of flows past bodies in the half-plane.

Findings

Increased accuracy in drag and lift computations.

Boundary condition depends on a single constant.

Flow solutions exhibit expected streamline behavior.

Abstract

We discuss 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. The new boundary conditions are universal in the sense that they depend on a given body only through one constant, which can be determined in a feed-back loop as part of the solution process.