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

• Artificial boundary conditions for an exterior flow with fluid–structure interaction.
• The conditions are easy-to-implement Dirichlet b.c. based on the asymptotic expansion of the mathematical solution.
• Independent of the underlying numerical resolution scheme.
• Improved precision on computation of drag and lift, more ”physical” streamlines.
• Reduced computational domain size and thus memory savings.

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.