Accurate Solution of Steady Navier--Stokes System in Unbounded Domains

A long--term goal of this research is to accurately compute solutions of the steady Navier--Stokes equations in unbounded domains and identify the Euler flows arising as limits when $Re \rightarrow \infty$. Motivated by results in the mathematical literature on the ``Physically Reasonable'' solutions (Finn \& Smith, 1967), we ensure our solutions are characterized by a suitable rate of decay at infinity. Since this cannot be achieved in classical CFD methods based on a truncation of the infinite domain to a finite ``computational box'', we propose an alternative approach in which the Navier--Stokes equation is rewritten as a perturbation to the Oseen equations whose solutions are determined in a semi--analytic form. The resulting problem is discretized using a combination of Fourier--Galerkin and tau--collocation method based on the rational Chebyshev functions. We will present results showing how the wake structure changes with increasing Reynolds number.