Computation of Airfoils at Very Low Reynolds Numbers

D. Bichsel1, and P. Wittwer2
1HESSO, Ecole d'Ingénieurs de Genève, Geneva, Switzerland
2DPT, Université de Genève, Geneva, Switzerland

We discuss a new numerical scheme involving adaptive boundary conditions which allows to compute, at very low Reynolds numbers, drag and lift of airfoils with rough surfaces; efficiently and with great precision.

As an example, we present the numerical implementation for an airfoil consisting of a line segment. The solution of the Navier-Stokes equations is singular at the leading and trailing edges of this airfoil, and the computation of drag and lift by integration of the stress tensor along the segment are therefore delicate.

However for our numerical purposes, the infinite exterior domain has to be truncated to a finite computational domain. Yet, this problem can be avoided by integrating over the surface of the truncated domain, instead of over the airfoil. Together with using adaptive boundary conditions, this allows us to determine drag and lift with greater precision than on smaller computational domains.