Computation of Airfoils at Very Low Reynolds Numbers

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 with great precision. As an example we present the numerical implementation for an airfoil consisting of a line segment. The solution of the NavierStokes equations is singular at the leading and the trailing edge of this airfoil, and the computation of drag and lift by integration of the stress tensor along the segment therefore delicate. However, since for numerical purposes the infinite exterior domain has to be truncated to a finite computational domain anyway, this problem can be avoided by integrating not over the airfoil, but over the surface of the truncated domain instead. Together with the adaptive boundary conditions this allows to determine drag and lift with great precision already on small computational domains.