S. Boenisch and V. Heuveline and P. Wittwer
Second order adaptive boundary conditions for exterior flow problems:
non-symmetric stationary flows in two dimensions
(825K, pdf)
ABSTRACT. We consider the problem of solving numerically the stationary incompressible
Navier-Stokes equations in an exterior domain in two dimensions. For numerical
purposes we truncate the domain to a finite sub-domain, which leads to the
problem of finding so called \textquotedblleft artificial boundary
conditions\textquotedblright\ to replace the boundary conditions at infinity.
To solve this problem we construct -- by combining results from dynamical
systems theory with matched asymptotic expansion techniques based on the old
ideas of Goldstein and Van Dyke -- a smooth divergence free vector field
depending explicitly on drag and lift and describing the solution to second
and dominant third order, asymptotically at large distances from the body. The
resulting expression appears to be new, even on a formal level. This improves
the method introduced by the authors in a previous paper and generalizes it to
non-symmetric flows. The numerical scheme determines the boundary conditions
and the forces on the body in a self-consistent way as an integral part of the
solution process. When compared with our previous paper where first order
asymptotic expressions were used on the boundary, the inclusion of second and
third order asymptotic terms further reduces the computational cost for
determining lift and drag to a given precision by typically another order of magnitude.