- 03-73 Sebastian Boenisch Vincent Heuveline Peter Wittwer
- Adaptive boundary conditions for exterior flow problems
Feb 24, 03
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Abstract. We consider the problem of solving numerically the stationary incompressible
Navier-Stokes equations in an exterior domain in two dimensions. This
corresponds to studying the stationary fluid flow past a body. The necessity
to truncate for numerical purposes the infinite exterior domain to a finite
domain leads to the problem of finding appropriate boundary conditions on the
surface of the truncated domain. We solve this problem by providing a vector
field describing the leading asymptotic behavior of the solution. This vector
field is given in the form of an explicit expression depending on a real
parameter. We show that this parameter can be determined from the total drag
exerted on the body. Using this fact we set up a self-consistent numerical
scheme that determines the parameter, and hence the boundary conditions and
the drag, as part of the solution process.
We compare the values of the drag obtained with our adaptive scheme
with the results from using traditional constant boundary conditions.
Computational times are typically reduced by several orders of magnitude.