Journal of Mathematical Fluid Mechanics

, Volume 12, Issue 4, pp 554–575 | Cite as

Adaptive Boundary Conditions for Exterior Stationary Flows in Three Dimensions



Recently there has been an increasing interest for a better understanding of ultra low Reynolds number flows. In this context we present a new setup which allows to efficiently solve the stationary incompressible Navier-Stokes equations in an exterior domain in three dimensions numerically. The main point is that the necessity to truncate for numerical purposes the exterior domain to a finite sub-domain leads to the problem of finding so called “artificial boundary conditions” to replace the conditions at infinity. To solve this problem we provide a vector filed that describes the leading asymptotic behavior of the solution at large distances. This vector field depends explicitly on drag and lift which are determined in a self-consistent way as part of the solution process. When compared with other numerical schemes the size of the computational domain that is needed to obtain the hydrodynamic forces with a given precision is drastically reduced, which in turn leads to an overall gain in computational efficiency of typically several orders of magnitude.

Mathematics Subject Classification (2000).

76D05 76D25 76M10 41A60 35Q35 


Navier–Stokes equations artificial boundary conditions drag lift 


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Copyright information

© Birkhäuser Verlag, Basel 2009

Authors and Affiliations

  1. 1.AG Numerische Simulation Optimierung und Hochleistungsrechnen, Institut für Angewandte und Numerische Mathematik IVUniversity of KarlsruheKarlsruheGermany
  2. 2.Département de Physique ThéoriqueUniversité de GenèveGeneveSwitzerland

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