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Artificial Boundary Conditions of Pressure Type for Viscous Flows in a System of Pipes

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Abstract.

In a three-dimensional domain Ω with J cylindrical outlets to infinity the problem is treated how solutions to the stationary Stokes and Navier–Stokes system with pressure conditions at infinity can be approximated by solutions on bounded subdomains. The optimal artificial boundary conditions turn out to have singular coefficients. Existence, uniqueness and asymptotically precise estimates for the truncation error are proved for the linear problem and for the nonlinear problem with small data. The results include also estimates for the so called “do-nothing” condition.

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Authors and Affiliations

  1. Paderborn Center for Parallel Computing, Universität Paderborn, Fürstenallee 11, 33102, Paderborn, Germany

    Stephan Blazy

  2. Institute of Mechanical Engineering Problems, V.O. Bol’shoy pr., 61, 199178, St. Petersburg, Russia

    Sergueï Nazarov

  3. Mathematik/Informatik, Universität Kassel, Fachbereich 17, Heinrich Plett. Str. 40, 34132, Kassel, Germany

    Maria Specovius-Neugebauer

Authors
  1. Stephan Blazy
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  2. Sergueï Nazarov
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  3. Maria Specovius-Neugebauer
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Correspondence to Stephan Blazy.

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Communicated by K. I. Pileckas

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Blazy, S., Nazarov, S. & Specovius-Neugebauer, M. Artificial Boundary Conditions of Pressure Type for Viscous Flows in a System of Pipes. J. math. fluid mech. 9, 1–33 (2007). https://doi.org/10.1007/s00021-005-0189-z

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  • DOI: https://doi.org/10.1007/s00021-005-0189-z

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