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On coupled problems for viscous flow in exterior domains

by M. Feistauer and Ch. Schwab

(Report number 1996-07)

Abstract
The use of the complete Navier-Stokes system in an unbounded domain is not always convenient in computations and, therefore, the Navier-Stokes problem is often truncated to a bounded domain. In this paper we simulate the interaction between the flow in this domain and the exterior flow with the aid of a coupled problem. We propose in particular a linear approximation of the exterior flow (here the Stokes flow or potential flow) coupled with the interior Navier-Stokes problem via suitable transmission conditions on the artificial interface between the interior and exterior domain. Our choice of the transmission conditions ensures the existence of a solution of the coupled problem, also for large data.

Keywords: viscous incompressible flow, Navier-Stokes equations, exterior Stokes problem, potential flow equation, transmission conditions, coupled problem, weak solution

@Techreport{FS96_190,
  author = {M. Feistauer and Ch. Schwab},
  title = {On coupled problems for viscous flow in exterior domains},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1996-07},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1996/1996-07.pdf },
  year = {1996}
}

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