Report 1996-07

On coupled problems for viscous flow in exterior domains

M. Feistauer and C. Schwab

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

Paper: Available as PDF (391 KB) or as hardcopy to order reports@sam.math.ethz.ch.

Publishing information: In press in: Math. Mod. Meth. Appl. Sci., (1998)