Original scientific paper

https://doi.org/10.3336/gm.47.2.12

On a free piston problem for Stokes and Navier-Stokes equations

Boris Muha ; Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia
Zvonimir Tutek ; Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia

Abstract

Our goal is to model and analyze a stationary fluid flow through the junction of two pipes in the gravity field. Inside 'vertical' pipe there is a heavy piston which can freely move along the pipe. We are interested in the equilibrium position of the piston in dependence on geometry of junction. Fluid is modeled with the Navier-Stokes equations and the piston is modeled as a rigid body. We formulate corresponding boundary value problem and prove an existence result. The problem is nonlinear even in case of the Stokes equations for fluid flow; we prove non-uniqueness of solutions and illustrate it with some numerical examples. Furthermore, derivation and analysis of the linearized problem are presented.

Keywords

Navier-Stokes equations; free piston problem; fluid-rigid body interaction

Hrčak ID:

93952

URI

https://hrcak.srce.hr/93952

Publication date:

19.12.2012.

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