Viscous fluid-thin cylindrical elastic body interaction: asymptotic analysis on contrasting properties

ABSTRACT

A periodic, axially symmetric time-dependent model of interaction between a viscous fluid and a thin cylindrical elastic tube is considered. The problem depends on a small parameter $\epsilon$, representing the ratio of the thickness of the wall and the radius of the cylinder. We consider Young’s modulus of the elastic medium and its density great or small parameters equal to some powers of $\epsilon$. An asymptotic expansion is constructed for various magnitudes of the rigidity and of the density of the elastic tube. The generality of the considered model requires to take into account six different combinations of the three parameters depending on $\epsilon$. We obtain in this way different limit problems which are Stokes equations with some special boundary conditions. The expansion is justified by the high-order estimates for the difference of the exact solution and truncated asymptotic approximation.

KEYWORDS:

• Fluid-elastic medium interaction
• cylindrical elastic tube
• axially symmetric problem
• periodicity
• asymptotic analysis
• limit problems
• error estimates

AMS SUBJECT CLASSIFICATIONS:

• 74F10
• 35Q35
• 35Q74
• 76M45
• 76M30

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the European Social Fund according to the activity ‘Improvement of researchers’ qualification by implementing world-class R and D projects’ of Measure [grant number 09.3.3-LMT-K-712].