Published 6 issues per year
ISSN Print: 1543-1649
ISSN Online: 1940-4352
Indexed in
Asymptotic and Numerical Modeling of a Flow in a Thin Channel with Viscoelastic Wall
ABSTRACT
This article deals with a theoretical and numerical study of a fluid-structure interaction problem. We consider the nonstationary flow of a viscous fluid in a thin rectangle with an elastic wall as the upper part of the boundary. The physical problem that corresponds to nonhomogeneous boundary conditions is stated. By using a boundary layer method, an asymptotic solution is constructed. The properties of the boundary layer functions are established, and an error estimate is obtained. The asymptotic expansions are justified both by the error estimates and by the numerical simulations.
-
Panasenko Grigory, Stavre Ruxandra, Asymptotic analysis of the Stokes flow with variable viscosity in a thin elastic channel, Networks & Heterogeneous Media, 5, 4, 2010. Crossref
-
Panasenko G.P., Stavre R., Asymptotic analysis of the Stokes flow in a thin cylindrical elastic tube, Applicable Analysis, 91, 11, 2012. Crossref
-
Panasenko Grigory, Pileckas Konstantin, Asymptotic analysis of the non-steady Navier–Stokes equations in a tube structure. I. The case without boundary-layer-in-time, Nonlinear Analysis: Theory, Methods & Applications, 122, 2015. Crossref
-
Malakhova-Ziablova Irina, Panasenko Grigory, Stavre Ruxandra, Asymptotic analysis of a thin rigid stratified elastic plate – viscous fluid interaction problem, Applicable Analysis, 95, 7, 2016. Crossref
-
Panasenko G. P., Stavre R., Viscous fluid-thin cylindrical elastic body interaction: asymptotic analysis on contrasting properties, Applicable Analysis, 98, 1-2, 2019. Crossref
-
Panasenko Grigory P., Stavre Ruxandra, Well Posedness and Asymptotic Expansion of Solution of Stokes Equation Set in a Thin Cylindrical Elastic Tube, in Around the Research of Vladimir Maz'ya II, 12, 2010. Crossref
-
Panasenko G. P., Stavre R., Three Dimensional Asymptotic Analysis of an Axisymmetric Flow in a Thin Tube with Thin Stiff Elastic Wall, Journal of Mathematical Fluid Mechanics, 22, 2, 2020. Crossref