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Pregled bibliografske jedinice broj: 597614

Existence of a weak solution to a nonlinear fluid- structure interaction problem modeling the flow of an incompressible, viscous fluid in a cylinder with deformable walls


Muha, Boris; Čanić, Sunčica
Existence of a weak solution to a nonlinear fluid- structure interaction problem modeling the flow of an incompressible, viscous fluid in a cylinder with deformable walls // Archive for rational mechanics and analysis, 207 (2013), 3; 919-968 doi:10.1007/s00205-012-0585-5 (međunarodna recenzija, članak, znanstveni)


Naslov
Existence of a weak solution to a nonlinear fluid- structure interaction problem modeling the flow of an incompressible, viscous fluid in a cylinder with deformable walls

Autori
Muha, Boris ; Čanić, Sunčica

Izvornik
Archive for rational mechanics and analysis (0003-9527) 207 (2013), 3; 919-968

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Fluid-structure interaction; weak solution; Lie splitting

Sažetak
We study a nonlinear, unsteady, moving boundary, fluid-structure interaction (FSI) problem arising in modeling blood flow through elastic and viscoelastic arteries. The fluid flow, which is driven by the time- dependent pressure data, is governed by 2D incompressible Navier-Stokes equations, while the elastodynamics of the cylindrical wall is modeled by the 1D cylindrical Koiter shell model. Two cases are considered: the linearly viscoelastic and the linearly elastic Koiter shell. The fluid and structure are fully coupled (2-way coupling) via the kinematic and dynamic lateral boundary conditions describing continuity of velocity (the no-slip condition), and balance of contact forces at the fluid- structure interface. We prove existence of weak solutions to the two FSI problems (the viscoelastic and the elastic case) as long as the cylinder radius is greater than zero. The proof is based on a novel semi-discrete, operator splitting numerical scheme, known as the kinematically coupled scheme, introduced in \cite{; ; ; ; GioSun}; ; ; ; to numerically solve the underlying FSI problems. The backbone of the kinematically coupled scheme is the well-known Marchuk-Yanenko scheme, also known as the Lie splitting scheme. We effectively prove convergence of that numerical scheme to a solution of the corresponding FSI problem.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekt / tema
037-0693014-2765 - Matematička analiza kompozitnih i tankih struktura (Zvonimir Tutek, )

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Autor s matičnim brojem:
Boris Muha, (267374)

Časopis indeksira:


  • Current Contents Connect (CCC)
  • Web of Science Core Collection (WoSCC)
    • Science Citation Index Expanded (SCI-EXP)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus


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