Finite Difference and Finite Volume Techniques for the Solution of Navier-Stokes Equations in Cardiovascular Fluid Mechanics

Tsangaris, S.; Pappou, Theodora

doi:10.1007/978-3-7091-2542-7_3

Cited by 3 publications

(2 citation statements)

References 33 publications

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“…Examining closely Eqs. (9)(10)(11)(12)(13)(14)(15)(16), it is evident that the above system of equations can be analyzed into representations of derivatives R , R , S only. The discretization process must result to representations of R i , S i .…”

Section: Numerical Process For the Membrane Modelmentioning

confidence: 99%

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Fluid flow of incompressible viscous fluid through a non-linear elastic tube

Lazopoulos

Tsangaris

2008

Arch Appl Mech

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The study of viscous flow in tubes with deformable walls is of specific interest in industry and biomedical technology and in understanding various phenomena in medicine and biology (atherosclerosis, artery replacement by a graft, etc) as well. The present work describes numerically the behavior of a viscous incompressible fluid through a tube with a non-linear elastic membrane insertion. The membrane insertion in the solid tube is composed by non-linear elastic material, following Fung's (Biomechanics: mechanical properties of living tissue, 2nd edn. Springer, New York, 1993) type strain-energy density function. The fluid is described through a Navier-Stokes code coupled with a system of non linear equations, governing the interaction with the membrane deformation. The objective of this work is the study of the deformation of a non-linear elastic membrane insertion interacting with the fluid flow. The case of the linear elastic material of the membrane is also considered. These two cases are compared and the results are evaluated. The advantages of considering membrane nonlinear elastic material are well established. Finally, the case of an axisymmetric elastic tube with variable stiffness along the tube and membrane sections is studied, trying to substitute the solid tube with a membrane of high stiffness, exhibiting more realistic response.Keywords Fluid flow · Elastic membrane · Nonlinear elastic material · Linear elastic material · Fluid flow membrane interaction A. Lazopoulos · S. Tsangaris (B) Fluids Section,

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Section: Numerical Process For the Membrane Modelmentioning

confidence: 99%

“…More specifically those phenomena have been studied at first in one-dimensional models, see Lighthill [2] and Pedley [3]. Afterwards, two-dimensional plane models were developed, which are still accurate and useful [4][5][6][7][8][9][10][11][12][13][14][15][16]. However, the membrane is reduced to a string problem in all these studies.…”

Section: Introductionmentioning

confidence: 99%

Fluid flow of incompressible viscous fluid through a non-linear elastic tube

Lazopoulos

Tsangaris

2008

Arch Appl Mech

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Identification of DVT diseases using numerical simulations

Simão

Ferreira

Rodríguez

et al. 2016

Med Biol Eng Comput

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This research provides useful insights for better diagnosis and understanding the vein blockage induced by a deep venous thrombosis and the occurrence of reverse flow in human veins, allowing a proper detection of serious diseases related to deep venous insufficiency. An arbitrary Lagrangian-Eulerian formulation is used in a coupled model (i.e. fluid and structure equations solved together), considering two domains, specifically the blood flow and the flexible structures (i.e. vein and valves). Computational fluid dynamics mathematical model based on finite element method, with special elements and boundary characterization, is addressed to find the best solution. This research presents a novel model to study the interaction between non-Newtonian laminar fluid flows, the blood, within nonlinear structures, the vein walls. Simulation results are validated using in vivo echo-Doppler measurements.

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A weak Legendre collocation spectral method for the solution of the incompressible Navier–Stokes equations in unstructured quadrilateral subdomains

Kondaxakis

Tsangaris

2003

Journal of Computational Physics

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Finite Difference and Finite Volume Techniques for the Solution of Navier-Stokes Equations in Cardiovascular Fluid Mechanics

Cited by 3 publications

References 33 publications

Fluid flow of incompressible viscous fluid through a non-linear elastic tube

Fluid flow of incompressible viscous fluid through a non-linear elastic tube

Identification of DVT diseases using numerical simulations

A weak Legendre collocation spectral method for the solution of the incompressible Navier–Stokes equations in unstructured quadrilateral subdomains

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