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Computationally efficient finite element formulation for blood flow analysis in multi‐layered aorta modeled as viscoelastic material
Author(s) -
Hasan Mohammad,
Patel B. P.,
Pradyumna S.
Publication year - 2021
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6704
Subject(s) - finite element method , discretization , mathematical analysis , boundary value problem , viscoelasticity , galerkin method , mathematics , flow (mathematics) , partial differential equation , mechanics , blood flow , geometry , physics , medicine , thermodynamics
In the literature, blood flow study in an arterial segment/arterial network, using one‐dimensional wave propagation model, has been carried out considering flat/parabolic/logarithmic/different degree polynomial velocity profile functions. However, such assumptions are not capable of capturing actual blood and arterial wall interaction occurring while the blood flows through the arteries. In this study, a computationally efficient axisymmetric‐formulation of the Navier–Stokes equation is presented to eliminate the requirement of a priori assumed velocity profile function. Present formulation in terms of axial velocity ( u ), pressure ( p ), and domain radius ( R ) leads to the evolution of velocity profile as flow progresses with the time and space. We propose a multi‐layered structural model of the arterial wall with each layer idealized using four‐element Maxwell viscoelastic material model. Partial differential equations, mathematically representing the physical phenomena of blood flow in the complaint blood vessels, are discretized in the spatial domain by finite element method and in time domain by Galerkin time integration technique. A velocity boundary condition is prescribed at inlet and outlet boundary condition is prescribed in terms of three‐parameter based Windkessel model. Results of flow characteristics are found to be in excellent agreement with the three‐dimensional results available in the literature.