Advertisement

Applied Mathematics and Mechanics

, Volume 22, Issue 9, pp 1012–1018 | Cite as

Finite element Galerkin approach for a computational study of arterial flow

  • G. C. Sharma
  • Madhu Jain
  • Anil Kumar
Article

Abstract

A finite element solution for the Navier-Stokes equations for steady flow through a double branched two dimensional section of three dimensional model of canine aorta is obtained. The numerical technique involves transformation of the physical coordinates to a curvilinear boundary fitted coordinate system. The shear stress at the wall is calculated for Reynolds number of 1000 with branch to main aortic flow rate ratio as a parameter. The results are compared with earlier works involving experimental data and it is observed that the results are very close to their solutions. This work in fact is an improvement of the work of Sharma and Kapoor (1995) in the sense that computations scheme is economic and Reynolds number is large.

Key words

shear stress blood flow arterial flow Galerkin approach 

CLC numbers

O242.21 O357.1 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Fry D L. Certain histological and chemical responses of the vascular interface to acutely induced mechanical stress in the aorta of the dog [J].Circulation Res, 1969, 93–108.Google Scholar
  2. [2]
    Thompson J F, Thomes F C, Mastin C W. Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any of arbitrary two dimensional bodies [J].J. Comput Phys, 1994,15:299–319.CrossRefGoogle Scholar
  3. [3]
    Gokhale V V, Tanner R I, Bischoff K B. Finite element solution of the Navier-Stokes equations for two dimensional steady flow through a section of a canine aorta model [J].Journal of Biomechanics, 1978,11:241–249.CrossRefGoogle Scholar
  4. [4]
    Gresho P M, Lee R L, Sani R L. Lawrence Livermore Laboratory Rept UCRL-83282, Sept, 1979.Google Scholar
  5. [5]
    Lutz R J, Hsu L, Menawat A, et al. Fluid mechanics and boundary layer mass transport in an arterial model during steady and unsteady flow [A]. In: 74th Annual AICHE [C]. New Orleans, LA, 1981.Google Scholar
  6. [6]
    Mishra J C, Singh S T. A large deformation analysis for aortic walls under a physiological loading [J].J Engg Sciences, 1983,21:1193–1202.CrossRefGoogle Scholar
  7. [7]
    Sharma G C, Kapoor J. Finite element computation of two dimensional arterial flow in the presence of a transverse magnetic field [J].Internal J Numer Methods Fluids, 1995,20:1153–1161.zbMATHCrossRefGoogle Scholar
  8. [8]
    Dash R K, Jayarman G, Mehta K M. Estimation of increased flow resistance in a narrow catheterized arteries [J].Journal of Biomechanics, 1996,29A:917–930.CrossRefGoogle Scholar
  9. [9]
    Ku N. Blood flow in arteries [J].Annual Review of Fluid Mechanics, 1997,29:399–434.MathSciNetCrossRefGoogle Scholar
  10. [10]
    Dash R K, Jayarman G, Mehta K M. Flow in cathertized curved artery with stenosis [J].Journal of Biomechanics, 1999,32:46–61.CrossRefGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics All rights reserved 1980

Authors and Affiliations

  • G. C. Sharma
    • 1
  • Madhu Jain
    • 1
  • Anil Kumar
    • 1
  1. 1.School of Mathematical SciencesInstitute of Basic ScienceKhandariIndia

Personalised recommendations