A unified formulation for continuum mechanics applied to fluid–structure interaction in flexible tubes

This paper outlines the development of a new procedure for analysing continuum mechanics problems with a particular focus on fluid-structure interaction in flexible tubes. A review of current methods of fluid-structure coupling highlights common limitations of high computational cost and solution instability. It is proposed that these limitations can be overcome by an alternative approach in which both fluid and solid components are solved within a single discretized continuum domain. A single system of momentum and continuity equations is therefore derived that governs both fluids and solids and which are solved with a single mesh using finite volume discretization schemes. The method is validated first by simulating dynamic oscillation of a clamped elastic beam. It is then applied to study the case of interest-wave propagation in highly flexible tubes-in which a predicted wave speed of 8.58m/s falls within 2% of an approximate analytical solution. The method shows further good agreement with analytical solutions for tubes of increasing rigidity, covering a range of wave speeds from those found in arteries to that in the undisturbed fluid.

[1]  S. Muzaferija,et al.  Finite volume method for stress analysis in complex domains , 1994 .

[2]  D. Ku,et al.  A 3-D thin-wall model with fluid–structure interactions for blood flow in carotid arteries with symmetric and asymmetric stenoses , 1999 .

[3]  A. Gosman,et al.  High resolution NVD differencing scheme for arbitrarily unstructured meshes , 1999 .

[4]  Timothy J. Pedley,et al.  The fluid mechanics of large blood vessels , 1980 .

[5]  C. Rhie,et al.  A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation , 1982 .

[6]  Hrvoje Jasak,et al.  Application of the finite volume method and unstructured meshes to linear elasticity , 2000 .

[7]  D. Steinman,et al.  The effect of wall distensibility on flow in a two-dimensional end-to-side anastomosis. , 1994, Journal of biomechanical engineering.

[8]  K. Perktold,et al.  Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model. , 1995, Journal of biomechanics.

[9]  David M. Young,et al.  Applied Iterative Methods , 2004 .

[10]  Hrvoje Jasak,et al.  A tensorial approach to computational continuum mechanics using object-oriented techniques , 1998 .

[11]  Thomas Young,et al.  XIII. Hydraulic investigations, subservient to an intended Croonian Lecture on the motion of the blood , 1808, Philosophical Transactions of the Royal Society of London.

[12]  Werner Goldsmith,et al.  Longitudinal waves in liquid-filled tubes—II: Experiments , 1979 .

[13]  C. Bailey,et al.  Discretisation procedures for multi-physics phenomena , 1999 .

[14]  I. Demirdzic,et al.  Numerical method for coupled fluid flow, heat transfer and stress analysis using unstructured moving meshes with cells of arbitrary topology , 1995 .

[15]  B Hillen,et al.  Linear and nonlinear one-dimensional models of pulse wave transmission at high Womersley numbers. , 1989, Journal of biomechanics.

[16]  I. Demirdžić,et al.  Finite volume method for thermo-elasto-plastic stress analysis , 1993 .

[17]  David C. Wiggert,et al.  The influence of pipe motion on acoustic wave propagation , 1985 .

[18]  A. Gosman,et al.  Solution of the implicitly discretised reacting flow equations by operator-splitting , 1986 .

[19]  Marcus Wheel,et al.  A mixed finite volume formulation for determining the small strain deformation of incompressible materials , 1999 .

[20]  D. Korteweg.  Ueber die Fortpflanzungsgeschwindigkeit des Schalles in elastischen Rhren , 1878 .

[21]  M W Collins,et al.  The numerical analysis of fluid-solid interactions for blood flow in arterial structures Part 2: Development of coupled fluid-solid algorithms , 1998, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[22]  L. E. Malvern.  Introduction to the mechanics of a continuous medium , 1969 .

[23]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[24]  R. Kamm,et al.  A fluid--structure interaction finite element analysis of pulsatile blood flow through a compliant stenotic artery. , 1999, Journal of biomechanical engineering.

[25]  M. Cross,et al.  An enthalpy control‐volume—unstructured‐mesh (cv—um) algorithm for solidification by conduction only , 1992 .

[26]  T. Pedley.  The Fluid Mechanics of Large Blood Vessels: Contents , 1980 .