Unsteady flow in a 2D elastic tube with the LBGK method

We report results of unsteady, harmonic flow simulations with the lattice BGK method in two-dimensional elastic tubes. The tubes are assumed to obey a simple constitutive equation, linearly relating the diameter of the tube to the pressure difference inside and outside the tube. First, as a benchmark, we present results of steady flow in such elastic tubes, and compare the performance of three different boundary conditions for the solid wall. Next, we present results of unsteady (harmonic) flow in the elastic tube, and validate the results by comparing them with theoretical expressions for the dispersion relation of the complex speed of traveling waves in the tube. Within the range of Womersley numbers tested the agreement between the simulations and the theory is good.

[1]  F. N. van de Vosse,et al.  The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model. , 1999, Journal of biomechanics.

[2]  Thomas J. R. Hughes,et al.  Finite Element Modeling of Three-Dimensional Pulsatile Flow in the Abdominal Aorta: Relevance to Atherosclerosis , 2004, Annals of Biomedical Engineering.

[3]  Zhifang Lin,et al.  Lattice Boltzmann method for simulating the viscous flow in large distensible blood vessels. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  D. Ku.  BLOOD FLOW IN ARTERIES , 1997 .

[5]  C. Ross Ethier,et al.  Computational modeling of arterial biomechanics , 2001, Comput. Sci. Eng..

[6]  P. Lallemand,et al.  Momentum transfer of a Boltzmann-lattice fluid with boundaries , 2001 .

[7]  G. Rappitsch,et al.  Computer Simulation of Arterial Blood Flow , 1995 .

[8]  Peter M. A. Sloot,et al.  3D Pulsatile flow with the Lattice Boltzmann BGK Method , 2002 .

[9]  Q. Zou,et al.  On pressure and velocity boundary conditions for the lattice Boltzmann BGK model , 1995, comp-gas/9611001.

[10]  D A Steinman,et al.  Computational blood flow modelling: errors associated with reconstructing finite element models from magnetic resonance images. , 1997, Journal of biomechanics.

[11]  J. P. Paul,et al.  Biomechanics , 1966 .

[12]  Peter M. A. Sloot,et al.  Simulated vascular reconstruction in a virtual operating theatre , 2001, CARS.

[13]  J. Womersley.  XXIV. Oscillatory motion of a viscous liquid in a thin-walled elastic tube—I: The linear approximation for long waves , 1955 .

[14]  A. Hoekstra,et al.  Mesoscopic simulations of systolic flow in the human abdominal aorta. , 2006, Journal of biomechanics.

[15]  J. Boon.  The Lattice Boltzmann Equation for Fluid Dynamics and Beyond , 2003 .

[16]  Peter M. A. Sloot,et al.  The Design of Dynamic Exploration Environments for Computational Steering Simulations , 2000 .

[17]  van de Fn Frans Vosse,et al.  The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 90° curved tube , 1999 .

[18]  A. Hoekstra,et al.  Simulation of a Systolic Cycle in a Realistic Artery with the Lattice Boltzmann BGK Method , 2003 .