The application of the Lattice Boltzmann method to the one-dimensional modeling of pulse waves in elastic vessels |
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Institution: | 1. Université de Monastir, École Nationale d''Ingénieurs de Monastir, Laboratoire d''Études des Systèmes Thermiques et Énergétiques (LESTE), Rue Ibn Jazza, 5019 Monastir, Tunisia;2. Univ. Artois, Univ. Lille, IMT Lille-Douai, Yncréa-HEI Hauts de France, Laboratoire Génie Civil & géo-Environnement (ULR 4515), Technoparc Futura, F-62400 Béthune, France |
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Abstract: | The one-dimensional nonlinear equations for the blood flow motion in distensible vessels are considered using the kinetic approach. It is shown that the Lattice Boltzmann (LB) model for non-ideal gas is asymptotically equivalent to the blood flow equations for compliant vessels at the limit of low Knudsen numbers. The equations of state for non-ideal gas are transformed to the pressure-luminal area response. This property allows to model arbitrary pressure-luminal area relations. Several test problems are considered: the propagation of a sole nonlinear wave in an elastic vessel, the propagation of a pulse wave in a vessel with varying mechanical properties (artery stiffening) and in an artery bifurcation, in the last problem Resistor–Capacitor–Resistor (RCR) boundary conditions are considered. The comparison with the previous results shows a good precision. |
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Keywords: | Lattice Boltzmann methods Kinetic theory of gases and liquids Biological fluid dynamics |
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