The application of the lattice Boltzmann method to the one-dimensional modeling of pulse waves in elastic vessels. (English) Zbl 1483.76073
Summary: 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.
MSC:
| 76Z05 | Physiological flows |
| 92C35 | Physiological flow |
| 76M28 | Particle methods and lattice-gas methods |
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