Informace o kvalifikační práci Využití lattice Boltzmannovy metody pro numerické řešení proudění krve ve vybraných problémech kardiovaskulární biomechaniky
This diploma thesis deals with the implementation of the lattice Boltzmann method for the numerical solution of selected problems of cardiovascular biomechanics. A literature search is performed, which focuses on the use of the lattice Boltzmann method in the field of cardiovascular biomechanics. The basic principles of kinetic theory on which the method is based are described. Subsequently, the algorithm of lattice Boltzmann method is presented, including the implementation of Zou-He boundary conditions in planar regions of various geometries. Numerical simulations of steady blood flow in both idealized and real 2D model of vascular bifurcation are presented. At the end of the work, the influence of the angle between the daughter branches of the idealized symmetric 2D vascular bifurcation on the velocity field, specifically on the values of shear stress on its wall, is studied.
Anotace v angličtině
This diploma thesis deals with the implementation of the lattice Boltzmann method for the numerical solution of selected problems of cardiovascular biomechanics. A literature search is performed, which focuses on the use of the lattice Boltzmann method in the field of cardiovascular biomechanics. The basic principles of kinetic theory on which the method is based are described. Subsequently, the algorithm of lattice Boltzmann method is presented, including the implementation of Zou-He boundary conditions in planar regions of various geometries. Numerical simulations of steady blood flow in both idealized and real 2D model of vascular bifurcation are presented. At the end of the work, the influence of the angle between the daughter branches of the idealized symmetric 2D vascular bifurcation on the velocity eld, specically on the values of shear stress on its wall, is studied.
Klíčová slova
lattice Boltzmannova metoda, kardiovaskulární biomechanika,
idealizovaná cévní bifurkace, karotida, numerické simulace, okrajové
podmínky typu "Zou-He"
This diploma thesis deals with the implementation of the lattice Boltzmann method for the numerical solution of selected problems of cardiovascular biomechanics. A literature search is performed, which focuses on the use of the lattice Boltzmann method in the field of cardiovascular biomechanics. The basic principles of kinetic theory on which the method is based are described. Subsequently, the algorithm of lattice Boltzmann method is presented, including the implementation of Zou-He boundary conditions in planar regions of various geometries. Numerical simulations of steady blood flow in both idealized and real 2D model of vascular bifurcation are presented. At the end of the work, the influence of the angle between the daughter branches of the idealized symmetric 2D vascular bifurcation on the velocity field, specifically on the values of shear stress on its wall, is studied.
Anotace v angličtině
This diploma thesis deals with the implementation of the lattice Boltzmann method for the numerical solution of selected problems of cardiovascular biomechanics. A literature search is performed, which focuses on the use of the lattice Boltzmann method in the field of cardiovascular biomechanics. The basic principles of kinetic theory on which the method is based are described. Subsequently, the algorithm of lattice Boltzmann method is presented, including the implementation of Zou-He boundary conditions in planar regions of various geometries. Numerical simulations of steady blood flow in both idealized and real 2D model of vascular bifurcation are presented. At the end of the work, the influence of the angle between the daughter branches of the idealized symmetric 2D vascular bifurcation on the velocity eld, specically on the values of shear stress on its wall, is studied.
Klíčová slova
lattice Boltzmannova metoda, kardiovaskulární biomechanika,
idealizovaná cévní bifurkace, karotida, numerické simulace, okrajové
podmínky typu "Zou-He"
Provedení rešerše zaměřené na aplikaci lattice Boltzmannovy metody v úlohách kardiovaskulární biomechaniky.
Vytvoření geometricky variabilního výpočtového modelu arteriální bifurkace ve 2D.
Vývoj výpočetních algoritmů pro implementaci lattice Boltzmannovy metody pro numerické řešení proudění krve.
Posouzení vlivu vybraných geometrických parametrů 2D modelu arteriální bifurkace na proudové pole.
Vyhodnocení a diskuse dosažených numerických výsledků, formulace závěrů.
Zásady pro vypracování
Provedení rešerše zaměřené na aplikaci lattice Boltzmannovy metody v úlohách kardiovaskulární biomechaniky.
Vytvoření geometricky variabilního výpočtového modelu arteriální bifurkace ve 2D.
Vývoj výpočetních algoritmů pro implementaci lattice Boltzmannovy metody pro numerické řešení proudění krve.
Posouzení vlivu vybraných geometrických parametrů 2D modelu arteriální bifurkace na proudové pole.
Vyhodnocení a diskuse dosažených numerických výsledků, formulace závěrů.
Seznam doporučené literatury
S. Chen, D. O. Martinez, R. Mei: On boundary conditions in lattice Boltzmann methods. Physics of Fluids 8, 1996.
Q. Zon, X. He: On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Physics of Fluids 9, 1997.
S. Succi: The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Numerical Mathematics and Scientific Computation. Oxford University Press, 2001.
A. M. Artoli, D. Kandhai, H. C. J. Hoefsloot, A. G. Hoekstra, P. M. A. Sloot: Lattice BGK simulations of flow in a symmetric bifurcation. Future Generation Computer Systems 20: 909-916, 2004.
M. Nagargoje, R. Gupta: Effect of asymmetry on the flow behavior in an idealized arterial bifurcation. Computer Methods in Biomechanics and Biomedical Engineering 23 (6): 232-247, 2020.
Seznam doporučené literatury
S. Chen, D. O. Martinez, R. Mei: On boundary conditions in lattice Boltzmann methods. Physics of Fluids 8, 1996.
Q. Zon, X. He: On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Physics of Fluids 9, 1997.
S. Succi: The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Numerical Mathematics and Scientific Computation. Oxford University Press, 2001.
A. M. Artoli, D. Kandhai, H. C. J. Hoefsloot, A. G. Hoekstra, P. M. A. Sloot: Lattice BGK simulations of flow in a symmetric bifurcation. Future Generation Computer Systems 20: 909-916, 2004.
M. Nagargoje, R. Gupta: Effect of asymmetry on the flow behavior in an idealized arterial bifurcation. Computer Methods in Biomechanics and Biomedical Engineering 23 (6): 232-247, 2020.