MODELLING OF VISCOUS INHOMOGENEOUS FLUID FLOW IN LARGE BLOOD VESSELS
Abstract
In this paper we propose a mathematical model for describing the viscous inhomogeneous fluid flow in a canal with flexible walls. We present the results of modeling of a blood vessel aneurysm, and the flow of admixture inside the vessel.
About the Authors
D. A. DolgovRussian Federation
Dmitry A. Dolgov – post-graduate student at the Department of Computational Mathematics
Yu. N. Zakharov
Russian Federation
Yury N. Zakharov – Doctor of Physics and Mathematics, Professor at the Department of Computational Mathematics
References
1. Белоцерковский О. М. Численное моделирование в механике сплошных сред. М.: Наука, 1984. 520 с.
2. Яненко Н. Н. Метод дробных шагов решения многомерных задач математической физики. Новосибирск.: Наука, 1967. 197 с.
3. Black M. M., Howard I. C., Huang X., Patterson E. A. A three-dimensional analysis of a bioprosthetic heart valve // J. Biomech. 1991. 24(9). P. 793 – 801.
4. Boyce E. G. Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions // International Journal for Numerical Methods in Biomedical Engineering. 2011. 1 – 29.
5. Fai T. G., Boyce E. G., Mori Y., Peskin C. S. Immersed boundary method for variable viscosity and variable density problems using fast constant-coefficient linear solvers I: Numerical method and results // SIAM Journal on Scientific Computing. 2013. 35(5). B1132 – B1161.
6. Geidarov N. A., Zakharov Y. N., Shokin Yi. I. Solution of the problem of viscous fluid flow with a given pressure differential // Russian Journal of Numerical Analysis and Mathematical Modeling. 2011. V. 26. № 1. P. 39 – 48.
7. Gummel E. E., Milosevic H., Ragulin V. V., Zakharov Y. N., Zimin A. I. Motion of viscous inhomogeneous incompressible fluid of variable viscosity // Zbornik radova konferencije MIT 2013. Beograd. 2014. 760 p. (Proceedings of International Conference “Mathematical and Informational Technologies MIT-2013” Врнячка Баня, Сербия, Будва, Черногория, 5.09.2013 – 14.09.2013). Kosovska Mitrovica. 2014. P. 267 – 274.
8. Jian D., Robert D. G., Aaron L. F. An immersed boundary method for two-fluid mixtures // Journal of Computational Physics. 2014. Volume 262. P. 231 – 243.
9. Lee P., Boyce E. G., Peskin C. S. The immersed boundary method for advection-electrodiffusion with implicit timestepping and local mesh refinement // Journal of computational physics. 2010. Volume 229. P. 5208 – 5227.
10. Ma X., Gao H., Boyce E. G., Berry C., Luo X. Image-based fluid–structure interaction model of the human mitral valve // Computers & Fluids. 2013. 71. P. 417 – 425.
11. Milosevic H., Gaydarov N. A., Zakharov Y. N. Model of incompressible viscous fluid flow driven by pressure difference in a given channel // International Journal of Heat and Mass Transfer. 2013. July. Vol. 62. P. 242 – 246.
12. Peskin C. S. Numerical Analysis of Blood Flow in the Heart // JC. 1977. 25. P. 220 – 252.
13. Peskin C. S. The immersed boundary method // Acta Numerica. 2002. 11. P. 479 – 517
14. Pilhwa L., Boyce E. G., Peskin C. S., The immersed boundary method for advection-electrodiffusion with implicit timestepping and local mesh refinement // Comput Phys. 2010. July 1. 229(13).
15. Taylor C. A., Hughes T. J. R., Zarins C. K. Finite Element Modeling of Blood Flow in Arteries // Computer Methods in Applied Mechanics and Engineering. 1998. Vol. 158. P. 155 – 196.
16. Yoganathan A. P., He Z. M., Jones S. C. Fluid mechanics of heart valves // Annu. Rev. Biomed Eng. 2004. Vol. 6. P. 331 – 362.
17. Zhang Y, Bajaj C. Finite element meshing for cardiac analysis // ICES Technical Report. 2004. Р. 4 – 26.
Review
For citations:
Dolgov D.A., Zakharov Yu.N. MODELLING OF VISCOUS INHOMOGENEOUS FLUID FLOW IN LARGE BLOOD VESSELS. SibScript. 2015;1(2-1):30-34. (In Russ.)