All issues
- 2024 Vol. 16
- 2023 Vol. 15
- 2022 Vol. 14
- 2021 Vol. 13
- 2020 Vol. 12
- 2019 Vol. 11
- 2018 Vol. 10
- 2017 Vol. 9
- 2016 Vol. 8
- 2015 Vol. 7
- 2014 Vol. 6
- 2013 Vol. 5
- 2012 Vol. 4
- 2011 Vol. 3
- 2010 Vol. 2
- 2009 Vol. 1
The modeling of nonlinear pulse waves in elastic vessels using the Lattice Boltzmann method
pdf (633K)
/ Annotation
List of references:
- Математическаямодель гемодинамики сердечно-сосудистой системы // Дифференц. уравнения. — 1997. — Т. 33. — С. 892–898.
- A mathematical model of the hemodynamics of a cardio-vascular system // Differ. Equ. — 1997. — V. 33. — P. 895–901. — MathSciNet: MR1615495. , , , , , , , .
- Matematicheskaya model’ gemodinamiki serdechno-sosudistoy sistemy // Differents. uravneniya. — 1997. — V. 33. — P. 892–898. — Original Russian paper. — Math-Net: Mi eng/de9478. , , , , , , , .
, , , , , , , . - Анализ и сравнение некоторых аналитических и численных решений задач гемодинамики // Дифференц. уравнения. — 2000. — Т. 36. — С. 919–924.
- Analysis and comparison of some analytic and numerical solutions of hemodynamic problems // Differ. Equ. — 2000. — V. 36. — P. 1021–1026. — DOI: 10.1007/BF02754503. — Math-Net: Mi eng/de10190. — MathSciNet: MR1819596. , , , , .
- Analiz i sravneniye nekotorykh analiticheskikh i chislennykh resheniy zadach gemodinamiki // Differents. uravneniya. — 2000. — V. 36. — P. 919–924. — Original Russian paper. — Math-Net: Mi eng/de10174. , , , , .
, , , , . - Краеваязадача длялинеаризованных гемодинамических уравнений на графе // Дифференц. уравнения. — 2004. — Т. 40. — С. 87–97.
- A Boundary Value Problem for the Linearized Haemodynamic Equations on a Graph // Differ. Equ. — 2004. — V. 40. — P. 94–104. — DOI: 10.1023/B:DIEQ.0000028718.86794.b9. — MathSciNet: MR2167233. , , , .
- Krayevaya zadacha dlya linearizovannykh gemodinamicheskikh uravneniy na grafe // Differents. uravneniya. — 2004. — V. 40. — P. 87–97. — Original Russian paper. — Math-Net: Mi eng/de11007. , , , .
, , , . - Осредненнаянелинейнаямодель гемодинамики на графе сосудов // Дифференц. уравнения. — 2001. — Т. 37. — С. 905—912.
- An Averaged Nonlinear Model of Hemodynamics on the Vessel Graph // Differ. Equ. — 2001. — V. 37. — P. 949–956. — DOI: 10.1023/A:1011905604368. — MathSciNet: MR1887266. , , , .
- Osrednennaya nelineynaya model’ gemodinamiki na grafe sosudov // Differents. uravneniya. — 2001. — V. 37. — P. 905–912. — Original Russian paper. — Math-Net: Mi eng/de10410. , , , .
, , , . - Об эластичности сосудов в одномерных моделях гемодинамики // Ж. вычисл. матем. и матем. физ. — 2015. — Т. 55. — С. 1599— 1610.
- On the elasticity of blood vessels in one-dimensional problems of hemodynamics // Comput. Math. Math. Phys. — 2015. — V. 55. — P. 1567–1578. — DOI: 10.1134/S0965542515090134. — Math-Net: Mi eng/zvmmf10269. — MathSciNet: MR3396534. , , .
- Ob elastichnosti sosudov v odnomernykh modelyakh gemodinamiki // Zh. vychisl. matem. i matem. fiz. — 2015. — V. 55. — P. 1599–1610. — Original Russian paper. , , .
, , . - Современные методы математического моделирования кровотока c помощью осредненных моделей // Компьютерные исследования и моделирование. — 2018. — Т. 10. — С. 581 — 604. — DOI: 10.20537/2076-7633-2018-10-5-581-604.
- Modern methods of mathematical modeling of blood flow using reduced order methods // Computer Research and Modeling. — 2018. — V. 10. — P. 581–604. — in Russian. — DOI: 10.20537/2076-7633-2018-10-5-581-604. .
. - Methods of Blood Flow Modelling // Math. Model. Nat. Phenom. — 2016. — V. 11. — P. 1–25. — DOI: 10.1051/mmnp/201611101. — MathSciNet: MR3452632. , , , , .
- Multiscale hemodynamics using clusters of GPU // Commun. Comput. Phys. — 2011. — V. 11. — P. 48–64. — DOI: 10.4208/cicp.210910.250311a. , , , , .
- Simulation of blood flow using extended Boltzmann kinetic approach // Physica A. — 2006. — V. 362. — P. 174–181. — DOI: 10.1016/j.physa.2005.09.009. — ads: 2006PhyA..362..174C. , , , , , , , , .
- Lattice Boltzmann method for simulating the viscous flow in large distensible blood vessels // Phys. Rev. E. — 2002. — V. 65. — 051925. — DOI: 10.1103/PhysRevE.65.051925. — ads: 2002PhRvE..65e1925F. , , , .
- A framework for comparing vascular hemodynamics at different points in time // Comput. Phys. Comm. — 2019. — V. 235. — P. 1–8. — DOI: 10.1016/j.cpc.2018.05.014. — ads: 2019CoPhC.235....1G. , , .
- One-dimensional models for blood flow in arteries // J. Engng. Maths. — 2003. — V. 47. — P. 251–276. — DOI: 10.1023/B:ENGI.0000007980.01347.29. — MathSciNet: MR2038983. , , .
- A 1D arterial blood flow model incorporating ventricular pressure, aortic valve and regional coronary flow using the locally conservative Galerkin (LCG) method // Commun. in Numer. Meth. in Eng. — 2008. — V. 24. — P. 367–417. — DOI: 10.1002/cnm.1117. — MathSciNet: MR2412048. , .
- On the one-dimensional theory of blood flow in the larger vessels // Math. Biosci. — 1973. — V. 18. — P. 161–170. — DOI: 10.1016/0025-5564(73)90027-8. , .
- Nonlinear pressure–velocity waveforms in large arteries, shock waves and wave separation // Wave Motion. — 2019. — V. 84. — P. 56–67. — DOI: 10.1016/j.wavemoti.2018.09.016. — MathSciNet: MR3873968. .
- Elements of the lattice Boltzmann method II: kinetics and hydrodynamics in one dimension // Commun. in Comput. Phys. — 2007. — V. 2. — P. 196–238. — MathSciNet: MR2303926. , , .
- The Lattice Boltzmann Method. Principles and Practice. — Springer, 2017. — MathSciNet: MR3524989. , , , , , .
- On equations of state in a lattice Boltzmann method // Comput. Math. Appl. — 2009. — V. 58. — P. 965–974. — DOI: 10.1016/j.camwa.2009.02.024. — MathSciNet: MR2548181. , , .
- Criterion of numerical instability of liquid state in LBE simulations // Comput. Math. Appl. — 2010. — V. 59. — P. 2236–2245. — DOI: 10.1016/j.camwa.2009.08.058. — MathSciNet: MR2603032. .
- Thermal lattice Boltzmann method for multiphase flows // Phys. Rev. E. — 2018. — V. 98. — 023308. — DOI: 10.1103/PhysRevE.98.023308. — ads: 2018PhRvE..98b3308K. , , .
- The static elastic properties of 45 human thoracic and 20 abdominal aortas in vitro and the parameters of a new model // J. Biomech. — 1984. — V. 17. — P. 425–435. — DOI: 10.1016/0021-9290(84)90034-4. , , .
- Waves in Fluids. — Cambridge University Press, 1978. — MathSciNet: MR0642980. .
- Endothelial shear stress hemodynamic simulation // Philos. Trans. A: Math. Phys. Eng. Sci. — 2011. — V. 369. — P. 2354–2361. — DOI: 10.1098/rsta.2011.0042. — ads: 2011RSPTA.369.2354M. , , , .
- Structured tree outflow condition for blood flow in larger systemic arteries // Am. J. Physiol. — 1999. — V. 276. — P. H257 — H268. .
- On the lattice Boltzmann method as a computational framework for multiscale hemodynamics // Math. Comp. Model. of Dyn. Syst. — 2014. — V. 20. — P. 470–490. — DOI: 10.1080/13873954.2013.833523. — MathSciNet: MR3212676. , , , , .
- One-dimensional modelling of a vascular network in spacetime variables // J. Engng. Maths. — 2003. — V. 47. — P. 217–250. — DOI: 10.1023/B:ENGI.0000007979.32871.e2. — MathSciNet: MR2038982. , , , .
- Non-reflecting Boundary Conditions for the Lattice Boltzmann Method. — Technical University of Munich, 2013. — MathSciNet: MR2712387. .
- The Lattice Boltzmann Equation: For Complex States of Flowing Matter. — Oxford, 2018. — MathSciNet: MR3793623. .
- Experimental and computational methods in cardiovascular fluid mechanics // Rev. Fluid Mech. — 2004. — V. 36. — P. 197–231. — DOI: 10.1146/annurev.fluid.36.050802.121944. — MathSciNet: MR2062312. — ads: 2004AnRFM..36..197T. , .
- Pulse Wave Propagation in the Arterial Tree // Ann. Rev. of Fluid Mech. — 2011. — V. 43. — P. 467–499. — DOI: 10.1146/annurev-fluid-122109-160730. — MathSciNet: MR2768023. — ads: 2011AnRFM..43..467V. , .
- The arterial Windkessel // Med. Biol. Eng. Comput. — 2009. — V. 47. — P. 131 — 141. — DOI: 10.1007/s11517-008-0359-2. , , .
- Equations of state in a lattice Boltzmann model // Phys. Fluids. — 2006. — V. 18. — 042101. — DOI: 10.1063/1.2187070. — MathSciNet: MR2259275. — ads: 2006PhFl...18d2101Y. , .
- Lattice Boltzmann method for simulations of liquid-vapor thermal flows // Phys. Rev. E. — 2003. — V. 67. — 066711. , .
Indexed in Scopus
Full-text version of the journal is also available on the web site of the scientific electronic library eLIBRARY.RU
The journal is included in the Russian Science Citation Index
The journal is included in the RSCI
International Interdisciplinary Conference "Mathematics. Computing. Education"
Copyright © 2009–2024 Institute of Computer Science