<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">kemsu</journal-id><journal-title-group><journal-title xml:lang="ru">СибСкрипт</journal-title><trans-title-group xml:lang="en"><trans-title>SibScript</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2949-2122</issn><issn pub-type="epub">2949-2092</issn><publisher><publisher-name>Kemerovo State University</publisher-name></publisher></journal-meta><article-meta><article-id custom-type="elpub" pub-id-type="custom">kemsu-1246</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Математика</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MATHEMATICS</subject></subj-group></article-categories><title-group><article-title>МОДЕЛИРОВАНИЕ ДВИЖЕНИЯ ВЯЗКОЙ НЕОДНОРОДНОЙ ЖИДКОСТИ В КРУПНЫХ КРОВЕНОСНЫХ СОСУДАХ</article-title><trans-title-group xml:lang="en"><trans-title>MODELLING OF VISCOUS INHOMOGENEOUS FLUID FLOW IN LARGE BLOOD VESSELS</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Долгов</surname><given-names>Д. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Dolgov</surname><given-names>D. A.</given-names></name></name-alternatives><bio xml:lang="ru"/><bio xml:lang="en"/><email xlink:type="simple">zaxarovyn@rambler.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Захаров</surname><given-names>Ю. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Zakharov</surname><given-names>Yu. N.</given-names></name></name-alternatives><bio xml:lang="ru"/><bio xml:lang="en"/><email xlink:type="simple">zaxarovyn@rambler.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru">Кемеровский государственный университет<country>Россия</country></aff><aff xml:lang="en">Kemerovo State University<country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2015</year></pub-date><pub-date pub-type="epub"><day>23</day><month>03</month><year>2016</year></pub-date><volume>1</volume><issue>2-1</issue><fpage>30</fpage><lpage>34</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Долгов Д.А., Захаров Ю.Н., 2015</copyright-statement><copyright-year>2015</copyright-year><copyright-holder xml:lang="ru">Долгов Д.А., Захаров Ю.Н.</copyright-holder><copyright-holder xml:lang="en">Dolgov D.A., Zakharov Y.N.</copyright-holder><license license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.sibscript.ru/jour/article/view/1246">https://www.sibscript.ru/jour/article/view/1246</self-uri><abstract><p>В работе рассматривается математическая модель, описывающая течение неоднородной несжимаемой жидкости с переменной вязкостью в канале с гибкими стенками, а также метод ее численного решения. Приведены результаты моделирования аневризмы стенки кровеносного сосуда, а также движения примеси в нем.</p></abstract><trans-abstract xml:lang="en"><p>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.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>вязкая неоднородная жидкость</kwd><kwd>аневризма сосуда</kwd><kwd>метод погруженной границы</kwd></kwd-group><kwd-group xml:lang="en"><kwd>viscous inhomogeneous fluid</kwd><kwd>aneurysm of blood vessel</kwd><kwd>immersed boundary method.</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Белоцерковский О. М. Численное моделирование в механике сплошных сред. М.: Наука, 1984. 520 с.</mixed-citation><mixed-citation xml:lang="en">Белоцерковский О. М. Численное моделирование в механике сплошных сред. М.: Наука, 1984. 520 с.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Яненко Н. Н. Метод дробных шагов решения многомерных задач математической физики. Новосибирск.: Наука, 1967. 197 с.</mixed-citation><mixed-citation xml:lang="en">Яненко Н. Н. Метод дробных шагов решения многомерных задач математической физики. Новосибирск.: Наука, 1967. 197 с.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">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.</mixed-citation><mixed-citation xml:lang="en">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.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">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.</mixed-citation><mixed-citation xml:lang="en">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.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">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.</mixed-citation><mixed-citation xml:lang="en">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.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">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.</mixed-citation><mixed-citation xml:lang="en">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.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">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.</mixed-citation><mixed-citation xml:lang="en">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.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">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.</mixed-citation><mixed-citation xml:lang="en">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.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">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.</mixed-citation><mixed-citation xml:lang="en">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.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Ma X., Gao H., Boyce E. G., Berry C., Luo X. Image-based fluid–structure interaction model of the human mitral valve // Computers &amp; Fluids. 2013. 71. P. 417 – 425.</mixed-citation><mixed-citation xml:lang="en">Ma X., Gao H., Boyce E. G., Berry C., Luo X. Image-based fluid–structure interaction model of the human mitral valve // Computers &amp; Fluids. 2013. 71. P. 417 – 425.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">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.</mixed-citation><mixed-citation xml:lang="en">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.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Peskin C. S. Numerical Analysis of Blood Flow in the Heart // JC. 1977. 25. P. 220 – 252.</mixed-citation><mixed-citation xml:lang="en">Peskin C. S. Numerical Analysis of Blood Flow in the Heart // JC. 1977. 25. P. 220 – 252.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Peskin C. S. The immersed boundary method // Acta Numerica. 2002. 11. P. 479 – 517</mixed-citation><mixed-citation xml:lang="en">Peskin C. S. The immersed boundary method // Acta Numerica. 2002. 11. P. 479 – 517</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">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).</mixed-citation><mixed-citation xml:lang="en">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).</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">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.</mixed-citation><mixed-citation xml:lang="en">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.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Yoganathan A. P., He Z. M., Jones S. C. Fluid mechanics of heart valves // Annu. Rev. Biomed Eng. 2004. Vol. 6. P. 331 – 362.</mixed-citation><mixed-citation xml:lang="en">Yoganathan A. P., He Z. M., Jones S. C. Fluid mechanics of heart valves // Annu. Rev. Biomed Eng. 2004. Vol. 6. P. 331 – 362.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Zhang Y, Bajaj C. Finite element meshing for cardiac analysis // ICES Technical Report. 2004. Р. 4 – 26.</mixed-citation><mixed-citation xml:lang="en">Zhang Y, Bajaj C. Finite element meshing for cardiac analysis // ICES Technical Report. 2004. Р. 4 – 26.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
