Abstract:
Some exact analytical solutions of the quasi-onedimensional hemodynamic equations in the contracting or expanding vessel are considered in the article. Such equations appear in the modeling of lymph flow in the lymphatic system. Solutions of the linearised problem in the case of periodical changing of the vessel lumen with small amplitude are presented. Also the solution of the not linear problem is obtained in the case when crosssection area depends only on time. Analytical solutions are reproduced numerically.
Citation:
A. S. Mozokhina, S. I. Mukhin, “Some exact solutions of the problem of liquid flow in the contracting or expanding vessel”, Mat. Model., 31:3 (2019), 124–140; Math. Models Comput. Simul., 11:6 (2019), 894–904
\Bibitem{MozMuk19}
\by A.~S.~Mozokhina, S.~I.~Mukhin
\paper Some exact solutions of the problem of liquid flow in the contracting or expanding vessel
\jour Mat. Model.
\yr 2019
\vol 31
\issue 3
\pages 124--140
\mathnet{http://mi.mathnet.ru/mm4059}
\crossref{https://doi.org/10.1134/S0234087919030092}
\elib{https://elibrary.ru/item.asp?id=37180442}
\transl
\jour Math. Models Comput. Simul.
\yr 2019
\vol 11
\issue 6
\pages 894--904
\crossref{https://doi.org/10.1134/S2070048219060140}
Linking options:
https://www.mathnet.ru/eng/mm4059
https://www.mathnet.ru/eng/mm/v31/i3/p124
This publication is cited in the following 8 articles:
A. Yu. Morozov, D. L. Reviznikov, “Adaptive interpolation algorithm on sparse meshes for numerical integration of systems of ordinary differential equations with interval uncertainties”, Differ. Equ., 57:7 (2021), 947–958
S. V. Meleshko, E. Shultz, “Application of the method of differential constraints to systems of equations written in Riemann invariants”, J. Appl. Mech. Tech. Phys., 62:3 (2021), 351–360
N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Numerical modelling of the transition of infected cells and virions between two lymph nodes in a stochastic model of HIV-1 infection”, Russ. J. Numer. Anal. Math. Model, 36:5 (2021), 293–302
S. V. Meleshko, S. Moyo, S. V. Sukhinin, “Sedov type solution of the equations of hydraulic longitudinal waves”, Int. J. Non-Linear Mech., 131 (2021), 103674
N. V. Pertsev, “Application of Differential Equations with Variable Delay in the Compartmental Models of Living Systems”, J. Appl. Ind. Math., 15:3 (2021), 466
A. Yu. Morozov, A. A. Zhuravlev, D. L. Reviznikov, “Analysis and optimization of an adaptive interpolation algorithm for the numerical solution of a system of ordinary differential equations with interval parameters”, Differ. Equ., 56:7 (2020), 935–949
A. Mozokhina, G. Lobov, “Simulation of lymph flow with consideration of natural gravity force influence”, International Conference Mathematical Modelling in Biomedicine 2019, Itm Web of Conferences, 31, eds. V. Volpert, F. Syomin, EDP Sciences, 2020, 01003
A. S. Mozokhina, S. I. Mukhin, G. I. Lobov, “Pump eflciency of lymphatic vessels: numeric estimation”, Russ. J. Numer. Anal. Math. Model, 34:5 (2019), 261–268
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