NUMERICAL SIMULATION OF BLOOD FLOW IN A BLOOD VESSEL

Aleksandr N. Tynda, Anastasiya A. Pivkina

Abstract


The paper proposes a finite-difference method for solving a boundary value problem for a hyperbolic equation describing the movement of blood in a blood vessel. The stability conditions of the method are given, and numerical results are presented. The method allows to track the amplitude and frequency of heartbeats in various modes, and a numerical model can be used in the study of atrial fibrillation.


Keywords


nonlinear hyperbolic PDE; hydrodynamics of blood circulation; finite-difference method

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References


Hydrodynamics of blood circulation: Collection of Scientific Paper // editor S.A. Regiger. - Moscow, Mir, 1971.

Polyanin A.D., Zaitsev V.F. Handbook of Nonlinear Equations of Mathematical Physics: Exact Solutions. Moscow, Fizmatlit, 2002.

Tynda A.N., Krevchik V.D., Gorbatov A.V. Numerical Implementation of a Model of Blood Flow in a Blood Vessel. Mathematical and computer modeling of natural science and social problems: collection of paper, Penza, PSU, 2015, pp. 121-125.

Kalitkin N.N. Numerical Methods. Moscow, Nauka, 1978.

Samarsky A.A. Introduction to the Theory of Difference Schemes. Moscow, Nauka, 1971.


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