Abstract
The computational modeling of the propagation of pressure and velocity impulses in a blood vessel is presented in linear approximation. Numerical solution of the linear set of hemodynamic equations is formed as the superposition of progressing waves (Riemann’s invariants) satisfying the transport equations. In this connection, the design of the composite difference scheme for the transport equation is emphasized in this article. Calculated examples are presented for the transport equation and the linear hemodynamic equations set. The proposed algorithm can be generalized to the case of the quasi-linear system.
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References
I. V. Ashmetkov, A. Ya. Bunicheva, V. A. Lukshin, et al., Mathematical Simulation of Blood Circulation. Computer Models and Medical Progress (Nauka, Moscow, 2001) [in Russian].
S. I. Mukhin, N. V. Sosnin, A. P. Favorskii, and A. B. Khrulenko, Linear Analysis of Pressure and Velocity Waves in the System of Elastic Vessels (MAKS-Press, Moscow, 2001) [in Russian].
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 2: The Classical Theory of Fields (Nauka, Moscow, 1988; Pergamon, Oxford, 1975).
A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Problems of How to Solve Numerically the Set of Hyperbolic Equations (Fizmatlit, Moscow, 2001) [in Russian].
V. M. Goloviznin and S. A. Karabasov, “Nonlinear Correction of “Kabare” Scheme,” Mat. Model. 10(12), 107–123 (1998).
M. P. Galanin and T. G. Elenina, “Difference Schemes Testing for Linear Transport Equation,” Preprint No. 40, Keldysh Institute of Applied Mathematics (IPM im. M.V. Keldysha RAN, Moscow, 1999).
M. P. Galanin and T. G. Elenina, “Nonlinear Monotonization of Difference Schemes for Linear Transport Equation,” Preprint No. 44, Keldysh Institute of Applied Mathematics (IPM im. M.V. Keldysha RAN, Moscow, 1999).
A. P. Favorskii, N. N. Tyurina, M. A. Tygliyan, and A. P. Babii, Numerical Simulation of Hemodynamical Pulses Propagation (MAKS-Press, Moscow, 2008) [in Russian].
A. A. Samarskii and Yu. P. Popov, Difference Methods for Solving the Gas Dynamics Problems (Nauka, Moscow, 1992) [in Russian].
A. A. Samarskii, Theory of Difference Schemes (Nauka, Moscow, 1989) [in Russian].
A. A. Samarskii and A. V. Gulin, Numerical Methods of Mathematical Physics (Nauchnyi Mir, Moscow, 2000) [in Russian].
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Original Russian Text © A.P. Favorskii, M.A. Tygliyan, N.N. Tyurina, A.M. Galanina, V.A. Isakov, 2009, published in Matematicheskoe Modelirovanie, 2009, Vol. 21, No. 12, pp. 21–34.
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Favorskii, A.P., Tygliyan, M.A., Tyurina, N.N. et al. Computational modeling of the propagation of hemodynamic impulses. Math Models Comput Simul 2, 470–481 (2010). https://doi.org/10.1134/S207004821004006X
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DOI: https://doi.org/10.1134/S207004821004006X