Geodesic
Computational modeling of hemodynamic impulses propagation
Matematičeskoe modelirovanie, Tome 21 (2009) no. 12, pp. 21-34 
A. P. Favorskiy; M. A. Tygliyan; N. N. Tyurina; N. N. Galanina; V. A. Isakov. Computational modeling of hemodynamic impulses propagation. Matematičeskoe modelirovanie, Tome 21 (2009) no. 12, pp. 21-34. http://geodesic.mathdoc.fr/item/MM_2009_21_12_a1/
@article{MM_2009_21_12_a1,
     author = {A. P. Favorskiy and M. A. Tygliyan and N. N. Tyurina and N. N. Galanina and V. A. Isakov},
     title = {Computational modeling of hemodynamic impulses propagation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {21--34},
     year = {2009},
     volume = {21},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2009_21_12_a1/}
}
TY  - JOUR
AU  - A. P. Favorskiy
AU  - M. A. Tygliyan
AU  - N. N. Tyurina
AU  - N. N. Galanina
AU  - V. A. Isakov
TI  - Computational modeling of hemodynamic impulses propagation
JO  - Matematičeskoe modelirovanie
PY  - 2009
SP  - 21
EP  - 34
VL  - 21
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/MM_2009_21_12_a1/
LA  - ru
ID  - MM_2009_21_12_a1
ER  - 
%0 Journal Article
%A A. P. Favorskiy
%A M. A. Tygliyan
%A N. N. Tyurina
%A N. N. Galanina
%A V. A. Isakov
%T Computational modeling of hemodynamic impulses propagation
%J Matematičeskoe modelirovanie
%D 2009
%P 21-34
%V 21
%N 12
%U http://geodesic.mathdoc.fr/item/MM_2009_21_12_a1/
%G ru
%F MM_2009_21_12_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

The computational modeling of the pressure and velocity impulses propagation in a blood vessel is presented in linear approximation. Numerical solution of the linear set of hemodynamic equations is formed as superposition of progressing waves (Riemann's invariants) satisfying transport equations. In this connection, design of composite difference scheme for transport equation is emphasized in this article. The examples of calculation are presented for transport equation and linear hemodynamic equations set. The proposed algorithm can be generalized to quasi-linear system case.

[1] Ashmetkov I. V., Bunicheva A. Ya., Lukshin V. A., Koshelev V. B., Mukhin S. I., Sosnin N. V., Favorskii A. P., Khrulenko A. B., Matematicheskoe modelirovanie krovoobrascheniya. Kompyuternye modeli i progress meditsiny, Nauka, M., 2001, 194–218

[2] Mukhin S. I., Sosnin N. V., Favorskii A. P., Khrulenko A. B., Lineinyi analiz voln davleniya i skorosti v sisteme elastichnykh sosudov, preprint, MAKS-Press, M., 2001, 37 pp.

[3] Landau L. D., Lifshits E. M., Gidrodinamika, Nauka, M., 1988, 736 pp. | MR

[4] Kulikovskii A. G., Pogorelov N. V., Semenov A. Yu., Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2001, 607 pp. | MR

[5] Goloviznin V. M., Karabasov S. A., “Nelineinaya korrektsiya skhemy ‘Kabare’ ”, Mat. modelirovanie, 10:12 (1998), 107–123

[6] Galanin M. P., Elenina T. G., Testirovanie raznostnykh skhem dlya lineinogo uravneniya perenosa, preprint No 40, IPM im. M. V. Keldysha RAN, M., 1999, 42 pp.

[7] Galanin M. P., Elenina T. G., Nelineinaya monotonizatsiya raznostnykh skhem dlya lineinogo uravneniya perenosa, preprint No 44, IPM im. M. V. Keldysha RAN, M., 1999, 30 pp.

[8] Favorskii A. P., Tyurina N. N., Tygliyan M. A., Babii A. P., Chislennoe modelirovanie rasprostraneniya gemodinamicheskikh impulsov, preprint, MAKS-Press, M., 2008, 24 pp.

[9] Samarskii A. A., Popov Yu. P., Raznostnye metody resheniya zadach gazovoi dinamiki, Nauka, M., 1992, 422 pp. | MR

[10] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989, 616 pp. | MR

[11] Samarskii A. A., Gulin A. V., Chislennye metody matematicheskoi fiziki, Nauchnyi mir, M., 2000, 315 pp.