This paper provides new results of consistence and convergence of the lumped parameters (ODE models) toward one-dimensional (hyperbolic or parabolic) models for blood flow. Indeed, lumped parameter models (exploiting the electric circuit analogy for the circulatory system) are shown to discretize continuous 1D models at first order in space. We derive the complete set of equations useful for the blood flow networks, new schemes for electric circuit analogy, the stability criteria that guarantee the convergence, and the energy estimates of the limit 1D equations.
Mots-clés : multiscale modelling, parabolic equations, hyperbolic systems, lumped parameters models, blood flow modelling
@article{M2AN_2004__38_4_613_0,
author = {Mili\v{s}i\'c, Vuk and Quarteroni, Alfio},
title = {Analysis of lumped parameter models for blood flow simulations and their relation with {1D} models},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {613--632},
publisher = {EDP-Sciences},
volume = {38},
number = {4},
year = {2004},
doi = {10.1051/m2an:2004036},
mrnumber = {2087726},
zbl = {1079.76053},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2004036/}
}
TY - JOUR AU - Milišić, Vuk AU - Quarteroni, Alfio TI - Analysis of lumped parameter models for blood flow simulations and their relation with 1D models JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 613 EP - 632 VL - 38 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2004036/ DO - 10.1051/m2an:2004036 LA - en ID - M2AN_2004__38_4_613_0 ER -
%0 Journal Article %A Milišić, Vuk %A Quarteroni, Alfio %T Analysis of lumped parameter models for blood flow simulations and their relation with 1D models %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 613-632 %V 38 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2004036/ %R 10.1051/m2an:2004036 %G en %F M2AN_2004__38_4_613_0
Milišić, Vuk; Quarteroni, Alfio. Analysis of lumped parameter models for blood flow simulations and their relation with 1D models. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 4, pp. 613-632. doi : 10.1051/m2an:2004036. http://www.numdam.org/articles/10.1051/m2an:2004036/
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