# Analysis of lumped parameter models for blood flow simulations and their relation with 1D models

- Volume: 38, Issue: 4, page 613-632
- ISSN: 0764-583X

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topMilišić, Vuk, and Quarteroni, Alfio. "Analysis of lumped parameter models for blood flow simulations and their relation with 1D models." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 38.4 (2004): 613-632. <http://eudml.org/doc/244861>.

@article{Milišić2004,

abstract = {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.},

author = {Milišić, Vuk, Quarteroni, Alfio},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {multiscale modelling; parabolic equations; hyperbolic systems; lumped parameters models; blood flow modelling; convergence; electric circuit analogy; stability; energy estimates},

language = {eng},

number = {4},

pages = {613-632},

publisher = {EDP-Sciences},

title = {Analysis of lumped parameter models for blood flow simulations and their relation with 1D models},

url = {http://eudml.org/doc/244861},

volume = {38},

year = {2004},

}

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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2004

PB - EDP-Sciences

VL - 38

IS - 4

SP - 613

EP - 632

AB - 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.

LA - eng

KW - multiscale modelling; parabolic equations; hyperbolic systems; lumped parameters models; blood flow modelling; convergence; electric circuit analogy; stability; energy estimates

UR - http://eudml.org/doc/244861

ER -

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