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

Vuk Milišić; Alfio Quarteroni

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

Abstract

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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.

How to cite

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Milišić, 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 38.4 (2010): 613-632. <http://eudml.org/doc/194230>.

@article{Milišić2010,
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},
keywords = {Multiscale modelling; parabolic equations; hyperbolic systems; lumped parameters models; blood flow modelling.; convergence; electric circuit analogy; stability; energy estimates},
language = {eng},
month = {3},
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/194230},
volume = {38},
year = {2010},
}

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
DA - 2010/3//
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/194230
ER -

References

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