Geodesic
Analysis of lumped parameter models for blood flow simulations and their relation with 1D models
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 4, pp. 613-632

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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.

DOI : 10.1051/m2an:2004036
Classification : 35L50, 35M20, 47H10, 65L05, 76Z05
Keywords: multiscale modelling, parabolic equations, hyperbolic systems, lumped parameters models, blood flow modelling 
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     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: Mathematical Modelling and Numerical Analysis },
     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://geodesic.mathdoc.fr/articles/10.1051/m2an:2004036/}
}
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Milišić, Vuk; Quarteroni, Alfio. Analysis of lumped parameter models for blood flow simulations and their relation with 1D models. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 4, pp. 613-632. doi: 10.1051/m2an:2004036

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