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.

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

QUARTERONI, ALFIO MARIA
2004-01-01

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.
2004
Blood flow modelling, Hyperbolic systems, Lumped parameters models, Multiscale modelling, Parabolic equations
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/513844
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