Vidard, M. Owen (2024) Numerical simulations of blood flow and low rank approximation PRE - Research Project, ?? - ??.

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Abstract

We present a 1D mathematical model of blood flow in a vessel, formulated as a nonlinear system of PDEs. A numerical resolution is achieved using "finite volume" (VF) methods ; however, this approach entails high computational costs when simulating a large number of vessels. To enhance efficiency, we use an approximation method called "Dynamical Low Rank" (DLR), which enables to represent the information of large, low-rank matrices with smaller, maximalrank matrices. This requires effective evaluation of the nonlinear term, which we achieve through discret empirical interpolation (DEIM). The results demonstrate that this approach is justified in terms of accuracy and performance when simulations involve many vessels with relatively concentrated characteristic parameters.

Item Type:Thesis (PRE - Research Project)
Uncontrolled Keywords:écoulement sanguin, EDP, volumes finis, DLR, DEIM, erreur, temps de calcul
Subjects:Mathematics and Applications
ID Code:10380
Deposited By:Owen VIDARD
Deposited On:24 sept. 2024 13:09
Dernière modification:24 sept. 2024 13:09

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