Partitioned Analysis for Dimensionally-Heterogeneous Hydraulic Networks

Leiva, Jorge S.; Blanco, Pablo; Buscaglia, Gustavo C.

doi:10.1137/100809301

Cited by 25 publications

(24 citation statements)

References 20 publications

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“…In [110], a non-linear system of equations involving the interface unknowns related to the pressure and the flow rate has been derived for a general network composed by "complex" (3D or 2D) and "simple" (1D or 0D) models, with an arbitrary connectivity. Then, the authors proposed to apply to this interface equation either the Broyden method or the Newton one used in combination with GMRes -see also Sect.…”

Section: Further Developments and Commentsmentioning

confidence: 99%

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

169

157

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This review paper addresses the so called geometric multiscale approach for the numerical simulation of blood flow problems, from its origin (that we can collocate in the second half of '90s) to our days. By this approach the blood fluid-dynamics in the whole circulatory system is described mathematically by means of heterogeneous featuring different degree of detail and different geometric dimension that interact together through appropriate interface coupling conditions.Our review starts with the introduction of the stand-alone problems, namely the 3D fluidstructure interaction problem, its reduced representation by means of 1D models, and the so-called lumped parameters (aka 0D) models, where only the dependence on time survives. We then address specific methods for stand-alone 3D models when the available boundary data are not enough to ensure the mathematical well posedness. These so-called "defective problems" naturally arise in practical applications of clinical relevance but also because of the interface coupling of heterogeneous problems that are generated by the geometric multiscale process. We also describe specific issues related to the boundary treatment of reduced models, particularly relevant to the geometric multiscale coupling. Next, we detail the most popular numerical algorithms for the solution of the coupled problems. Finally, we review some of the most representative works -from different research groups -which addressed the geometric multiscale approach in the past years.A proper treatment of the different scales relevant to the hemodynamics and their interplay is essential for the accuracy of numerical simulations and eventually for their clinical impact. This paper aims at providing a state-of-the-art picture of these topics, where the gap between theory and practice demands rigorous mathematical models to be reliably filled.

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Section: Further Developments and Commentsmentioning

confidence: 99%

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

169

157

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“…Regarding the description of the numerical methodologies to address the solution of the 3D Navier-Stokes equations in compliant domains and its coupling with the 1D model the reader is referred to [7,8,29]. Here we provide a brief account of the domain decomposition strategy employed to iteratively couple the 1D and 3D models.…”

Section: Dimensionally-heterogeneous Modelingmentioning

confidence: 99%

“…Figure 10 shows the embedding of the 3D geometry within the 1D model presented in Section 4. The decomposition approach described in [29] amounts to define at each interface the coupling degrees of freedom, namely flow rate and pressure (Q i , P i ), i = 1, . .…”

Section: Dimensionally-heterogeneous Modelingmentioning

confidence: 99%

Mathematical Model of Blood Flow in an Anatomically Detailed Arterial Network of the Arm

2013

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Abstract.A distributed-parameter (one-dimensional) anatomically detailed model for the arterial network of the arm is developed in order to carry out hemodynamics simulations. This work focuses on the specific aspects related to the model set-up. In this regard, stringent anatomical and physiological considerations have been pursued in order to construct the arterial topology and to provide a systematic estimation of the involved parameters. The model comprises 108 arterial segments, with 64 main arteries and 44 perforator arteries, with lumen radii ranging from 0.24 cm -axillary artery-to 0.018 cmperforator arteries. The modeling of blood flow in deformable vessels is governed by a well-known set of hyperbolic partial differential equations that accounts for mass and momentum conservation and a constitutive equation for the arterial wall. The variational formulation used to solve the problem and the related numerical approach are described. The model rendered consistent pressure and flow rate outputs when compared with patient records already published in the literature. In addition, an application to dimensionally-heterogeneous modeling is presented in which the developed arterial network is employed as an underlying model for a three-dimensional geometry of a branching point to be embedded in order to perform local analyses.Mathematics Subject Classification. 76Z05, 92C10, 92C30.

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“…However, a better solution in the same direction is to use a Broyden approach for the update of the Jacobian matrix at each nonlinear Richardson iteration. Indeed, this approach has been proven to perform successfully for cardiovascular applications made of networks of 1-D models [4,31] and for heterogeneous networks of rigid fluid problems [28], requiring just a cheap evaluation of the global residuals vector of the interface problem.…”

Section: Numerical Approachmentioning

confidence: 99%

Implicit Coupling of One-Dimensional and Three-Dimensional Blood Flow Models with Compliant Vessels

Malossi

Blanco

Crosetto

et al. 2013

Multiscale Model. Simul.

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Abstract. The blood flow in arterial trees in the cardiovascular system can be simulated with the help of different models, depending on the outputs of interest and the desired degree of accuracy. In particular, one-dimensional fluid-structure interaction models for arteries are very effective in reproducing physiological pressure wave propagation and in providing quantities like pressure and velocity, averaged on the cross section of the arterial lumen. In locations where onedimensional models cannot capture the complete flow dynamics, e.g., in the presence of stenoses and aneurysms or other strong geometric perturbations, three-dimensional coupled fluid-structure interaction models are necessary to evaluate more accurately, for instance, critical factors responsible for pathologies which are associated with hemodynamics, such as wall shear stress. In this work we formalize and investigate the geometrical multiscale problem, where heterogeneous fluid-structure interaction models for arteries are implicitly coupled. We introduce new coupling algorithms, describe their implementation, and investigate on simple geometries the numerical reflections that occur at the interface between the heterogeneous models. We also simulate on a supercomputer a threedimensional abdominal aorta under physiological conditions, coupled with up to six one-dimensional models representing the surrounding arterial branches. Finally, we compare CPU times and number of coupling iterations for different algorithms and time discretizations.

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Partitioned Analysis for Dimensionally-Heterogeneous Hydraulic Networks

Cited by 25 publications

References 20 publications

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Mathematical Model of Blood Flow in an Anatomically Detailed Arterial Network of the Arm

Implicit Coupling of One-Dimensional and Three-Dimensional Blood Flow Models with Compliant Vessels

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