Numerical treatment of boundary conditions to replace lateral branches in hemodynamics

Porpora, Azzurra; Zunino, Paolo; Vergara, Christian; Piccinelli, Marina

doi:10.1002/cnm.2488

Cited by 24 publications

(24 citation statements)

References 44 publications

(110 reference statements)

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“…In addition, it deals with non standard bilinear forms that require ad hoc implementation. Two dimensional numerical results shown in [209] highlight the accuracy of the method, whereas three-dimensional results reported in [158] demonstrate that this is an effective approach for real applications. A similar approach has been extended to fulfill the mean pressure condition (20) and the FSI case in [198].…”

Section: Further Developments and Commentsmentioning

confidence: 89%

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

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

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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: 89%

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

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

Self Cite

169

157

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“…In the last years, different variants of Equation 11 have been proposed in the literature in the context of physiological flows, all of them independent from the original work. 14 In particular, the choice u 0 = 0 has been widely used in both hemodynamics [16][17][18][19] and respiratory regimes. 20,21 While ⩾ 1 assures energy stability, the numerical results of Esmaily et al 18 showed that decreasing the value of the parameter up to = 0.4 still yields stable solutions in the case of blood flow, thus suggesting that the lack of stability (and hence the magnitude of the required stabilization) depends on the considered flow regime.…”

Section: Velocity-penalization Methodsmentioning

confidence: 99%

“…23 A uniqueness result in the case of small data for ⩾ 1 can be found in Braack and Mucha. 24 It is worth mentioning that, for sufficiently small data, the analysis of Baffico et al 25 A further variant was proposed by Porpora et al, 19 where u 0 was taken as a plug profile for a given flow rate at the inlet of the ascending aorta.…”

Section: Velocity-penalization Methodsmentioning

confidence: 99%

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Benchmark problems for numerical treatment of backflow at open boundaries

Bertoglio

Caiazzo

Bazilevs

et al. 2017

Numer Methods Biomed Eng

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In computational fluid dynamics, incoming velocity at open boundaries, or backflow, often yields unphysical instabilities already for moderate Reynolds numbers. Several treatments to overcome these backflow instabilities have been proposed in the literature. However, these approaches have not yet been compared in detail in terms of accuracy in different physiological regimes, in particular because of the difficulty to generate stable reference solutions apart from analytical forms. In this work, we present a set of benchmark problems in order to compare different methods in different backflow regimes (with a full reversal flow and with propagating vortices after a stenosis). The examples are implemented in FreeFem++, and the source code is openly available, making them a solid basis for future method developments.

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“…Then it leads to difficulties that we will investigate in this paper. Although this basic form is often used (see, e.g., [40,58,74,75,22,62,31,55,1]), some numerical studies (see, e.g., [40,31]) have pointed out that the stability is not guaranteed when dealing with realistic physiological or physical parameters.…”

Section: Introductionmentioning

confidence: 99%

Artificial boundaries and formulations for the incompressible Navier–Stokes equations: applications to air and blood flows

Fouchet-Incaux

2014

SeMA

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We deal with numerical simulations of incompressible Navier-Stokes equations in truncated domain. In this context, the formulation of these equations has to be selected carefully in order to guarantee that their associated artificial boundary conditions are relevant for the considered problem. In this paper, we review some of the formulations proposed in the literature, and their associated boundary conditions. Some numerical results linked to each formulation are also presented. We compare different schemes, giving successful computations as well as problematic ones, in order to better understand the difference between these schemes and their behaviours dealing with systems involving Neumann boundary conditions. We also review two stabilization methods which aim at suppressing the instabilities linked to these natural boundary conditions.

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Numerical treatment of boundary conditions to replace lateral branches in hemodynamics

Cited by 24 publications

References 44 publications

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

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

Benchmark problems for numerical treatment of backflow at open boundaries

Artificial boundaries and formulations for the incompressible Navier–Stokes equations: applications to air and blood flows

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