Fluid–Structure Interaction in Hemodynamics: Modeling, Analysis, and Numerical Simulation

Čanić, Sunčica; Muha, Boris; Bukač, Martina

doi:10.1007/978-3-0348-0822-4_2

Cited by 14 publications

(13 citation statements)

References 112 publications

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“…An artery is a large blood vessel whose thickness is negligible in front of the radius of its section. For more details about the modelling of such systems we refer to [27,29,5] and the references therein.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Maximal-in-Time Existence and Uniqueness of Strong Solution of a 3D Fluid-Structure Interaction Model

Maity¹,

Raymond²,

Roy³

2020

SIAM J. Math. Anal.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Maximal-in-Time Existence and Uniqueness of Strong Solution of a 3D Fluid-Structure Interaction Model

Maity¹,

Raymond²,

Roy³

2020

SIAM J. Math. Anal.

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“…and equations ( 10); (2) to (7) after time discretisation (omitting the subscript n + 1 of u n+1 and d n+1 for notation simplicity).…”

Section: Time Discretisation and The Piecewise Control Problemmentioning

confidence: 99%

A monolithic one-velocity-field optimal control formulation for fluid-structure interaction problems with large solid deformation

Wang

2021

Preprint

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In this article, we formulate a monolithic optimal control method for general time-dependent Fluid-Structure Interaction (FSI) systems with large solid deformation. We consider a displacement-tracking type of objective with a constraint of the solid velocity, tackle the time-dependent control problems by a piecewise-in-time control, cope with large solid displacement using a one-velocity fictitious domain method, and solve the fully-coupled FSI and the corresponding adjoint equations in a monolithic manner. We implement the proposed method in the open-source software package FreeFEM++ and assess it by three numerical experiments, in the aspects of stability of the numerical scheme for different regularisation parameters, and efficiency of reducing the objective function with control of the solid velocity.

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“…We denoted by p ref the reference (external) pressure, namely, the pressure at which the displacement of the arterial wall is zero, i.e., the cross-sectional area a D a 0 . For the corresponding nonlinear membrane model see [37].…”

Section: Network Of Open Canalsmentioning

confidence: 99%

Flows on networks: recent results and perspectives

Bressan¹,

Čanić²,

Garavello³

et al. 2014

EMS Surv. Math. Sci.

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158

151

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The broad research thematic of flows on networks was addressed in recent years by many researchers, in the area of applied mathematics, with new models based on partial differential equations. The latter brought a significant innovation in a field previously dominated by more classical techniques from discrete mathematics or methods based on ordinary differential equations. In particular, a number of results, mainly dealing with vehicular traffic, supply chains and data networks, were collected in two monographs: Traffic flow on networks, AIMSciences, Springfield, 2006, and Modeling, simulation, and optimization of supply chains, SIAM, Philadelphia, 2010. The field continues to flourish and a considerable number of papers devoted to the subject is published every year, also because of the wide and increasing range of applications: from blood flow to air traffic management. The aim of the present survey paper is to provide a view on a large number of themes, results and applications related to this broad research direction. The authors cover different expertise (modeling, analysis, numeric, optimization and other) so to provide an overview as extensive as possible. The focus is mainly on developments which appeared subsequently to the publication of the aforementioned books. 1 The author acknowledges partial support of 2013 GNAMPA project "Leggi di Conservazione: Teoria e Applicazioni". 2 The author acknowledges support by BMBF KinOpt, DFG Cluster of Excellence EXC128 and DAAD 54365630, 55866082. 3 The author acknowledges partial support of NSF Research Network in the Mathematical Sciences KI-Net "Kinetic description of emerging challenges in multiscale problems of natural sciences" Grant # : 1107444.

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Fluid–Structure Interaction in Hemodynamics: Modeling, Analysis, and Numerical Simulation

Cited by 14 publications

References 112 publications

Maximal-in-Time Existence and Uniqueness of Strong Solution of a 3D Fluid-Structure Interaction Model

Maximal-in-Time Existence and Uniqueness of Strong Solution of a 3D Fluid-Structure Interaction Model

A monolithic one-velocity-field optimal control formulation for fluid-structure interaction problems with large solid deformation

Flows on networks: recent results and perspectives

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