Convergence Analysis of a Projection Semi-Implicit Coupling Scheme for Fluid-Structure Interaction Problems

In this paper, we provide a convergence analysis of a projection semi-implicit scheme for the simulation of fluid-structure systems involving an incompressible viscous fluid. The error analysis is performed on a fully discretized linear coupled problem: a finite element approximation and a semi-implicit time-stepping strategy are respectively used for space and time discretization. The fluid is described by the Stokes equations, the structure by the classical linear elastodynamics equations and all changes of geometry are neglected. We derive an error estimate in finite time and we prove that the time discretization error for the coupling scheme is at least $\sqrt{\delta t}$. Finally, some numerical experiments that confirm the theoretical analysis are presented

A time-parallel framework for coupling finite element and lattice Boltzmann methods

International audienceIn this work we propose a new numerical procedure for the simulation of time-dependent problems based on the coupling between the finite element method and the lattice Boltzmann method. The procedure is based on the Parareal paradigm and allows to couple efficiently the two numerical methods, each one working with its own grid size and time-step size. The motivations behind this approach are manifold. Among others, we have that one technique may be more efficient, or physically more appropriate or less memory consuming than the other depending on the target of the simulation and/or on the sub-region of the computational domain. Furthermore, the coupling with finite element method may circumvent some difficulties inherent to lattice Boltzmann discretization, for some domains with complex boundaries, or for some boundary conditions. The theoretical and numerical framework is presented for parabolic equations, in order to describe and validate numerically the methodology in a simple situation

Robin Based Semi-Implicit Coupling in Fluid-Structure Interaction: Stability Analysis and Numerics

International audienceIn this report, we propose a semi-implicit coupling scheme for the numerical simulation of fluid-structure interaction systems involving a viscous incompressible fluid. The scheme is stable irrespectively of the so-called added-mass effect and allows for conservative time-stepping within the structure. The efficiency of the scheme is based on the explicit splitting of the viscous effects and geometrical/convective non-linearities, through the use of the Chorin-Temam projection scheme within the fluid. Stability comes from the implicit pressure-solid coupling and a specific Robin treatment of the explicit viscous-solid coupling, derived from Nitsche's method

Convergence Analysis of a Projection Semi-Implicit Coupling Scheme for Fluid-Structure Interaction Problems

In this paper, we provide a convergence analysis of a projection semi-implicit scheme for the simulation of fluid-structure systems involving an incompressible viscous fluid. The error analysis is performed on a fully discretized linear coupled problem: a finite element approximation and a semi-implicit time-stepping strategy are respectively used for space and time discretization. The fluid is described by the Stokes equations, the structure by the classical linear elastodynamics equations and all changes of geometry are neglected. We derive an error estimate in finite time and we prove that the time discretization error for the coupling scheme is at least $\sqrt{\delta t}$. Finally, some numerical experiments that confirm the theoretical analysis are presented

Convergence analysis of a projection semi-implicit coupling scheme for fluid-structure interaction problems.

International audienceIn this paper, we provide a convergence analysis of a projection semi- implicit scheme for the simulation of fluid-structure systems involving an incom- pressible viscous fluid. The error analysis is performed on a fully discretized linear coupled problem: a finite element approximation and a semi-implicit time-stepping strategy are respectively used for space and time discretization. The fluid is described by the Stokes equations, the structure by the classical linear elastodynamics equations (linearized elasticity, plate or shell models) and all changes of geometry are neglected. We derive an error estimate in finite time and we prove that the time discretization error of the coupling scheme is of order 1/2. Finally, some numerical experiments that confirm the theoretical analysis are presented

Computational analysis of an aortic valve jet with Lagrangian coherent structures

International audienceImportant progress has been achieved in recent years in simulating the fluid-structure interaction around cardiac valves. An important step in making these computational tools useful to clinical practice is the development of postprocessing techniques to extract clinically relevant information from these simulations. This work focuses on flow through the aortic valve and illustrates how the computation of Lagrangian coherent structures can be used to improve insight into the transport mechanics of the flow downstream of the valve, toward the goal of aiding clinical decision making and the understanding of pathophysiology

Geometrical multiscale model of an idealized left ventricle with fluid-structure interaction effects coupled to a one-dimensional viscoelastic arterial network

A geometrical multiscale model for blood flow through an ideal left ventricle and the main arteries is presented. The blood flow in the three-dimensional idealized left ventricle is solved through a monolithic fluid-structure interaction solver. To account for the interaction between the heart and the circulatory system the heart flow is coupled through an ideal valve with a network of viscoelastic one-dimensional models representing the arterial network. The geometrical multiscale approach used in this work is based on the exchange of averaged/integrated quantities between the fluid problems. The peripheral circulation is modelled by zero-dimensional windkessel terminals. We demonstrate that the geometrical multiscale model is (i) highly modular in that component models can be easily replaced with higher-fidelity ones whenever the user has a specific interest in modelling a particular part of the system, (ii) passive in that it reaches a stable limit cycle of flow rate and pressure in a few heartbeat cycles when driven by a periodic force acting on the epicardium, and (iii) capable of operating at physiological regimes

Italian Guidelines in diagnosis and treatment of alopecia areata

Alopecia areata (AA) is an organ-specific autoimmune disorder that targets anagen phase hair follicles. The course is unpredictable and current available treatments have variable efficacy. Nowadays, there is relatively little evidence on treatment of AA from well-designed clinical trials. Moreover, none of the treatments or devices commonly used to treat AA are specifically approved by the Food and Drug Administration. The Italian Study Group for Cutaneous Annexial Disease of the Italian Society of dermatology proposes these Italian guidelines for diagnosis and treatment of Alopecia Areata deeming useful for the daily management of the disease. This article summarizes evidence-based treatment associated with expert-based recommendations

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject

Interaction Fluide-Structure dans le Système Cardiovasculaire. Analyse Numérique et Simulation

In this thesis we focus on the numerical analysis and the development of efficient partitioned algorithms for fluid-structure interaction (FSI) problems arising in hemodynamics. In particular we consider the mechanical interaction of the blood with the large arteries, with the cardiac valves and with the myocardium. In partitioned FSI procedures the coupling between the fluid and the structure can be enforced in different ways: implicit, semi-implicit or explicit. In the first part of this thesis, the convergence properties of a projection semi-implicit coupling scheme are investigated from the theoretical and numerical viewpoints. Then, for the same scheme, we propose a modification that aims at improving its stability properties. This modification relies on the reinterpretation of the Nitsche's interface coupling as a particular Robin-Robin coupling. In the second part fluid-structure interaction problems with cardiac valves are addressed. For these problems we devise a modular partitioned strategy for the numerical simulation of 3D FSI problems where contact among multiple elastic solids can occur. For the analysis of the computational results, we also investigate the use of an advanced post-processing technique based on the notion of Lagrangian coherent structures. Finally, in the last part, a new reduced model for cardiac valves simulations is presented. This new model offers a compromise between standard lumped parameter models and fully 3D FSI problems. Various numerical experiments are presented to validate its efficiency and robustness. With this model, numerical simulations of the cardiac hemodynamics can be performed with a reduced computational cost.Dans cette thèse, nous proposons et analysons des méthodes numériques partitionnées pour la simulation de phénomènes d'interaction fluide-structure (IFS) dans le système cardiovasculaire. Nous considérons en particulier l'interaction mécanique du sang avec la paroi des grosses artères, avec des valves cardiaques et avec le myocarde. Dans les algorithmes IFS partitionnés, le couplage entre le fluide et la structure peut être imposé de manière implicite, semi-implicite ou explicite. Dans la première partie de cette thèse, nous faisons l'analyse de convergence d'un algorithme de projection semi-implicite. Puis, nous proposons une nouvelle version de ce schéma qui possède de meilleures propriétés de stabilité. La modification repose sur un couplage Robin-Robin résultant d'une ré-interprétation de la formulation de Nitsche. Dans la seconde partie, nous nous intéressons à la simulation de valves cardiaques. Nous proposons une stratégie partionnée permettant la prise en compte du contact entre plusieurs structures immergées dans un fluide. Nous explorons également l'utilisation d'une technique de post-traitement récente, basée sur la notion de structures Lagrangiennes cohérentes, pour analyser qualitativement l'hémodynamique complexe en aval des valves aortiques. Dans la dernière partie, nous proposons un modèle original de valves cardiaques. Ce modèle simplifié offre un compromis entre les approches 0D classiques et les simulations complexes d'interaction fluide-structure 3D. Diverses simulations numériques sont présentées pour illustrer l'efficacité et la robustesse de ce modèle, qui permet d'envisager des simulations réalistes de l'hémodynamique cardiaque, à un coût de calcul modéré