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A 2D model for hydrodynamics and biology coupling applied to algae growth simulations

Olivier Bernard, Anne-Céline Boulanger, Marie-Odile Bristeau, Jacques Sainte-Marie (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Cultivating oleaginous microalgae in specific culturing devices such as raceways is seen as a future way to produce biofuel. The complexity of this process coupling non linear biological activity to hydrodynamics makes the optimization problem very delicate. The large amount of parameters to be taken into account paves the way for a useful mathematical modeling. Due to the heterogeneity of raceways along the depth dimension regarding temperature, light intensity or nutrients availability, we adopt...

A quasi-Newton algorithm based on a reduced model for fluid-structure interaction problems in blood flows

Jean-Frédéric Gerbeau, Marina Vidrascu (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We propose a quasi-Newton algorithm for solving fluid-structure interaction problems. The basic idea of the method is to build an approximate tangent operator which is cost effective and which takes into account the so-called added mass effect. Various test cases show that the method allows a significant reduction of the computational effort compared to relaxed fixed point algorithms. We present 2D and 3D fluid-structure simulations performed either with a simple 1D structure model or with shells...

A Quasi-Newton Algorithm Based on a Reduced Model for Fluid-Structure Interaction Problems in Blood Flows

Jean-Frédéric Gerbeau, Marina Vidrascu (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose a quasi-Newton algorithm for solving fluid-structure interaction problems. The basic idea of the method is to build an approximate tangent operator which is cost effective and which takes into account the so-called added mass effect. Various test cases show that the method allows a significant reduction of the computational effort compared to relaxed fixed point algorithms. We present 2D and 3D fluid-structure simulations performed either with a simple 1D structure model or with...

An object-oriented approach to the design of fluid mechanics software

Christophe Calvin, Olga Cueto, Philippe Emonot (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This article presents the guiding principles of the architecture of Trio_U, a new generation of software for thermohydraulic calculations. Trio_U is designed to serve as a thermohydraulic development platform. Its basic conception is object-oriented and it is written in C++. The article demonstrates how this type of design enables an open, modular software architecture.

An object-oriented approach to the design of fluid mechanics software

Christophe Calvin, Olga Cueto, Philippe Emonot (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This article presents the guiding principles of the architecture of Trio_U, a new generation of software for thermohydraulic calculations. Trio_U is designed to serve as a thermohydraulic development platform. Its basic conception is object-oriented and it is written in C++. The article demonstrates how this type of design enables an open, modular software architecture.

Analysis of lumped parameter models for blood flow simulations and their relation with 1D models

Vuk Milišić, Alfio Quarteroni (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper provides new results of consistence and convergence of the lumped parameters (ODE models) toward one-dimensional (hyperbolic or parabolic) models for blood flow. Indeed, lumped parameter models (exploiting the electric circuit analogy for the circulatory system) are shown to discretize continuous 1D models at first order in space. We derive the complete set of equations useful for the blood flow networks, new schemes for electric circuit analogy, the stability criteria that guarantee...

Analysis of lumped parameter models for blood flow simulations and their relation with 1D models

Vuk Milišić, Alfio Quarteroni (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper provides new results of consistence and convergence of the lumped parameters (ODE models) toward one-dimensional (hyperbolic or parabolic) models for blood flow. Indeed, lumped parameter models (exploiting the electric circuit analogy for the circulatory system) are shown to discretize continuous 1D models at first order in space. We derive the complete set of equations useful for the blood flow networks, new schemes for electric circuit analogy, the stability criteria that...

Application of a center manifold theory to a reaction-diffusion system of collective motion of camphor disks and boats

Shin-Ichiro Ei, Kota Ikeda, Masaharu Nagayama, Akiyasu Tomoeda (2014)

Mathematica Bohemica

Unidirectional motion along an annular water channel can be observed in an experiment even with only one camphor disk or boat. Moreover, the collective motion of camphor disks or boats in the water channel exhibits a homogeneous and an inhomogeneous state, depending on the number of disks or boats, which looks like a kind of bifurcation phenomena. In a theoretical research, the unidirectional motion is represented by a traveling wave solution in a model. Hence it suffices to investigate a linearized...

Asymptotic analysis of blood flow in stented arteries: time dependency and direct simulations***

Vuk Milišić, Amélie Rambaud, Kirill Pichon Gostaf (2010)

ESAIM: Proceedings

This work aims to extend in two distinct directions results recently obtained in [10]. In a first step we focus on the possible extension of our results to the time dependent case. Whereas in the second part some preliminary numerical simulations aim to give orders of magnitudes in terms of numerical costs of direct 3D simulations. We consider, in the first part, the time dependent rough problem for a simplified heat equation in a straight channel that mimics the axial...

Blood Flow Simulation in Atherosclerotic Vascular Network Using Fiber-Spring Representation of Diseased Wall

Yu. Vassilevski, S. Simakov, V. Salamatova, Yu. Ivanov, T. Dobroserdova (2011)

Mathematical Modelling of Natural Phenomena

We present the fiber-spring elastic model of the arterial wall with atherosclerotic plaque composed of a lipid pool and a fibrous cap. This model allows us to reproduce pressure to cross-sectional area relationship along the diseased vessel which is used in the network model of global blood circulation. Atherosclerosis attacks a region of systemic arterial network. Our approach allows us to examine the impact of the diseased region onto global haemodynamics....

Controllability properties of a class of systems modeling swimming microscopic organisms

Mario Sigalotti, Jean-Claude Vivalda (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a finite-dimensional model for the motion of microscopic organisms whose propulsion exploits the action of a layer of cilia covering its surface. The model couples Newton's laws driving the organism, considered as a rigid body, with Stokes equations governing the surrounding fluid. The action of the cilia is described by a set of controlled velocity fields on the surface of the organism. The first contribution of the paper is the proof that such a system is generically controllable...

Diffusion models of multicomponent mixtures in the lung*

L. Boudin, D. Götz, B. Grec (2010)

ESAIM: Proceedings

In this work, we are interested in two different diffusion models for multicomponent mixtures. We numerically recover experimental results underlining the inadequacy of the usual Fick diffusion model, and the importance of using the Maxwell-Stefan model in various situations. This model nonlinearly couples the mole fractions and the fluxes of each component of the mixture. We then consider a subregion of the lower part of the lung, in which we compare...

Dynamics of Biomembranes: Effect of the Bulk Fluid

A. Bonito, R.H. Nochetto, M.S. Pauletti (2011)

Mathematical Modelling of Natural Phenomena

We derive a biomembrane model consisting of a fluid enclosed by a lipid membrane. The membrane is characterized by its Canham-Helfrich energy (Willmore energy with area constraint) and acts as a boundary force on the Navier-Stokes system modeling an incompressible fluid. We give a concise description of the model and of the associated numerical scheme. We provide numerical simulations with emphasis on the comparisons between different types of flow:...

Ecological modeling and Lagrangian approach

Boris Arkhipov, Viacheslav Solbakov, Mikhail Solov’ev, Dmitry Shapochkin (2013)

Open Mathematics

A mathematical model is proposed for a quantitative estimation of the damage to biological resources resulting from a pollutant discharge into an aqueous environment. On the basis of the Lagrangian description of fluid motion a set of hydrophysical parameters is introduced with help of which hydrobiologists can estimate the damage. The computation of parameters introduced is illustrated by the example of a model problem of a pollutant spreading in a canal. For the discretization of the problem a...

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