Mathematical modeling and numerical simulation of a bioreactor landfill using Feel++

In this paper, we propose a mathematical model to describe the functioning of a bioreactor landfill, that is a waste management facility in which biodegradable waste is used to generate methane. The simulation of a bioreactor landfill is a very complex multiphysics problem in which bacteria catalyze a chemical reaction that starting from organic carbon leads to the production of methane, carbon dioxide and water. The resulting model features a heat equation coupled with a non-linear reaction equation describing the chemical phenomena under analysis and several advection and advection-diffusion equations modeling multiphase flows inside a porous environment representing the biodegradable waste. A framework for the approximation of the model is implemented using Feel++, a C++ open-source library to solve Partial Differential Equations. Some heuristic considerations on the quantitative values of the parameters in the model are discussed and preliminary numerical simulations are presented

Tomographie optique diffuse et de fluorescence pour la détection de tumeurs

The Time-Resolved Diffuse Optical Tomography and Fluorescence (TR-DOTF) is a method to obtain optical properties information on diffusion and asbsorption of biological tissues. This Phd manuscript details this method state of the art and highlight the different possible path to reconstruct multidimensionnal 2D/3D images for the optical maps of the turbid medium. The project ultimate goal is to build a measurement instrument (tomograph), eventually portative, in order to detect tumours presence. The challenge is to obtain images with sufficient resolution to be used in medical environment for preclinical diagnosis. However the inverse problem ill-posedness makes the situation more difficult. The first part of this document is devoted to the problem modelization. In particular, we are interested to the diffusion approximation for the radiative transfer equation in a turbid medium. In a second part, we treat this problem from a mathematical point of view considering the diffusion problem coupled with fluorescence for two measurement types: contact and non-contact. Then we focus on the inverse prob- lem as a minimization problem for cost objective function solved by an adjoint method. Last, but not least, the third part of this document details the different numerical aspects involved to achieve an efficient reconstruction code using advanced technics from the high performance computing world.La tomographie optique diffuse et de fluorescence résolue en temps (TR-TODF) est une méthode qui permet de fournir une information sur les propriétés optiques de diffusion et d’absorption des tissus biologiques. Ce manuscrit de thèse fait l’état de l’art de la méthode et propose des pistes pour reconstruire des images multidimensionnelles 2D/3D des cartes optiques du milieu. L’objectif ultime du projet présenté dans ce document est de concevoir un appareil de mesure (tomographe), éventuellement portatif, pour détecter la présence de tumeurs. Le défi est de pouvoir obtenir des images avec une ré- solution suffisante pour être utilisée en milieu hospitalier à des fins de diagnostic préclinique. Hors le caractère naturellement mal posé du problème inverse rend la tâche complexe. La première partie du document est consacrée à la modélisation du problème physique. En particulier nous nous intéressons à l’approximation de diffusion de l’équation du transfert radiatif dans un milieu quelconque. Dans une deuxième partie, nous traitons le problème du point de vue mathématiques en considérant le problème direct de diffusion couplé avec de la fluorescence pour deux type de mesures: en mode contact et non-contact. Puis nous nous intéressons au problème inverse comme un problème de minimisation d’une fonctionnelle que nous traitons par une méthode de l’adjoint. Enfin et pour finir, la troisième partie du document détaille les différents aspects numérique pour parvenir à un code de reconstruction efficace à l’aide de techniques issues du calcul haute performance

SiViBiR++ projet: Simulation d'un bioréacteur virtuel avec la librairie Feel++

International audienceCEMRACS 2015 final presentation, SiViBiR++ project.Présentation finale du CEMRACS 2015, projet SiViBiR++

The Direct Robin Boundary Value Parabolic System of Time-Resolved Diffuse Optical Tomography with Fluorescence

International audienc

Diffuse optical tomography for tumour detection

<p><em>Time-resolved diffuse optical tomography</em> aims to reconstruct images for internal parts of a body (diffusive objects owning one or several inclusions, small animals, ...) from its boundary measures.<br> This poster gives an overview of the experimental setup created by the ICube/IMIS team and the mathematical model used for the reconstruction. Numerical results are obtained using FEEL++, a C++ library for finite element methods.</p

Mathematical modeling and numerical simulation of a bioreactor landfill using Feel++*

In this paper, we propose a mathematical model to describe the functioning of a bioreactor landfill, that is a waste management facility in which biodegradable waste is used to generate methane. The simulation of a bioreactor landfill is a very complex multiphysics problem in which bacteria catalyze a chemical reaction that starting from organic carbon leads to the production of methane, carbon dioxide and water. The resulting model features a heat equation coupled with a non-linear reaction equation describing the chemical phenomena under analysis and several advection and advection-diffusion equations modeling multiphase flows inside a porous environment representing the biodegradable waste. A framework for the approximation of the model is implemented using Feel++, a C++ open-source library to solve Partial Differential Equations. Some heuristic considerations on the quantitative values of the parameters in the model are discussed and preliminary numerical simulations are presented

Towards a better Monitoring and Control System: Integrating Modeling Toolchain

International audienc

Diffuse Optical Tomography and Fluorescence Simulation

<p>Diffusion of a source of light (Dirac) in a turbid medium. The object owns two inclusions, one more absorbant and one more diffusive than the background. These inclusions can be seen as tumours that have different optical and fluorescence properties compared to the "homogeneous" background.</p> <p>This simulation shows the forward problem solutions for choosen optical and fluorescence parameters and computed with FEEL++, a C++ library for Generalized Garlerkin methods (FEM, HP-FEM, ...).</p