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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...

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.

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...

Modelling of Cancer Growth, Evolution and Invasion: Bridging Scales and Models

A. R.A. Anderson, K. A. Rejniak, P. Gerlee, V. Quaranta (2010)

Mathematical Modelling of Natural Phenomena

Since cancer is a complex phenomenon that incorporates events occurring on different length and time scales, therefore multiscale models are needed if we hope to adequately address cancer specific questions. In this paper we present three different multiscale individual-cell-based models, each motivated by cancer-related problems emerging from each of the spatial scales: extracellular, cellular or subcellular, but also incorporating relevant information from other levels. We apply these hybrid...

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