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Modelling and Numerics for Respiratory Aerosols

Part of: Equations of mathematical physics and other areas of application Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  14 September 2015

Laurent Boudin ,
Céline Grandmont ,
Alexander Lorz  and
Ayman Moussa
Laurent Boudin
Affiliation:
Sorbonne Universités, UPMC Univ Paris 06 & CNRS, UMR 7598 LJLL, Paris, F-75005, France Inria, Équipe-projet Reo, BP 105, F-78153 Le Chesnay Cedex, France
Céline Grandmont
Affiliation:
Sorbonne Universités, UPMC Univ Paris 06 & CNRS, UMR 7598 LJLL, Paris, F-75005, France Inria, Équipe-projet Reo, BP 105, F-78153 Le Chesnay Cedex, France
Alexander Lorz*
Affiliation:
Sorbonne Universités, UPMC Univ Paris 06 & CNRS, UMR 7598 LJLL, Paris, F-75005, France Inria, Équipe-projet Mamba, BP 105, F-78153 Le Chesnay Cedex, France
Ayman Moussa
Affiliation:
Sorbonne Universités, UPMC Univ Paris 06 & CNRS, UMR 7598 LJLL, Paris, F-75005, France Inria, Équipe-projet Reo, BP 105, F-78153 Le Chesnay Cedex, France
*
*Corresponding author. Email addresses: laurent.boudin@upmc.fr (L. Boudin), celine.grandmont@inria.fr (C. Grandmont), alexander.lorz@upmc.fr (A. Lorz), ayman.moussa@upmc.fr (A. Moussa)
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Abstract

In this work, we present a model for an aerosol (air/particle mixture) in the respiratory system. It consists of the incompressible Navier-Stokes equations for the air and the Vlasov equation for the particles in a fixed or moving domain, coupled through a drag force. We propose a discretization of the model, investigate stability properties of the numerical code and sensitivity to parameter perturbation. We also focus on the influence of the aerosol on the airflow.

Keywords

AerosolsNavier-Stokes-Vlasov systemdiscretizationfinite-element methodparticle-in-cell methodstability properties

MSC classification

Secondary: 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 35Q30: Navier-Stokes equations 35Q83: Vlasov-like equations 35Q92: PDEs in connection with biology and other natural sciences
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 3 , September 2015 , pp. 723 - 756
Copyright
Copyright © Global-Science Press 2015 

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