Numerical schemes for mixture theory models with filling constraint: application to biofilm ecosystems
ESAIM. Proceedings, Tome 77 (2024), pp. 249-266
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The mixture theory framework is a powerful way to describe multi-phasic systems at an intermediary scale between microscopic and macroscopic scales. In particular, mixture theory reveals a powerful approach to represent microbial biofilms where a consortium of cells is embedded in a polymeric structure. To simulate a model of microalgal biofilm, we propose an upgraded numerical scheme, consolidating the one proposed by Berthelin et al. (2016) to enforce the volume-filling constraint in mixture models including mass exchanges. The strategy consists in deducing the discrete version of the incompressibility constraint from the discretized mass balance equations. Numerical simulations show that this method constrains the total volume filling constraint, even at the discrete level. Moreover, we add viscous terms in the biofilm model to properly represent biofilms interactions with its fluidic environment. It turns out that a well-balanced numerical scheme becomes of outmost importance to capture the biofilm dynamic when including the viscosity. This modelling upgrade also involves recalibrating model parameters. In particular, the elastic tensors to recover realistic front features. With the new parameters, the numerical set-up becomes more demanding to reach convergence.
Affiliations des auteurs :
Olivier Bernard 1 ; Mickael Bestard 2 ; Thierry Goudon 3 ; Leo Meyer 4 ; Sebastian Minjeaud 3 ; Florent Noisette 5 ; Bastien Polizzi 6
@article{EP_2024_77_a12,
author = {Olivier Bernard and Mickael Bestard and Thierry Goudon and Leo Meyer and Sebastian Minjeaud and Florent Noisette and Bastien Polizzi},
title = {Numerical schemes for mixture theory models with filling constraint: application to biofilm ecosystems},
journal = {ESAIM. Proceedings},
pages = {249--266},
year = {2024},
volume = {77},
doi = {10.1051/proc/202477249},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202477249/}
}
TY - JOUR AU - Olivier Bernard AU - Mickael Bestard AU - Thierry Goudon AU - Leo Meyer AU - Sebastian Minjeaud AU - Florent Noisette AU - Bastien Polizzi TI - Numerical schemes for mixture theory models with filling constraint: application to biofilm ecosystems JO - ESAIM. Proceedings PY - 2024 SP - 249 EP - 266 VL - 77 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/202477249/ DO - 10.1051/proc/202477249 LA - en ID - EP_2024_77_a12 ER -
%0 Journal Article %A Olivier Bernard %A Mickael Bestard %A Thierry Goudon %A Leo Meyer %A Sebastian Minjeaud %A Florent Noisette %A Bastien Polizzi %T Numerical schemes for mixture theory models with filling constraint: application to biofilm ecosystems %J ESAIM. Proceedings %D 2024 %P 249-266 %V 77 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/202477249/ %R 10.1051/proc/202477249 %G en %F EP_2024_77_a12
Olivier Bernard; Mickael Bestard; Thierry Goudon; Leo Meyer; Sebastian Minjeaud; Florent Noisette; Bastien Polizzi. Numerical schemes for mixture theory models with filling constraint: application to biofilm ecosystems. ESAIM. Proceedings, Tome 77 (2024), pp. 249-266. doi: 10.1051/proc/202477249
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