Long time simulations of transport equations raise computational challenges since they require both a large domain of calculation and sufficient accuracy. It is therefore advantageous, in terms of computational costs, to use a time varying adaptive mesh, with small cells in the region of interest and coarser cells where the solution is smooth. Biological models involving cell dynamics fall for instance within this framework and are often non conservative to account for cell division. In that case the threshold controlling the spatial adaptivity may have to be time-dependent in order to keep up with the progression of the solution. In this article we tackle the difficulties arising when applying a Multiresolution method to a transport equation with discontinuous fluxes modeling localized mitosis. The analysis of the numerical method is performed on a simplified model and numerical scheme. An original threshold strategy is proposed and validated thanks to extensive numerical tests. It is then applied to a biological model in both cases of distributed and localized mitosis.
Mots-clés : adaptive finite volumes, non conservative PDE, discontinuous flux
@article{M2AN_2014__48_5_1381_0,
author = {Aymard, Benjamin and Cl\'ement, Fr\'ed\'erique and Postel, Marie},
title = {Adaptive mesh refinement strategy for a non conservative transport problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1381--1412},
publisher = {EDP-Sciences},
volume = {48},
number = {5},
year = {2014},
doi = {10.1051/m2an/2014014},
mrnumber = {3264358},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2014014/}
}
TY - JOUR AU - Aymard, Benjamin AU - Clément, Frédérique AU - Postel, Marie TI - Adaptive mesh refinement strategy for a non conservative transport problem JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 1381 EP - 1412 VL - 48 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2014014/ DO - 10.1051/m2an/2014014 LA - en ID - M2AN_2014__48_5_1381_0 ER -
%0 Journal Article %A Aymard, Benjamin %A Clément, Frédérique %A Postel, Marie %T Adaptive mesh refinement strategy for a non conservative transport problem %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 1381-1412 %V 48 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2014014/ %R 10.1051/m2an/2014014 %G en %F M2AN_2014__48_5_1381_0
Aymard, Benjamin; Clément, Frédérique; Postel, Marie. Adaptive mesh refinement strategy for a non conservative transport problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 5, pp. 1381-1412. doi : 10.1051/m2an/2014014. http://www.numdam.org/articles/10.1051/m2an/2014014/
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