[Un problème d'optimization dynamique lié à la modélisation d'aérosols organiques]
Nous proposons un modèle pour le calcul de l'équilibre thermodynamique et la séparation de phases entre une particule et la phase gazeuse. La dynamique des transferts de masse entre particule et phase gazeuse est caractérisée par un système d'équations différentielles couplées avec un problème d'optimisation décrivant l'équilibre interne de la particule. Les conditions de premier ordre et une discrétisation implicite des équations différentielles forment un système d'équations non linéaires qui est traité avec une méthode de point intérieur couplée à une itération de Newton. Des résultats numériques et une comparaison des temps caractéristiques montrent la précision et l'efficacité de notre algorithme.
A model that rigorously computes the gas–particle partitioning and liquid–liquid equilibrium for organic atmospheric aerosol particles is presented. The dynamics of the mass transfers between the particle and the gas phase are modeled with differential equations and are coupled with a constrained optimization problem for the thermodynamic equilibrium inside the particle. The nonlinear system composed by the first order optimality conditions coupled with the discretized differential equations is solved with an interior-point method and a Newton method. The resulting linear system is decoupled with sequential quadratic programming techniques. Numerical results and comparisons of time scales show the accuracy and efficiency of our algorithm.
Accepté le :
Publié le :
Neal R. Amundson 1 ; Alexandre Caboussat 1 ; Jiwen He 1 ; Chantal Landry 2 ; John H. Seinfeld 3
@article{CRMATH_2007__344_8_519_0,
author = {Neal R. Amundson and Alexandre Caboussat and Jiwen He and Chantal Landry and John H. Seinfeld},
title = {A dynamic optimization problem related to organic aerosols},
journal = {Comptes Rendus. Math\'ematique},
pages = {519--522},
publisher = {Elsevier},
volume = {344},
number = {8},
year = {2007},
doi = {10.1016/j.crma.2007.03.002},
language = {en},
}
TY - JOUR AU - Neal R. Amundson AU - Alexandre Caboussat AU - Jiwen He AU - Chantal Landry AU - John H. Seinfeld TI - A dynamic optimization problem related to organic aerosols JO - Comptes Rendus. Mathématique PY - 2007 SP - 519 EP - 522 VL - 344 IS - 8 PB - Elsevier DO - 10.1016/j.crma.2007.03.002 LA - en ID - CRMATH_2007__344_8_519_0 ER -
%0 Journal Article %A Neal R. Amundson %A Alexandre Caboussat %A Jiwen He %A Chantal Landry %A John H. Seinfeld %T A dynamic optimization problem related to organic aerosols %J Comptes Rendus. Mathématique %D 2007 %P 519-522 %V 344 %N 8 %I Elsevier %R 10.1016/j.crma.2007.03.002 %G en %F CRMATH_2007__344_8_519_0
Neal R. Amundson; Alexandre Caboussat; Jiwen He; Chantal Landry; John H. Seinfeld. A dynamic optimization problem related to organic aerosols. Comptes Rendus. Mathématique, Volume 344 (2007) no. 8, pp. 519-522. doi : 10.1016/j.crma.2007.03.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.03.002/
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