In this work, two discrete formulations based on the finite volume approach for a reduced fragmentation model are developed. The important features such as mass conservation and accurate prediction of the zeroth order moments are accomplished by the modification of the selection function. The new schemes can compute the second order moment, which plays a significant role in predicting the area of the particles in real life applications, with high accuracy without taking any specific measures. A thorough convergence analysis of both schemes including Lipschitz condition and consistency is presented and exhibit second order convergence. The accuracy and efficiency of both schemes is demonstrated by applying them to the depolymerization problem which commonly arises in polymer sciences and chemical engineering. It is demonstrated that the new schemes are easy to implement, computationally efficient and able to compute the numerical results with higher precision even on a coarser grid.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2022023
Keywords: Integro-partial differential equations, finite volume scheme, reduced fragmentation model, convergence analysis, depolymerization
@article{M2AN_2022__56_3_943_0,
author = {Singh, Mehakpreet and Walker, Gavin and Randade, Vivek},
title = {New formulations and convergence analysis for reduced tracer mass fragmentation model: an application to depolymerization},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {943--967},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {3},
doi = {10.1051/m2an/2022023},
mrnumber = {4411483},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2022023/}
}
TY - JOUR AU - Singh, Mehakpreet AU - Walker, Gavin AU - Randade, Vivek TI - New formulations and convergence analysis for reduced tracer mass fragmentation model: an application to depolymerization JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2022 SP - 943 EP - 967 VL - 56 IS - 3 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2022023/ DO - 10.1051/m2an/2022023 LA - en ID - M2AN_2022__56_3_943_0 ER -
%0 Journal Article %A Singh, Mehakpreet %A Walker, Gavin %A Randade, Vivek %T New formulations and convergence analysis for reduced tracer mass fragmentation model: an application to depolymerization %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2022 %P 943-967 %V 56 %N 3 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2022023/ %R 10.1051/m2an/2022023 %G en %F M2AN_2022__56_3_943_0
Singh, Mehakpreet; Walker, Gavin; Randade, Vivek. New formulations and convergence analysis for reduced tracer mass fragmentation model: an application to depolymerization. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 3, pp. 943-967. doi: 10.1051/m2an/2022023
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