This work is focused on developing a numerical approximation based on finite volume scheme to solve a binary breakage population balance equation (PBE). The mathematical convergence analysis of the proposed scheme is discussed in detail for different grids. The proposed scheme is mathematical simple and can be implemented easily on general grids. The numerical results and findings are validated against the existing scheme over different benchmark problems. All numerical predictions demonstrate that the proposed scheme is highly accurate and efficient as compared to the existing method. Moreover, the theoretical observations concerning order of convergence are verified with the numerical order of convergence which shows second order convergence irrespective of grid chosen for discretization. The proposed scheme will be the first ever numerical approximation for a binary breakage PBE free from that the particles are concentrated on the representative of the cell.
Accepté le :
DOI : 10.1051/m2an/2019036
Mots-clés : Particles, binary breakage, population balance equation, finite volume scheme, nonuniform grids
@article{M2AN_2019__53_5_1695_0,
author = {Singh, Mehakpreet and Matsoukas, Themis and Albadarin, Ahmad B. and Walker, Gavin},
title = {New volume consistent approximation for binary breakage {Population} {Balance} {Equation} and its convergence analysis},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1695--1713},
publisher = {EDP-Sciences},
volume = {53},
number = {5},
year = {2019},
doi = {10.1051/m2an/2019036},
mrnumber = {4003469},
zbl = {1425.82022},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2019036/}
}
TY - JOUR AU - Singh, Mehakpreet AU - Matsoukas, Themis AU - Albadarin, Ahmad B. AU - Walker, Gavin TI - New volume consistent approximation for binary breakage Population Balance Equation and its convergence analysis JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2019 SP - 1695 EP - 1713 VL - 53 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2019036/ DO - 10.1051/m2an/2019036 LA - en ID - M2AN_2019__53_5_1695_0 ER -
%0 Journal Article %A Singh, Mehakpreet %A Matsoukas, Themis %A Albadarin, Ahmad B. %A Walker, Gavin %T New volume consistent approximation for binary breakage Population Balance Equation and its convergence analysis %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2019 %P 1695-1713 %V 53 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2019036/ %R 10.1051/m2an/2019036 %G en %F M2AN_2019__53_5_1695_0
Singh, Mehakpreet; Matsoukas, Themis; Albadarin, Ahmad B.; Walker, Gavin. New volume consistent approximation for binary breakage Population Balance Equation and its convergence analysis. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 5, pp. 1695-1713. doi : 10.1051/m2an/2019036. http://www.numdam.org/articles/10.1051/m2an/2019036/
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