Volume 56, Number 3, May-June 2022
|Page(s)||943 - 967|
|Published online||25 April 2022|
New formulations and convergence analysis for reduced tracer mass fragmentation model: an application to depolymerization
Bernal Institute, Department of Chemical Sciences, University of Limerick, V94 T9PX Limerick, Ireland
2 Bernal Institute, School of Engineering, University of Limerick, Limerick, Ireland
* Corresponding author: Mehakpreet.Singh@ul.ie
Accepted: 18 February 2022
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.
Mathematics Subject Classification: 37N30 / 35R09 / 80M12
Key words: Integro-partial differential equations / finite volume scheme / reduced fragmentation model / convergence analysis / depolymerization
© The authors. Published by EDP Sciences, SMAI 2022
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