Modified variational iteration method and its convergence analysis for solving nonlinear aggregation population balance equation

Publikationstyp
Journal Article
Date Issued
2024-04-30
Sprache
English
Author(s)
Yadav, Sonia
Singh, Mehakpreet  
Singh, Sukhjit
Heinrich, Stefan  
Feststoffverfahrenstechnik und Partikeltechnologie V-3  
Kumar, Jitendra  
TORE-DOI
10.15480/882.9670
TORE-URI
https://hdl.handle.net/11420/46518
Journal
Computers & fluids  
Volume
274
Article Number
106233
Citation
Computers & Fluids 274: 106233 (2024)
Publisher DOI
10.1016/j.compfluid.2024.106233
Scopus ID
2-s2.0-85186764822
Publisher
Elsevier Science
This study proposes a novel approach based on the variational iteration method to solve the nonlinear aggregation population balance equation. The approach provides great flexibility by allowing the selection of appropriate linear operators and efficiently determining the Lagrange multiplier in the nonlinear aggregation population balance equation. The mathematical derivation is supported by conducting a detailed convergence analysis using the contraction mapping principle in the Banach space. Furthermore, error estimates for the approximate solutions are derived, thereby improving our understanding of the accuracy and reliability of the proposed method. To validate the new approach, the obtained solutions are compared with the exact solutions for analytically tractable kernels. However, for more complex physically relevant kernels including polymerization, Ruckenstein/Pulvermacher, and bilinear kernels, due to lack exact solutions, the obtained series solutions corresponding to different initial conditions are verified against the finite volume scheme (kumar et al., 2016). The outcomes illustrate that the proposed approach offers superior approximations of number density functions with fewer terms and demonstrates higher accuracy over extended time domains than the traditional variational iterative method. The new approach also has the tendency to capture the zeroth and first order moments of the number density function with high precision.
Subjects
Contraction mapping principle
Convergence analysis
Lagrange multiplier
Nonlinear aggregation equation
Variational iteration method
DDC Class
004: Computer Sciences
510: Mathematics
530: Physics
Lizenz
https://creativecommons.org/licenses/by/4.0/
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