Analytical approach for solving population balances: A homotopy perturbation method

Gurmeet Kaur, Randhir Singh, Mehakpreet Singh, Jitendra Kumar, Themis Matsoukas

Research output: Contribution to journalArticle

Abstract

In the present work, a new approach is proposed for finding the analytical solution of population balances for aggregation and fragmentation process. This approach is relying on the idea of the homotopy perturbation method (HPM). The HPM solves both linear and nonlinear initial and boundary value problems without nonphysical restrictive assumptions such as linearization and discretization. It gives the solution in the form of series with easily computable solution components. The outcome of this study reveals that the proposed method can avoid numerical stability problems which often characterize in general numerical techniques related to this area. Several examples including Austin's kernel, available in literature, are examined to demonstrate the accuracy and applicability of the proposed method. In addition, the analytical solution to two new kernels (the power-law kernel in fragmentation and the Ruckenstein/Pulvermacher kernel in aggregation) are also introduced.

Original languageEnglish (US)
Article number385201
JournalJournal of Physics A: Mathematical and Theoretical
Volume52
Issue number38
DOIs
StatePublished - Aug 26 2019

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Population Balance
Homotopy Perturbation Method
boundary value problems
fragmentation
Agglomeration
kernel
perturbation
numerical stability
Initial value problems
Convergence of numerical methods
linearization
Fragmentation
Linearization
Boundary value problems
Aggregation
Analytical Solution
Numerical Stability
Numerical Techniques
Initial Value Problem
Nonlinear Problem

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

Kaur, Gurmeet ; Singh, Randhir ; Singh, Mehakpreet ; Kumar, Jitendra ; Matsoukas, Themis. / Analytical approach for solving population balances : A homotopy perturbation method. In: Journal of Physics A: Mathematical and Theoretical. 2019 ; Vol. 52, No. 38.
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Analytical approach for solving population balances : A homotopy perturbation method. / Kaur, Gurmeet; Singh, Randhir; Singh, Mehakpreet; Kumar, Jitendra; Matsoukas, Themis.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 52, No. 38, 385201, 26.08.2019.

Research output: Contribution to journalArticle

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