Approximate solutions to the nonlinear hyperbolic population balance equation: convergence, error estimate and numerical simulations

Das A, Saha J (2024)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2024

Journal

Zeitschrift für Angewandte Mathematik und Physik Springer Verlag (Germany)

Book Volume: 75

Article Number: 125

DOI: 10.1007/s00033-024-02264-1

Abstract

We consider a nonlinear, hyperbolic population balance equation that incorporates both aggregation and collisional breakage events simultaneously. Our approach revolves around the development of a novel time-explicit finite volume scheme. Under a suitable time-step stability condition, we prove the convergence of the approximate solution for any non-uniform mesh. A first-order convergence is obtained by a thorough error analysis of the proposed scheme for a suitable choice of kernels. Finally, we compute some numerical test examples to explore the behavior of the solution in steady-state conditions as well as the occurrence of gelation phenomena.

Authors with CRIS profile

Arijit Das Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

National Institute of Technology, Tiruchirappalli (NIT Trichy) IN India (IN)

How to cite

APA:

Das, A., & Saha, J. (2024). Approximate solutions to the nonlinear hyperbolic population balance equation: convergence, error estimate and numerical simulations. Zeitschrift für Angewandte Mathematik und Physik, 75. https://doi.org/10.1007/s00033-024-02264-1

MLA:

Das, Arijit, and Jitraj Saha. "Approximate solutions to the nonlinear hyperbolic population balance equation: convergence, error estimate and numerical simulations." Zeitschrift für Angewandte Mathematik und Physik 75 (2024).

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