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

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

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...

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Veröffentlicht in:Zeitschrift für angewandte Mathematik und Physik 2024-08, Vol.75 (4), Article 125
Hauptverfasser: Das, Arijit, Saha, Jitraj
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Sprache:eng
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Convergence
Engineering
Error analysis
Finite volume method
Mathematical Methods in Physics
Population balance models
Theoretical and Applied Mechanics
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description 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.
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subjects Convergence
Engineering
Error analysis
Finite volume method
Mathematical Methods in Physics
Population balance models
Theoretical and Applied Mechanics
title Approximate solutions to the nonlinear hyperbolic population balance equation: convergence, error estimate and numerical simulations
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