Rate of convergence and stability analysis of a modified fixed pivot technique for a fragmentation equation

Jitraj Saha, Mehakpreet Singh

Research output: Contribution to journalArticlepeer-review

Abstract

This study presents the convergence and stability analysis of a recently developed fixed pivot technique for fragmentation equations (Liao et al. in Int J Numer Methods Fluids 87(4):202–215, 2018). The approach is based on preserving two integral moments of the distribution, namely (a) the zeroth-order moment, which defines the number of particles, and (b) the first-order moment, which describes the total mass in the system. The present methodology differs mathematically in a way that it delivers the total breakage rate between a mother and a daughter particle immediately, whereas existing numerical techniques provide the partial breakup rate of a mother and daughter particle. This affects the computational efficiency and makes the current model reliable for CFD simulations. The consistency and unconditional second-order convergence of the method are proved. This demonstrates efficiency of the method over the fixed pivot technique (Kumar and Warnecke in Numer Math 110(4):539–559, 2008) and the cell average technique (Kumar and Warnecke in Numer Math 111(1):81–108, 2008). Numerical results are compared against the cell average technique and the experimental order of convergence is calculated to confirm the theoretical order of convergence.

Original languageEnglish
Pages (from-to)531-555
Number of pages25
JournalNumerische Mathematik
Volume153
Issue number2-3
DOIs
Publication statusPublished - Mar 2023

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