TY - JOUR
T1 - Rate of convergence and stability analysis of a modified fixed pivot technique for a fragmentation equation
AU - Saha, Jitraj
AU - Singh, Mehakpreet
N1 - Publisher Copyright:
© 2023, The Author(s).
PY - 2023/3
Y1 - 2023/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85147382318&partnerID=8YFLogxK
U2 - 10.1007/s00211-023-01344-0
DO - 10.1007/s00211-023-01344-0
M3 - Article
AN - SCOPUS:85147382318
SN - 0029-599X
VL - 153
SP - 531
EP - 555
JO - Numerische Mathematik
JF - Numerische Mathematik
IS - 2-3
ER -