New volume consistent approximation for binary breakage Population Balance Equation and its convergence analysis

被引:23
作者
Singh, Mehakpreet [1 ]
Matsoukas, Themis [2 ]
Albadarin, Ahmad B. [1 ]
Walker, Gavin [1 ]
机构
[1] Univ Limerick, Bernal Inst, Dept Chem Sci, Limerick V94 T9PX, Ireland
[2] Penn State Univ, Dept Chem Engn, 8H Thomas, State Coll, PA 16802 USA
来源
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2019年 / 53卷 / 05期
关键词
Particles; binary breakage; population balance equation; finite volume scheme; nonuniform grids; SECTIONAL METHODS; FRAGMENTATION; DISCRETIZATION; COAGULATION; SCHEME; AGGREGATION; FORMULATION; PARAMETERS; DISCRETE; KINETICS;
D O I
10.1051/m2an/2019036
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This work is focused on developing a numerical approximation based on finite volume scheme to solve a binary breakage population balance equation (PBE). The mathematical convergence analysis of the proposed scheme is discussed in detail for different grids. The proposed scheme is mathematical simple and can be implemented easily on general grids. The numerical results and findings are validated against the existing scheme over different benchmark problems. All numerical predictions demonstrate that the proposed scheme is highly accurate and efficient as compared to the existing method. Moreover, the theoretical observations concerning order of convergence are verified with the numerical order of convergence which shows second order convergence irrespective of grid chosen for discretization. The proposed scheme will be the first ever numerical approximation for a binary breakage PBE free from that the particles are concentrated on the representative of the cell.
引用
收藏
页码:1695 / 1713
页数:19
相关论文
共 34 条
  • [1] [Anonymous], 2013, SPRINGER SER COMPUT
  • [2] Solution of the droplet breakage equation for interacting liquid-liquid dispersions: a conservative discretization approach
    Attarakih, MM
    Bart, HJ
    Faqir, NM
    [J]. CHEMICAL ENGINEERING SCIENCE, 2004, 59 (12) : 2547 - 2565
  • [3] A new estimation technique for the determination of breakage and selection parameters in batch grinding
    Berthiaux, H
    Dodds, J
    [J]. POWDER TECHNOLOGY, 1997, 94 (02) : 173 - 179
  • [4] Bourgade JP, 2008, MATH COMPUT, V77, P851, DOI 10.1090/S0025-5718-07-02054-6
  • [5] Numerical study of a stochastic particle algorithm solving a multidimensional population balance model for high shear granulation
    Braumann, Andreas
    Kraft, Markus
    Wagner, Wolfgang
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2010, 229 (20) : 7672 - 7691
  • [6] EXACT-SOLUTIONS FOR THE COAGULATION FRAGMENTATION EQUATION
    DUBOVSKII, PB
    GALKIN, VA
    STEWART, IW
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1992, 25 (18): : 4737 - 4744
  • [7] A FINITE VOLUME PRESERVING SCHEME ON NONUNIFORM MESHES AND FOR MULTIDIMENSIONAL COALESCENCE
    Forestier-Coste, L.
    Mancini, S.
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2012, 34 (06) : B840 - B860
  • [8] AN OPERATOR-SPLITTING GALERKIN/SUPG FINITE ELEMENT METHOD FOR POPULATION BALANCE EQUATIONS: STABILITY AND CONVERGENCE
    Ganesan, Sashikumaar
    [J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2012, 46 (06): : 1447 - 1465
  • [9] Towards improved predictions for the enzymatic chain-end scission of natural polymers by population balances: The need for a non-classical rate kernel
    Ho, Yong Kuen
    Kirse, Christoph
    Briesen, Heiko
    Singh, Mehakpreet
    Chan, Chung-Hung
    Kow, Kien-Woh
    [J]. CHEMICAL ENGINEERING SCIENCE, 2018, 176 : 329 - 342
  • [10] A DISCRETIZED POPULATION BALANCE FOR NUCLEATION, GROWTH, AND AGGREGATION
    HOUNSLOW, MJ
    RYALL, RL
    MARSHALL, VR
    [J]. AICHE JOURNAL, 1988, 34 (11) : 1821 - 1832