Convergence analysis of volume preserving scheme for mass based coalescence equation

被引：4

作者：

Singh, Mehakpreet ^{[1
]}

Nayak, R. K. ^{[2
]}

Walker, Gavin ^{[1
]}

机构：

[1] Univ Limerick, Bernal Inst, Dept Chem Sci, Limerick V94 T9PX, Ireland

[2] KIIT Deemed Univ, Dept Math, Bhubaneswar, Orissa, India

来源：

APPLIED NUMERICAL MATHEMATICS | 2022年 / 173卷

关键词：

Coalescence; Integro-partial differential equations; Finite volume scheme; Consistency; Grids; Order of convergence; POPULATION BALANCE-EQUATIONS; COAGULATION-FRAGMENTATION EQUATIONS; SECTIONAL METHODS; SIMULATION; GELATION;

D O I：

10.1016/j.apnum.2021.12.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This study presents the convergence analysis of a mass based volume preserving scheme [Singh et al. (2019) [42]] for approximating a coalescence equation by establishing Lipschitz continuity of the numerical fluxes. The scheme accomplished the volume conservation law by modifying the coalescence kernel based on the principle of overlapping cells. A detailed investigation of the consistency of the method to show second-order convergence on the uniform, non-uniform smooth, and locally uniform grids independently of the coalescence kernel further reinforces the convergence study. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：365 / 379

页数：15

共 52 条

[1] On the use of sectional techniques for the solution of depolymerization population balances: Results on a discrete-continuous mesh [J].

Ahamed, Firnaaz ;

Singh, Mehakpreet ;

Song, Hyun-Seob ;

Doshi, Pankaj ;

Ooi, Chien Wei ;

Ho, Yong Kuen .

ADVANCED POWDER TECHNOLOGY, 2020, 31 (07) :2669-2679

[2]

[Anonymous], 1957, Trans. Amer. Math. Soc.

[3] Gelation of stochastic diffusion-coagulation systems [J].

Babovsky, Hans .

PHYSICA D-NONLINEAR PHENOMENA, 2006, 222 (1-2) :54-62

[4] Analytic fragmentation semigroups and continuous coagulation-fragmentation equations with unbounded rates [J].

Banasiak, Jacek ;

Lamb, Wilson .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 391 (01) :312-322

[5] On the derivation of macroscopic hyperbolic equations for binary multicellular growing mixtures [J].

Bellomo, N. ;

Bellouquid, A. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 57 (05) :744-756

[6] Nonlinear effects in particulate processes [J].

Bilgili, E. ;

Scarlett, B. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 63 (5-7) :E1131-E1141

[7] Coagulation and fragmentation with discrete mass loss [J].

Blair, Pamela N. ;

Lamb, Wilson ;

Stewart, Iain W. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 329 (02) :1285-1302

[8]

Bourgade JP, 2008, MATH COMPUT, V77, P851, DOI 10.1090/S0025-5718-07-02054-6

[9] Inverse Problems in Population Balances. Determination of Aggregation Kernel by Weighted Residuals [J].

Chakraborty, Jayanta ;

Kumar, Jitendra ;

Singh, Mehakpreet ;

Mahoney, Alan ;

Ramkrishna, Doraiswami .

INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH, 2015, 54 (42) :10530-10538

[10] EXISTENCE AND UNIQUENESS OF DENSITY CONSERVING SOLUTIONS TO THE COAGULATION-FRAGMENTATION EQUATIONS WITH STRONG FRAGMENTATION [J].

DA COSTA, FP .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 192 (03) :892-914

← 1 2 3 4 5 6 →