Numerical simulation and convergence analysis of a finite volume scheme for solving general breakage population balance equations

Kumar, Rajesh; Kumar, Jitendra

doi:10.1016/j.amc.2012.10.098

Cited by 34 publications

(57 citation statements)

References 27 publications

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“…Furthermore, a detailed convergence and stability analysis of the scheme proposed in [15] have been provided. It is found in [15], that the order of convergence of the scheme approximating the coupled aggregation-fragmentation equation depends upon the type of meshes, whereas in [13], the scheme approximating the pure BPBE (5), is of second order convergent independently of the meshes.…”

Section: Existing Literaturesmentioning

confidence: 97%

“…In literature the numerical methods like, finite volume methods [4,5,10,13], stochastic methods [19,23], moment methods [7,8], sectional methods [9,16] etc. have been used widely to approximate different forms of the population balance equations (PBEs).…”

Section: Existing Literaturesmentioning

confidence: 99%

“…It is to be noted that in both the works [1,4], the authors have considered the mass conservative formulation of the PBEs. Very recently, Kumar et al [13] have developed a finite volume scheme approximating the mass conservative form of the pure multiple fragmentation equation (5) and proved the convergence of the approximating solutions. In the article [15], Kumar et al have developed finite volume Int J Adv Eng Sci Appl Math schemes of coupled aggregation-fragmentation equations and in [14] they extended the idea for the PBEs incorporating aggregation, fragmentation, growth and nucleation.…”

Section: Existing Literaturesmentioning

confidence: 99%

“…Referring to [13], a mass conservative formulation of the Eq. (1) is written in the following form, xof ðx; tÞ…”

Section: Introductionmentioning

confidence: 99%

“…It is seen that besides conserving the total mass, the new scheme also gives a better prediction of the total number of the particles in the system as compared to the finite volume scheme of Kumar et al (Appl Math Comput 219(10):5140-5151, 2013). Unlike [13], the scheme in this paper is computationally very efficient and robust to apply on both the uniform and nonuniform meshes. The development of the new scheme is completed by providing a detailed consistency and convergence analysis of the numerical solution.…”

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Development of a mass conserving discretization technique for breakage problems and its convergence analysis

Saha

Kumar

2015

Int J Adv Eng Sci Appl Math

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In this work an efficient and accurate numerical scheme based on the finite volume method has been introduced to approximate the pure breakage population balance equations. The scheme is designed to conserve the total mass of the particles in the system. The simplicity of both the discrete formulation and its coding are the key features of the new method. It is seen that besides conserving the total mass, the new scheme also gives a better prediction of the total number of the particles in the system as compared to the finite volume scheme of Kumar et al. (Appl Math Comput 219(10):5140-5151, 2013). Unlike [13], the scheme in this paper is computationally very efficient and robust to apply on both the uniform and nonuniform meshes. The development of the new scheme is completed by providing a detailed consistency and convergence analysis of the numerical solution. It is observed that the new scheme is of second order convergent independently of the type of meshes. Moreover, numerical results are compared against several test problems, which include the problems whose solutions are analytically tractable and those which are practically oriented. The mathematical results on convergence analysis of the new scheme has also been verified numerically.

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Section: Existing Literaturesmentioning

confidence: 97%

Section: Existing Literaturesmentioning

confidence: 99%

Section: Existing Literaturesmentioning

confidence: 99%

“…Referring to [13], a mass conservative formulation of the Eq. (1) is written in the following form, xof ðx; tÞ…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 97%

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Development of a mass conserving discretization technique for breakage problems and its convergence analysis

Saha

Kumar

2015

Int J Adv Eng Sci Appl Math

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A method for numerical modelling of convection–reaction–diffusion using electrical analogues

Shafaq

Kennedy

Delauré

2015

Int J Numerical Modelling

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In this paper, a new method, called the lumped-component circuit method (LCM), is developed for one-dimensioal and two-dimensional convection-reaction-diffusion with low to moderate Peclet numbers, tested for modelling both steady-state and transient problems, and compared with standard finite volume method (FVM) schemes. The method has been developed principally for solving equations with piecewise-constant coefficients using nodes that are not positioned to correspond to the coefficient discontinuities. In such situations, the FVM solutions do not converge consistently as the node spacing is decreased, but LCM solutions do. In general, the LCM method is more accurate than the FVM schemes tested, and, while the computational cost of LCM is higher, results suggest that it can be more efficient. Like the transmission line method (TLM), it is an indirect scheme in which the problem to be solved is first represented by an analogous transmission line (TL). Unlike with TLM, however, the TL is then modelled using a lumped-component circuit, the voltages at nodes within that circuit being calculated.

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Improved accuracy and convergence analysis of finite volume methods for particle fragmentation models

Saha

Bück

2020

Math Methods in App Sciences

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In this work, two new number-and volume-consistent finite volume methods for the numerical solution of binary and multifragmentation problems are introduced. The new number-consistency is achieved by introducing a single weight function. Several benchmark problems of different complexity are solved to assess the accuracy. Mathematical convergence analysis suggests that both of the new methods are numerically second order convergent with respect to the grid size on uniform and nonuniform meshes.

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Numerical simulation and convergence analysis of a finite volume scheme for solving general breakage population balance equations

Cited by 34 publications

References 27 publications

Development of a mass conserving discretization technique for breakage problems and its convergence analysis

Development of a mass conserving discretization technique for breakage problems and its convergence analysis

A method for numerical modelling of convection–reaction–diffusion using electrical analogues

Improved accuracy and convergence analysis of finite volume methods for particle fragmentation models

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