Convergence analysis of finite volume scheme for nonlinear aggregation population balance equation

2019 ◽  
Vol 42 (9) ◽  
pp. 3236-3254 ◽  
Author(s):  
Mehakpreet Singh ◽  
Gurmeet Kaur
Keyword(s):  
Convergence Analysis ◽  
Finite Volume ◽  
Balance Equation ◽  
Population Balance ◽  
Population Balance Equation ◽  
Finite Volume Scheme ◽  
Volume Scheme

scholarly journals Characterization of Simultaneous Evolution of Size and Composition Distributions Using Generalized Aggregation Population Balance Equation

Pharmaceutics ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1152
Author(s):  
Mehakpreet Singh ◽  
Ashish Kumar ◽  
Saeed Shirazian ◽  
Vivek Ranade ◽  
Gavin Walker
Keyword(s):  
Finite Volume ◽  
Balance Equation ◽  
Numerical Scheme ◽  
Population Balance ◽  
Population Balance Equation ◽  
Finite Volume Scheme ◽  
Average Technique ◽  
Volume Scheme ◽  
Density Prediction ◽  
Cell Average

The application of multi-dimensional population balance equations (PBEs) for the simulation of granulation processes is recommended due to the multi-component system. Irrespective of the application area, numerical scheme selection for solving multi-dimensional PBEs is driven by the accuracy in (size) number density prediction alone. However, mixing the components, i.e., the particles (excipients and API) and the binding liquid, plays a crucial role in predicting the granule compositional distribution during the pharmaceutical granulation. A numerical scheme should, therefore, be able to predict this accurately. Here, we compare the cell average technique (CAT) and finite volume scheme (FVS) in terms of their accuracy and applicability in predicting the mixing state. To quantify the degree of mixing in the system, the sum-square χ2 parameter is studied to observe the deviation in the amount binder from its average. It has been illustrated that the accurate prediction of integral moments computed by the FVS leads to an inaccurate prediction of the χ2 parameter for a bicomponent population balance equation. Moreover, the cell average technique (CAT) predicts the moments with moderate accuracy; however, it computes the mixing of components χ2 parameter with higher precision than the finite volume scheme. The numerical testing is performed for some benchmarking kernels corresponding to which the analytical solutions are available in the literature. It will be also shown that both numerical methods equally well predict the average size of the particles formed in the system; however, the finite volume scheme takes less time to compute these results.

scholarly journals Mass-based finite volume scheme for aggregation, growth and nucleation population balance equation

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190552 ◽  
Author(s):  
Mehakpreet Singh ◽  
Hamza Y. Ismail ◽  
Themis Matsoukas ◽  
Ahmad B. Albadarin ◽  
Gavin Walker
Keyword(s):  
Finite Volume ◽  
Balance Equation ◽  
Population Balance ◽  
Distribution Functions ◽  
Population Balance Equation ◽  
Finite Volume Scheme ◽  
Number Density ◽  
Finite Volume Schemes ◽  
One Dimensional ◽  
Number Distribution

In this paper, a new mass-based numerical method is developed using the notion of Forestier-Coste & Mancini (Forestier-Coste & Mancini 2012, SIAM J. Sci. Comput. 34 , B840–B860. ( doi:10.1137/110847998 )) for solving a one-dimensional aggregation population balance equation. The existing scheme requires a large number of grids to predict both moments and number density function accurately, making it computationally very expensive. Therefore, a mass-based finite volume is developed which leads to the accurate prediction of different integral properties of number distribution functions using fewer grids. The new mass-based and existing finite volume schemes are extended to solve simultaneous aggregation-growth and aggregation-nucleation problems. To check the accuracy and efficiency, the mass-based formulation is compared with the existing method for two kinds of benchmark kernels, namely analytically solvable and practical oriented kernels. The comparison reveals that the mass-based method computes both number distribution functions and moments more accurately and efficiently than the existing method.

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

2019 ◽  
Vol 53 (5) ◽  
pp. 1695-1713 ◽  
Author(s):  
Mehakpreet Singh ◽  
Themis Matsoukas ◽  
Ahmad B. Albadarin ◽  
Gavin Walker
Keyword(s):  
Convergence Analysis ◽  
Balance Equation ◽  
Order Of Convergence ◽  
Numerical Approximation ◽  
Population Balance ◽  
Benchmark Problems ◽  
Population Balance Equation ◽  
Finite Volume Scheme ◽  
Numerical Predictions ◽  
Second Order Convergence

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.

Development and Convergence Analysis of a Finite Volume Scheme for Solving Breakage Equation

2015 ◽  
Vol 53 (4) ◽  
pp. 1672-1689 ◽  
Author(s):  
Jitendra Kumar ◽  
Jitraj Saha ◽  
Evangelos Tsotsas
Keyword(s):  
Convergence Analysis ◽  
Finite Volume ◽  
Finite Volume Scheme ◽  
Volume Scheme
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