Volume 53, Number 5, September-October 2019
|1695 - 1713
|13 September 2019
New volume consistent approximation for binary breakage Population Balance Equation and its convergence analysis
Bernal Institute, Department of Chemical Science, University of Limerick, V94 T9PX Limerick, Ireland
2 8H Thomas, Department of Chemical Engineering, Pennsylvania State University, State College, PA 16802, USA
Accepted: 7 May 2019
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.
Mathematics Subject Classification: 35R09 / 65R20
Key words: Particles / binary breakage / population balance equation / finite volume scheme / nonuniform grids
© EDP Sciences, SMAI 2019
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