Free Access
Issue
ESAIM: M2AN
Volume 46, Number 6, November-December 2012
Page(s) 1447 - 1465
DOI https://doi.org/10.1051/m2an/2012012
Published online 31 May 2012
  1. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods, 3th edition. Springer (2008).
  2. E. Burman, Consistent SUPG-method for transient transport problems : Stability and convergence. Comput. Methods Appl. Mech. Eng. 199 (2010) 1114–1123. [CrossRef] [MathSciNet]
  3. I.T. Cameron, F.Y. Wang, C.D. Immanuel and F. Stepanek, Process systems modelling and applications in granulation : a review. Chem. Eng. Sci. 60 (2005) 3723–375. [CrossRef]
  4. F.B. Campos and P.L.C. Lage, A numerical method for solving the transient multidimensional population balance equation using an Euler-Lagrange formulation. Chem. Eng. Sci. 58 (2003) 2725–2744. [CrossRef]
  5. P. Chen, J. Sanyal and M.P. Dudukovic, CFD modeling of bubble columns flows : implementation of population balance. Chem. Eng. Sci. 59 (2004) 5201–5207. [CrossRef]
  6. K. Eriksson and C. Johnson, Adaptive streamline diffusion finite element methods for stationary convection-diffusion problems. Math. Comput. 60 (1993) 167–188. [CrossRef]
  7. S. Ganesan and L. Tobiska, Implementation of an operator-splitting finite element method for high-dimensional parabolic problems. Faculty of Mathematics, University of Magdeburg, Preprint No. 11-04 (2011).
  8. S. Ganesan and L. Tobiska, An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems. Chem. Eng. Sci. 69 (2012) 59–68. [CrossRef]
  9. R. Glowinski, E.J. Dean, G. Guidoboni, D.H. Peaceman and H.H. Rachford, Applications of operator-splitting methods to the direct numerical simulation of particulate and free-surface flows and to the numerical solution of the two-dimensional elliptic Monge-Ampère equation. Japan J. Ind. Appl. Math. 25 (2008) 1–63. [CrossRef] [MathSciNet]
  10. R. Gunawan, I. Fusman and R.D. Braatz, High resolution algorithms for multidimensional population balance equations. AIChE J. 50 (2004) 2738–2749. [CrossRef]
  11. R. Gunawan, I. Fusman and R.D. Braatz, Parallel high-resolution finite volume simulation of particulate processes. AIChE J. 54 (2008) 1449–1458. [CrossRef]
  12. T.J.R. Hughes and A.N. Brooks, A multi-dimensional upwind scheme with no cross-wind diffusion, in Finite element methods for convection dominated flows, edited by T.J.R. Hughes. ASME, New York (1979) 19–35.
  13. H.M. Hulburt and S. Katz, Some problems in particle technology : A statistical mechanical formulation. Chem. Eng. Sci. 19 (1964) 555–574. [CrossRef]
  14. V. John and J. Novo, Error analysis of the SUPG finite element discretization of evolutionary convection-diffusion-reaction equations. SIAM J. Numer. Anal. 49 (2011) 1149–1176. [CrossRef]
  15. V. John, M. Roland, T. Mitkova, K. Sundmacher, L. Tobiska and A. Voigt, Simulations of population balance systems with one internal coordinate using finite element methods. Chem. Eng. Sci. 64 (2009) 733–741. [CrossRef]
  16. V. Kulikov, H. Briesen, R. Grosch, A. Yang, L. von Wedel and W. Marquardt, Modular dynamic simulation for integrated particulate processes by means of tool integration. Chem. Eng. Sci. 60 (2005) 2069–2083. [CrossRef]
  17. V. Kulikov, H. Briesen and W. Marquardt, A framework for the simulation of mass crystallization considering the effect of fluid dynamics. Chem. Eng. Sci. 45 (2006) 886–899.
  18. G. Lian, S. Moore and L. Heeney, Population balance and computational fluid dynamics modelling of ice crystallisation in a scraped surface freezer. Chem. Eng. Sci. 61 (2006) 7819–7826. [CrossRef]
  19. D.L. Ma, D.K. Tafti and R.D. Braatz, High-resolution simulation of multidimensional crystal growth. Ind. Eng. Chem. Res. 41 (2002) 6217–6223. [CrossRef]
  20. D.L. Ma, D.K. Tafti and R.D. Braatz, Optimal control and simulation of multidimensional crystallization processes. Comput. Chem. Eng. 26 (2002) 1103–1116. [CrossRef]
  21. A. Majumder, V. Kariwala, S. Ansumali and A. Rajendran, Fast high-resolution method for solving multidimensional population balances in crystallization. Ind. Eng. Chem. Res. 49 (2010) 3862–3872. [CrossRef]
  22. D. Marchisio and R. Fox, Solution of population balance equations using the direct quadrature method of moments. J. Aero. Sci. 36 (2005) 43–73. [CrossRef]
  23. D. L. Marchisio and R.O. Fox, Solution of population balance equations using the direct quadrature method of moments. J. Aero. Sci. 36 (2005) 43–73. [CrossRef]
  24. M. N. Nandanwara and S. Kumar, A new discretization of space for the solution of multi-dimensional population balance equations : Simultaneous breakup and aggregation of particles. Chem. Eng. Sci. 63 (2008) 3988–3997. [CrossRef]
  25. D. Ramkrishna, Population Balances, Theory and Applications to Particulate Systems in Engineering. Academic Press, San Diego (2000).
  26. D. Ramkrishna and A.W. Mahoney, Population balance modeling : Promise for the future. Chem. Eng. Sci. 57 (2002) 595–606. [CrossRef]
  27. V. Thomee, Galerkin Finite Element Methods for Parabolic Problems, 3th edition. Springer (2008).

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you