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Volumn 69, Issue 1, 2012, Pages 59-68

An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems

Author keywords

Crystallization; Finite elements; Mathematical modeling; Operator splitting; Population balance; Simulation

Indexed keywords

FINITE ELEMENT; MATHEMATICAL MODELING; OPERATOR-SPLITTING; POPULATION BALANCES; SIMULATION;

EID: 83955162318     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2011.09.031     Document Type: Article
Times cited : (22)

References (34)
  • 3
    • 79953050046 scopus 로고    scopus 로고
    • Crystal aggregation in a flow tube: image-based observation
    • Borchert C., Sundmacher K. Crystal aggregation in a flow tube: image-based observation. Chem. Eng. Technol. 2011, 34:545-556.
    • (2011) Chem. Eng. Technol. , vol.34 , pp. 545-556
    • Borchert, C.1    Sundmacher, K.2
  • 4
    • 0036396163 scopus 로고    scopus 로고
    • Advanced control of crystallization processes
    • Braatz R.D. Advanced control of crystallization processes. Annu. Rev. Control 2002, 26:87-99.
    • (2002) Annu. Rev. Control , vol.26 , pp. 87-99
    • Braatz, R.D.1
  • 5
    • 0036878107 scopus 로고    scopus 로고
    • Hydrodynamic transport properties of concentrated suspensions
    • Chang C., Powell R.L. Hydrodynamic transport properties of concentrated suspensions. AIChE J. 2002, 48:2475-2480.
    • (2002) AIChE J. , vol.48 , pp. 2475-2480
    • Chang, C.1    Powell, R.L.2
  • 6
    • 10044263287 scopus 로고    scopus 로고
    • CFD modeling of bubble columns flows: implementation of population balance
    • Chen P., Sanyal J., Dudukovic M. CFD modeling of bubble columns flows: implementation of population balance. Chem. Eng. Sci. 2004, 59:5201-5207.
    • (2004) Chem. Eng. Sci. , vol.59 , pp. 5201-5207
    • Chen, P.1    Sanyal, J.2    Dudukovic, M.3
  • 7
    • 33845743446 scopus 로고    scopus 로고
    • Considerations on the crystallization modeling: population balance solution
    • Costa C.B.B., Maciel M.R.W., Filho R.M. Considerations on the crystallization modeling: population balance solution. Comput. Chem. Eng. 2007, 31:206-218.
    • (2007) Comput. Chem. Eng. , vol.31 , pp. 206-218
    • Costa, C.B.B.1    Maciel, M.R.W.2    Filho, R.M.3
  • 8
    • 2942653250 scopus 로고    scopus 로고
    • Algorithm 832: UMFPACK V4.3-an unsymmetric-pattern multifrontal method
    • Davis T.A. Algorithm 832: UMFPACK V4.3-an unsymmetric-pattern multifrontal method. ACM Trans. Math. Software 2004, 30:196-199.
    • (2004) ACM Trans. Math. Software , vol.30 , pp. 196-199
    • Davis, T.A.1
  • 9
    • 2942655475 scopus 로고    scopus 로고
    • A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
    • Davis T.A. A column pre-ordering strategy for the unsymmetric-pattern multifrontal method. ACM Trans. Math. Software 2004, 30:167-195.
    • (2004) ACM Trans. Math. Software , vol.30 , pp. 167-195
    • Davis, T.A.1
  • 10
    • 0001946784 scopus 로고    scopus 로고
    • A combined unifrontal/multifrontal method for unsymmetric sparse matrices
    • Davis T.A., Duff I.S. A combined unifrontal/multifrontal method for unsymmetric sparse matrices. ACM Trans. Math. Software 1999, 25:1-20.
    • (1999) ACM Trans. Math. Software , vol.25 , pp. 1-20
    • Davis, T.A.1    Duff, I.S.2
  • 11
    • 83955160949 scopus 로고    scopus 로고
    • An operator-splitting heterogeneous finite element method for population balance equations: stability and convergence
    • Preprint 1531. WIAS, Berlin.
    • Ganesan, S., 2010. An operator-splitting heterogeneous finite element method for population balance equations: stability and convergence. Preprint 1531. WIAS, Berlin.
    • (2010)
    • Ganesan, S.1
  • 12
    • 80955127634 scopus 로고    scopus 로고
    • 2011. Implementation of an operator-splitting finite element method for high-dimensional parabolic problems
    • Preprint 04-11. Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik.
    • Ganesan, S., Tobiska, L., 2011. Implementation of an operator-splitting finite element method for high-dimensional parabolic problems. Preprint 04-11. Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik.
    • Ganesan, S.1    Tobiska, L.2
  • 13
    • 8544278921 scopus 로고    scopus 로고
    • High resolution algorithms for multidimensional population balance equations
    • Gunawan R., Fusman I., Braatz R.D. High resolution algorithms for multidimensional population balance equations. AIChE J. 2004, 50:2738-2749.
    • (2004) AIChE J. , vol.50 , pp. 2738-2749
    • Gunawan, R.1    Fusman, I.2    Braatz, R.D.3
  • 14
    • 44649170892 scopus 로고    scopus 로고
    • Parallel high-resolution finite volume simulation of particulate processes
    • Gunawan R., Fusman I., Braatz R.D. Parallel high-resolution finite volume simulation of particulate processes. AIChE J. 2008, 54:1449-1458.
    • (2008) AIChE J. , vol.54 , pp. 1449-1458
    • Gunawan, R.1    Fusman, I.2    Braatz, R.D.3
  • 15
    • 84863499542 scopus 로고    scopus 로고
    • A numerical method for the simulation of an aggregation-driven population balance system
    • doi: 10.1002/fld.2656. In press.
    • Hackbusch, W., John, V., Khachatryan, A., Suciu, C. A numerical method for the simulation of an aggregation-driven population balance system. Int. J. Numer. Methods Fluids, doi: 10.1002/fld.2656. In press.
    • Int. J. Numer. Methods Fluids
    • Hackbusch, W.1    John, V.2    Khachatryan, A.3    Suciu, C.4
  • 16
    • 50549203562 scopus 로고
    • Some problems in particle technology: a statistical mechanical formulation
    • Hulburt H., Katz S. Some problems in particle technology: a statistical mechanical formulation. Chem. Eng. Sci. 1964, 19:555-574.
    • (1964) Chem. Eng. Sci. , vol.19 , pp. 555-574
    • Hulburt, H.1    Katz, S.2
  • 17
    • 77952006385 scopus 로고    scopus 로고
    • On the impact of the scheme for solving the higher-dimensional equation in coupled population balance systems
    • John V., Roland M. On the impact of the scheme for solving the higher-dimensional equation in coupled population balance systems. Int. J. Numer. Methods Eng. 2010, 82:1450-1474.
    • (2010) Int. J. Numer. Methods Eng. , vol.82 , pp. 1450-1474
    • John, V.1    Roland, M.2
  • 18
    • 59249094912 scopus 로고    scopus 로고
    • Simulations of population balance systems with one internal coordinate using finite element methods
    • John V., Roland M., Mitkova T., Sundmacher K., Voigt L.T.A. Simulations of population balance systems with one internal coordinate using finite element methods. Chem. Eng. Sci. 2009, 64:733-741.
    • (2009) Chem. Eng. Sci. , vol.64 , pp. 733-741
    • John, V.1    Roland, M.2    Mitkova, T.3    Sundmacher, K.4    Voigt, L.T.A.5
  • 19
    • 0003734628 scopus 로고    scopus 로고
    • METIS-A Software Package for Partitioning Unstructured Graphs, Partitioning Meshes, and Computing Fill-Reducing Orderings of Sparse Matrices
    • Version 4.0. University of Minnesota.
    • Karypis, G., Kumar, V., 1998. METIS-A Software Package for Partitioning Unstructured Graphs, Partitioning Meshes, and Computing Fill-Reducing Orderings of Sparse Matrices. Version 4.0. University of Minnesota.
    • (1998)
    • Karypis, G.1    Kumar, V.2
  • 20
    • 77957974221 scopus 로고    scopus 로고
    • Model reduction techniques for the simulation of particle populations in fluid flow
    • Mathematical and Computer Modelling of Dynamical Systems. In press-a.
    • Krasnyk, M., Borchert, C., Mangold, M. Model reduction techniques for the simulation of particle populations in fluid flow. Mathematical and Computer Modelling of Dynamical Systems. In press-a.
    • Krasnyk, M.1    Borchert, C.2    Mangold, M.3
  • 21
    • 84855434544 scopus 로고    scopus 로고
    • Numerical reduction of a crystallizer model with internal and external coordinates by proper orthogonal decomposition
    • doi: 10.1016/j.ces.2011.05.053. In press-b.
    • Krasnyk, M., Mangold, M., Ganesan, S., Tobiska, L. Numerical reduction of a crystallizer model with internal and external coordinates by proper orthogonal decomposition. Chem. Eng. Sci., doi: 10.1016/j.ces.2011.05.053. In press-b.
    • Chem. Eng. Sci.
    • Krasnyk, M.1    Mangold, M.2    Ganesan, S.3    Tobiska, L.4
  • 22
    • 33750484334 scopus 로고    scopus 로고
    • Population balance and computational fluid dynamics modelling of ice crystallisation in a scraped surface freezer
    • Lian G., Moore S., Heeney L. Population balance and computational fluid dynamics modelling of ice crystallisation in a scraped surface freezer. Chem. Eng. Sci. 2006, 61:7819-7826.
    • (2006) Chem. Eng. Sci. , vol.61 , pp. 7819-7826
    • Lian, G.1    Moore, S.2    Heeney, L.3
  • 23
    • 0037065268 scopus 로고    scopus 로고
    • High-resolution simulation of multidimensional crystal growth
    • Ma D.L., Tafti D.K., Braatz R.D. High-resolution simulation of multidimensional crystal growth. Ind. Eng. Chem. Res. 2002, 41:6217-6223.
    • (2002) Ind. Eng. Chem. Res. , vol.41 , pp. 6217-6223
    • Ma, D.L.1    Tafti, D.K.2    Braatz, R.D.3
  • 24
    • 0037104859 scopus 로고    scopus 로고
    • Optimal control and simulation of multidimensional crystallization processes
    • Ma D.L., Tafti D.K., Braatz R.D. Optimal control and simulation of multidimensional crystallization processes. Comput. Chem. Eng. 2002, 26:1103-1116.
    • (2002) Comput. Chem. Eng. , vol.26 , pp. 1103-1116
    • Ma, D.L.1    Tafti, D.K.2    Braatz, R.D.3
  • 25
    • 79953321113 scopus 로고    scopus 로고
    • Fast high-resolution method for solving multidimensional population balances in crystallization
    • Majumder A., Kariwala V., Ansumali S., Rajendran A. Fast high-resolution method for solving multidimensional population balances in crystallization. Ind. Eng. Chem. Res. 2010, 49:3862-3872.
    • (2010) Ind. Eng. Chem. Res. , vol.49 , pp. 3862-3872
    • Majumder, A.1    Kariwala, V.2    Ansumali, S.3    Rajendran, A.4
  • 26
    • 0036449885 scopus 로고    scopus 로고
    • The inf-sup condition for the mapped Qk/Pk-1disc element in arbitrary space dimensions
    • Matthies G., Tobiska L. The inf-sup condition for the mapped Qk/Pk-1disc element in arbitrary space dimensions. Computing 2002, 69:119-139.
    • (2002) Computing , vol.69 , pp. 119-139
    • Matthies, G.1    Tobiska, L.2
  • 27
    • 38149073208 scopus 로고    scopus 로고
    • A two-level discretisation algorithm for the efficient solution of higher-dimensional population balance models
    • Pinto M.A., Immanuel C.D., III F.J.D. A two-level discretisation algorithm for the efficient solution of higher-dimensional population balance models. Chem. Eng. Sci. 2008, 63:1304-1314.
    • (2008) Chem. Eng. Sci. , vol.63 , pp. 1304-1314
    • Pinto, M.A.1    Immanuel, C.D.2    III, F.J.D.3
  • 28
    • 34447542581 scopus 로고    scopus 로고
    • Adaptive high-resolution schemes for multidimensional population balances in crystallization processes
    • Qamar S., Ashfaq A., Warnecke G., Angelov I., Elsner M., Seidel-Morgenstern A. Adaptive high-resolution schemes for multidimensional population balances in crystallization processes. Comput. Chem. Eng. 2007, 31:1296-1311.
    • (2007) Comput. Chem. Eng. , vol.31 , pp. 1296-1311
    • Qamar, S.1    Ashfaq, A.2    Warnecke, G.3    Angelov, I.4    Elsner, M.5    Seidel-Morgenstern, A.6
  • 29
    • 79851511158 scopus 로고    scopus 로고
    • Numerical solution of a multi-dimensional batch crystallization model with fines dissolution
    • Qamar S., Noor S., Rehman M., Seidel-Morgenstern A. Numerical solution of a multi-dimensional batch crystallization model with fines dissolution. Comput. Chem. Eng. 2011, 35:412-422.
    • (2011) Comput. Chem. Eng. , vol.35 , pp. 412-422
    • Qamar, S.1    Noor, S.2    Rehman, M.3    Seidel-Morgenstern, A.4
  • 31
    • 0037074624 scopus 로고    scopus 로고
    • Population balance modeling. Promise for the future
    • Ramkrishna D., Mahoney A.W. Population balance modeling. Promise for the future. Chem. Eng. Sci. 2002, 57:595-606.
    • (2002) Chem. Eng. Sci. , vol.57 , pp. 595-606
    • Ramkrishna, D.1    Mahoney, A.W.2
  • 32
    • 3943081295 scopus 로고    scopus 로고
    • Particle technology: Design of particulate products and dispersed systems
    • Teipel U. Particle technology: Design of particulate products and dispersed systems. Chem. Eng. Technol. 2004, 27:751-756.
    • (2004) Chem. Eng. Technol. , vol.27 , pp. 751-756
    • Teipel, U.1
  • 33
    • 61649116446 scopus 로고    scopus 로고
    • Modeling and computational fluid dynamics-population balance equation-micromixing simulation of impinging jet crystallizers
    • Woo X.Y., Tan R.B.H., Braatz R.D. Modeling and computational fluid dynamics-population balance equation-micromixing simulation of impinging jet crystallizers. Cryst. Growth Des. 2009, 9:156-164.
    • (2009) Cryst. Growth Des. , vol.9 , pp. 156-164
    • Woo, X.Y.1    Tan, R.B.H.2    Braatz, R.D.3
  • 34
    • 33745683564 scopus 로고    scopus 로고
    • Simulation of mixing effects in antisolvent crystallization using a coupled CFD-PDF-PBE approach
    • Woo X.Y., Tan R.B.H., Chow P.S., Braatz R.D. Simulation of mixing effects in antisolvent crystallization using a coupled CFD-PDF-PBE approach. Cryst. Growth Des. 2006, 6:1291-1303.
    • (2006) Cryst. Growth Des. , vol.6 , pp. 1291-1303
    • Woo, X.Y.1    Tan, R.B.H.2    Chow, P.S.3    Braatz, R.D.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.