메뉴 건너뛰기




Volumn 70, Issue , 2012, Pages 77-86

Numerical reduction of a crystallizer model with internal and external coordinates by proper orthogonal decomposition

Author keywords

Crystallization; Model order reduction; Numerical analysis; Particulate processes; Population balance; Proper orthogonal decomposition

Indexed keywords

ADVANCED PROCESS CONTROL; CRYSTALLIZATION PROCESS; HIGH-ORDER; INTERNAL COORDINATES; MODEL ORDER REDUCTION; MODEL-BASED OPC; NONLINEAR TERMS; NUMERICAL SOLUTION; PARTICLE FORMATIONS; PARTICULATE PROCESS; POPULATION BALANCES; PROPER ORTHOGONAL DECOMPOSITIONS; REAL-TIME APPLICATION; REDUCED MODEL; REDUCED ORDER MODELS; REFERENCE MODELS;

EID: 84855434544     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2011.05.053     Document Type: Article
Times cited : (12)

References (28)
  • 1
    • 38149027613 scopus 로고    scopus 로고
    • Reduced-order methodologies for feedback control of particle size distribution in semi-batch emulsion copolymerization
    • Dokucu M.T., Park M.J., Doyle F.J. Reduced-order methodologies for feedback control of particle size distribution in semi-batch emulsion copolymerization. Chem. Eng. Sci. 2008, 63:1230-1245.
    • (2008) Chem. Eng. Sci. , vol.63 , pp. 1230-1245
    • Dokucu, M.T.1    Park, M.J.2    Doyle, F.J.3
  • 2
    • 84855439354 scopus 로고    scopus 로고
    • An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems. Faculty of Mathematics, University of Magdeburg, Preprint No. 11-11.
    • Ganesan, S., Tobiska, L., 2011a. An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems. Faculty of Mathematics, University of Magdeburg, Preprint No. 11-11.
    • (2011)
    • Ganesan, S.1    Tobiska, L.2
  • 3
    • 84855441988 scopus 로고    scopus 로고
    • Implementation of an operator-splitting finite element method for high-dimensional parabolic problems. Faculty of Mathematics, University of Magdeburg, Preprint No. 11-04.
    • Ganesan, S., Tobiska, L., 2011b. Implementation of an operator-splitting finite element method for high-dimensional parabolic problems. Faculty of Mathematics, University of Magdeburg, Preprint No. 11-04.
    • (2011)
    • Ganesan, S.1    Tobiska, L.2
  • 4
    • 0033540943 scopus 로고    scopus 로고
    • Optimal control of vortex shedding using low-order models. Part I-open-loop model development
    • Graham W.R., Peraire J., Tang K.Y. Optimal control of vortex shedding using low-order models. Part I-open-loop model development. Int. J. Numer. Methods Eng. 1999, 44:945-972.
    • (1999) Int. J. Numer. Methods Eng. , vol.44 , pp. 945-972
    • Graham, W.R.1    Peraire, J.2    Tang, K.Y.3
  • 5
    • 41549118036 scopus 로고    scopus 로고
    • Reduced basis method for finite volume approximations of parametrized linear evolution equations
    • Haasdonk B., Ohlberger M. Reduced basis method for finite volume approximations of parametrized linear evolution equations. ESAIM: Math. Modelling Numer. Anal. 2008, 42:277-302.
    • (2008) ESAIM: Math. Modelling Numer. Anal. , vol.42 , pp. 277-302
    • Haasdonk, B.1    Ohlberger, M.2
  • 6
    • 79952041749 scopus 로고    scopus 로고
    • Diffusion coefficients in ethanol and in water at 298K: linear free energy relationships
    • Hills E.E., Abraham M.H., Hersey A., Bevan C.D. Diffusion coefficients in ethanol and in water at 298K: linear free energy relationships. Fluid Phase Equilibria 2011, 303:45-55.
    • (2011) Fluid Phase Equilibria , vol.303 , pp. 45-55
    • Hills, E.E.1    Abraham, M.H.2    Hersey, A.3    Bevan, C.D.4
  • 8
    • 0024104856 scopus 로고
    • A discretized population balance for nucleation, growth, and aggregation
    • Hounslow M.J., Ryall R.L., Marshall V.R. A discretized population balance for nucleation, growth, and aggregation. A.I.Ch.E. J. 1988, 34:1821-1832.
    • (1988) A.I.Ch.E. J. , vol.34 , pp. 1821-1832
    • Hounslow, M.J.1    Ryall, R.L.2    Marshall, V.R.3
  • 9
    • 0000104411 scopus 로고    scopus 로고
    • A reduced-order method for simulation and control of fluid flows
    • Ito K., Ravindran S.S. A reduced-order method for simulation and control of fluid flows. J. Comput. Phys. 1998, 143:403-425.
    • (1998) J. Comput. Phys. , vol.143 , pp. 403-425
    • Ito, K.1    Ravindran, S.S.2
  • 10
    • 7444244347 scopus 로고    scopus 로고
    • MooNMD-a program package based on mapped finite element methods
    • John V., Matthies G. MooNMD-a program package based on mapped finite element methods. Comput. Visualization Sci. 2004, 6:163-170.
    • (2004) Comput. Visualization Sci. , vol.6 , pp. 163-170
    • John, V.1    Matthies, G.2
  • 11
    • 84855461711 scopus 로고    scopus 로고
    • Model reduction techniques for the simulation of particle populations in fluid flow. Math. Comput. Modelling Dyn. Syst., accepted for publication.
    • Krasnyk, M., Borchert, C., Mangold, M. Model reduction techniques for the simulation of particle populations in fluid flow. Math. Comput. Modelling Dyn. Syst., accepted for publication.
    • Krasnyk, M.1    Borchert, C.2    Mangold, M.3
  • 12
    • 77957989637 scopus 로고    scopus 로고
    • Reduction of a urea crystallizer model by proper orthogonal decomposition and best-points interpolation
    • Krasnyk M., Mangold M. Reduction of a urea crystallizer model by proper orthogonal decomposition and best-points interpolation. Ind. Eng. Chem. Res. 2010, 49:9887-9898.
    • (2010) Ind. Eng. Chem. Res. , vol.49 , pp. 9887-9898
    • Krasnyk, M.1    Mangold, M.2
  • 13
    • 77957911248 scopus 로고    scopus 로고
    • Reduction procedure for parametrized fluid dynamics problems based on proper orthogonal decomposition and calibration
    • Krasnyk M., Mangold M., Kienle A. Reduction procedure for parametrized fluid dynamics problems based on proper orthogonal decomposition and calibration. Chem. Eng. Sci. 2010, 65:6238-6246.
    • (2010) Chem. Eng. Sci. , vol.65 , pp. 6238-6246
    • Krasnyk, M.1    Mangold, M.2    Kienle, A.3
  • 14
    • 0030128282 scopus 로고    scopus 로고
    • On the solution of population balance equations by discretization-I. A fixed pivot technique
    • Kumar S., Ramkrishna D. On the solution of population balance equations by discretization-I. A fixed pivot technique. Chem. Eng. Sci. 1996, 51:1311-1332.
    • (1996) Chem. Eng. Sci. , vol.51 , pp. 1311-1332
    • Kumar, S.1    Ramkrishna, D.2
  • 15
    • 0038693394 scopus 로고    scopus 로고
    • Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics
    • Kunisch K., Volkwein S. Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. SIAM J. Numer. Anal. 2003, 40:492-515.
    • (2003) SIAM J. Numer. Anal. , vol.40 , pp. 492-515
    • Kunisch, K.1    Volkwein, S.2
  • 16
    • 10044271895 scopus 로고    scopus 로고
    • Solution of population balance equations using the direct quadrature method of moments
    • Marchisio D.L., Fox R.O. Solution of population balance equations using the direct quadrature method of moments. J. Aerosol Sci. 2005, 36:43-73.
    • (2005) J. Aerosol Sci. , vol.36 , pp. 43-73
    • Marchisio, D.L.1    Fox, R.O.2
  • 18
    • 0037440820 scopus 로고    scopus 로고
    • Quadrature method of moments for aggregation-breakage processes
    • Marchisio D.L., Vigil R.D., Fox R.O. Quadrature method of moments for aggregation-breakage processes. J. Colloid Interface Sci. 2003, 258:322-334.
    • (2003) J. Colloid Interface Sci. , vol.258 , pp. 322-334
    • Marchisio, D.L.1    Vigil, R.D.2    Fox, R.O.3
  • 19
    • 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
  • 21
    • 38349195074 scopus 로고    scopus 로고
    • A "best points" interpolation method for efficient approximation of parametrized functions
    • Nguyen N.C., Patera A.T., Peraire J. A "best points" interpolation method for efficient approximation of parametrized functions. Int. J. Numer. Methods Eng. 2008, 73:521-543.
    • (2008) Int. J. Numer. Methods Eng. , vol.73 , pp. 521-543
    • Nguyen, N.C.1    Patera, A.T.2    Peraire, J.3
  • 22
    • 1942540476 scopus 로고    scopus 로고
    • Nonlinear model order reduction and control of particle size distribution in a semibatch vinyl acetate/butyl acrylate emulsion copolymerization reactor
    • Park M.J., Doyle F.J. Nonlinear model order reduction and control of particle size distribution in a semibatch vinyl acetate/butyl acrylate emulsion copolymerization reactor. Korean J. Chem. Eng. 2004, 21:168-176.
    • (2004) Korean J. Chem. Eng. , vol.21 , pp. 168-176
    • Park, M.J.1    Doyle, F.J.2
  • 23
    • 63449114224 scopus 로고    scopus 로고
    • On the solution of population balances for nucleation, growth, aggregation and breakage processes
    • Qamar S., Warnecke G., Elsner M.P. On the solution of population balances for nucleation, growth, aggregation and breakage processes. Chem. Eng. Sci. 2009, 64:2088-2095.
    • (2009) Chem. Eng. Sci. , vol.64 , pp. 2088-2095
    • Qamar, S.1    Warnecke, G.2    Elsner, M.P.3
  • 25
    • 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
  • 26
    • 53749107686 scopus 로고    scopus 로고
    • Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations
    • Rozza G., Huynh D.B.P., Patera A.T. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Arch. Comput. Methods Eng. 2008, 15:229-275.
    • (2008) Arch. Comput. Methods Eng. , vol.15 , pp. 229-275
    • Rozza, G.1    Huynh, D.B.P.2    Patera, A.T.3
  • 27
    • 0000246863 scopus 로고
    • Turbulence and the dynamics of coherent structures. Part 1: coherent structures
    • Sirovich L. Turbulence and the dynamics of coherent structures. Part 1: coherent structures. Q. Appl. Math. 1987, 45:561-571.
    • (1987) Q. Appl. Math. , vol.45 , pp. 561-571
    • Sirovich, L.1
  • 28
    • 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.