메뉴 건너뛰기




Volumn 196, Issue 2, 2006, Pages 619-633

Numerical calculation of the moments of the population balance equation

Author keywords

Least squares method; Population balance equation; Quadrature approximation

Indexed keywords

LEAST SQUARES APPROXIMATIONS; POPULATION STATISTICS; PROBABILITY DENSITY FUNCTION; PROBLEM SOLVING; QUADRATIC PROGRAMMING;

EID: 33746239169     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.10.015     Document Type: Article
Times cited : (51)

References (37)
  • 3
    • 33746182394 scopus 로고    scopus 로고
    • P. Bochev, Finite element methods based on least-squares and modified variational principles, Technical Report, POSTECH, 2001.
  • 5
    • 0030086888 scopus 로고    scopus 로고
    • A wavelet-Galerkin method for solving population balance equations
    • Chen M., Hwang C., and Shih Y. A wavelet-Galerkin method for solving population balance equations. Comput. Chem. Eng. 20 2 (1996) 131-145
    • (1996) Comput. Chem. Eng. , vol.20 , Issue.2 , pp. 131-145
    • Chen, M.1    Hwang, C.2    Shih, Y.3
  • 7
    • 33746245329 scopus 로고    scopus 로고
    • B. De Maerschalck, Space-Time least-squares spectral element method for unsteady flows-application and evaluation for linear and non-linear hyperbolic scalar equations, Master Thesis Report, Delft University of Technology, Department of Aerospace Engineering, The Netherlands, 2003.
  • 9
    • 0037189455 scopus 로고    scopus 로고
    • A moment methodology for coagulation and breakage problems: part 2. Moment models and distribution reconstruction
    • Diemer R.B., and Olson J.H. A moment methodology for coagulation and breakage problems: part 2. Moment models and distribution reconstruction. Chem. Eng. Sci. 57 (2002) 2211-2228
    • (2002) Chem. Eng. Sci. , vol.57 , pp. 2211-2228
    • Diemer, R.B.1    Olson, J.H.2
  • 10
    • 33746229400 scopus 로고    scopus 로고
    • C.A. Dorao, H.A. Jakobsen, Application of the least square method to population balance problems. Comput. Chem. Eng. (2005), submitted for publication.
  • 11
    • 33746258205 scopus 로고    scopus 로고
    • C.A. Dorao, H.A. Jakobsen, An evaluation of selected numerical methods for solving the population balance equation, Fourth International Conference on CFD in the Oil and Gas, Metallurgical and Process Industries. SINTEF/NTNU Trondheim, Norway, 6-8 June 2005.
  • 12
    • 33746229399 scopus 로고    scopus 로고
    • C.A. Dorao, H.A. Jakobsen, Time-space least squares spectral element method for the population balance problems. Advances in Computational Methods in Science and Engineering 2005, ICCMSE, 21-26 October 2005, Greece. Lecture Series on Computer and Computational Sciences, Vol. 4A, pp. 171-174.
  • 14
    • 0022162711 scopus 로고
    • Dynamics of discrete distribution for Smoluchowski coagulation model
    • Frenklach M. Dynamics of discrete distribution for Smoluchowski coagulation model. J. Colloid Interface Sci. 108 1 (1985) 237-242
    • (1985) J. Colloid Interface Sci. , vol.108 , Issue.1 , pp. 237-242
    • Frenklach, M.1
  • 15
    • 0037189451 scopus 로고    scopus 로고
    • Method of moments with interpolative closure
    • Frenklach M. Method of moments with interpolative closure. Chem. Eng. Sci. 57 (2002) 2229-2239
    • (2002) Chem. Eng. Sci. , vol.57 , pp. 2229-2239
    • Frenklach, M.1
  • 16
    • 0028388229 scopus 로고
    • Algorithm 726: ORTHPOL-a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules
    • Gautschi W. Algorithm 726: ORTHPOL-a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules. ACM Trans. Math. Software 20 1 (1994) 21-62
    • (1994) ACM Trans. Math. Software , vol.20 , Issue.1 , pp. 21-62
    • Gautschi, W.1
  • 17
    • 0000223746 scopus 로고
    • Calculation of Gauss quadrature rules
    • Golub G.H., and Welsh J.H. Calculation of Gauss quadrature rules. Math. Comp. 23 106 (1969) 221-230
    • (1969) Math. Comp. , vol.23 , Issue.106 , pp. 221-230
    • Golub, G.H.1    Welsh, J.H.2
  • 18
    • 0000072192 scopus 로고
    • Error Bounds in equilibrium statistical mechanics
    • Gordon R.G. Error Bounds in equilibrium statistical mechanics. J. Math. Phys. 9 5 (1968) 655-663
    • (1968) J. Math. Phys. , vol.9 , Issue.5 , pp. 655-663
    • Gordon, R.G.1
  • 19
    • 50549203562 scopus 로고
    • Some problems in particle technology
    • Hulburt H.M., and Katz S. Some problems in particle technology. Chem. Eng. Sci. 19 (1964) 555-574
    • (1964) Chem. Eng. Sci. , vol.19 , pp. 555-574
    • Hulburt, H.M.1    Katz, S.2
  • 20
    • 22944441941 scopus 로고    scopus 로고
    • Modeling of bubble column reactors: progress and limitations
    • Jakobsen H.A., Lindborg H., and Dorao C.A. Modeling of bubble column reactors: progress and limitations. Indust. Eng. Chem. Res. 44 14 (2005) 5107-5151
    • (2005) Indust. Eng. Chem. Res. , vol.44 , Issue.14 , pp. 5107-5151
    • Jakobsen, H.A.1    Lindborg, H.2    Dorao, C.A.3
  • 22
    • 0000601179 scopus 로고
    • Continued-fraction technique for tight-binding systems. A generalized-moments method
    • Lambin P., and Gaspard J.P. Continued-fraction technique for tight-binding systems. A generalized-moments method. Phys. Rev. B 26 8 (1982) 4356-4368
    • (1982) Phys. Rev. B , vol.26 , Issue.8 , pp. 4356-4368
    • Lambin, P.1    Gaspard, J.P.2
  • 23
    • 0035921731 scopus 로고    scopus 로고
    • A new wavelet-based method for the solution of the population balance equation
    • Liu Y., and Cameron T. A new wavelet-based method for the solution of the population balance equation. Chem. Eng. Sci. 56 (2001) 5283-5294
    • (2001) Chem. Eng. Sci. , vol.56 , pp. 5283-5294
    • Liu, Y.1    Cameron, T.2
  • 24
    • 0035890622 scopus 로고    scopus 로고
    • Numerical solution of multi-variable cell population balance models. II: Spectral methods
    • Mantzaris N.V., Daoutidis P., and Srienc F. Numerical solution of multi-variable cell population balance models. II: Spectral methods. Comput. Chem. Eng. 25 (2001) 1441-1462
    • (2001) Comput. Chem. Eng. , vol.25 , pp. 1441-1462
    • Mantzaris, N.V.1    Daoutidis, P.2    Srienc, F.3
  • 25
    • 0346368089 scopus 로고    scopus 로고
    • Application of the direct quadrature method of moments to polydisperse gas-solid fluidized beds
    • Marchisio D.L., Fox R.O., and Fan R. Application of the direct quadrature method of moments to polydisperse gas-solid fluidized beds. Powder Technol. 139 (2004) 7-20
    • (2004) Powder Technol. , vol.139 , pp. 7-20
    • Marchisio, D.L.1    Fox, R.O.2    Fan, R.3
  • 26
    • 0038625401 scopus 로고    scopus 로고
    • Quadrature method of moments for population-balance equations
    • Marchisio D.L., Pikturna J.T., Vigil R.D., Barresi A.A., and Fox R.O. Quadrature method of moments for population-balance equations. AIChE J. 49 5 (2004) 1266-1276
    • (2004) AIChE J. , vol.49 , Issue.5 , pp. 1266-1276
    • Marchisio, D.L.1    Pikturna, J.T.2    Vigil, R.D.3    Barresi, A.A.4    Fox, R.O.5
  • 27
    • 0037440820 scopus 로고    scopus 로고
    • Quadrature method of moments for aggregation-breakage processes
    • Marchisio D.L., Vikgil R.D., and Fox R.O. Quadrature method of moments for aggregation-breakage processes. J. Colloid Interface Sci. 258 2 (2003) 322-334
    • (2003) J. Colloid Interface Sci. , vol.258 , Issue.2 , pp. 322-334
    • Marchisio, D.L.1    Vikgil, R.D.2    Fox, R.O.3
  • 28
    • 0031214085 scopus 로고    scopus 로고
    • Description of aerosol dynamic by the quadrature method of moments
    • McGraw R. Description of aerosol dynamic by the quadrature method of moments. Aerosol Sci. Technol. 27 (1997) 255-265
    • (1997) Aerosol Sci. Technol. , vol.27 , pp. 255-265
    • McGraw, R.1
  • 29
    • 0032145759 scopus 로고    scopus 로고
    • Properties and evolution of aerosols with size distributions having identical moments
    • McGraw R., Nemesure S., and Schwartz E.S. Properties and evolution of aerosols with size distributions having identical moments. J. Aerosol Sci. 29 7 (1997) 761-772
    • (1997) J. Aerosol Sci. , vol.29 , Issue.7 , pp. 761-772
    • McGraw, R.1    Nemesure, S.2    Schwartz, E.S.3
  • 30
    • 0037297485 scopus 로고    scopus 로고
    • Chemically resolved aerosol dynamics for internal mixtures by the quadrature method of moments
    • McGraw R., and Wright D.L. Chemically resolved aerosol dynamics for internal mixtures by the quadrature method of moments. J. Aerosol Sci. 34 (2002) 189-209
    • (2002) J. Aerosol Sci. , vol.34 , pp. 189-209
    • McGraw, R.1    Wright, D.L.2
  • 31
    • 0141850310 scopus 로고    scopus 로고
    • Spectral/hp least-squares finite element formulation for the incompressible Navier-Stokes equation
    • (2003)
    • Pontaza J.P., and Reddy J.N. Spectral/hp least-squares finite element formulation for the incompressible Navier-Stokes equation. J. Computat. Phys. 190 2 (2004) 523-549 (2003)
    • (2004) J. Computat. Phys. , vol.190 , Issue.2 , pp. 523-549
    • Pontaza, J.P.1    Reddy, J.N.2
  • 32
    • 3242685785 scopus 로고    scopus 로고
    • Space-time coupled spectral/hp least squares finite element formulation for the incompressible Navier-Stokes equation
    • Pontaza J.P., and Reddy J.N. Space-time coupled spectral/hp least squares finite element formulation for the incompressible Navier-Stokes equation. J. Computat. Phys. 190 2 (2004) 418-459
    • (2004) J. Computat. Phys. , vol.190 , Issue.2 , pp. 418-459
    • Pontaza, J.P.1    Reddy, J.N.2
  • 33
    • 0010916838 scopus 로고    scopus 로고
    • A least-squares spectral element formulation for stokes problem
    • Proot M.M.J., and Gerritsma M.I. A least-squares spectral element formulation for stokes problem. J. Scientific Comput. 17 1-4 (2002) 285-296
    • (2002) J. Scientific Comput. , vol.17 , Issue.1-4 , pp. 285-296
    • Proot, M.M.J.1    Gerritsma, M.I.2
  • 35
    • 0002990802 scopus 로고
    • On the solution of statistical models of cell populations
    • Subramain G., and Ramkrishna D. On the solution of statistical models of cell populations. Math. Biosc. 10 (1971) 1-23
    • (1971) Math. Biosc. , vol.10 , pp. 1-23
    • Subramain, G.1    Ramkrishna, D.2
  • 36
    • 0022887652 scopus 로고
    • Some topics in nuclear aerosol dynamics
    • Williams M.M.R. Some topics in nuclear aerosol dynamics. Prog. Nuclear Energy 17 1 (1986) 1-52
    • (1986) Prog. Nuclear Energy , vol.17 , Issue.1 , pp. 1-52
    • Williams, M.M.R.1
  • 37
    • 42549172973 scopus 로고
    • New solutions to the fragmentation equation
    • Ziff R.M. New solutions to the fragmentation equation. J. Phys. A 24 (1991) 2821-2828
    • (1991) J. Phys. A , vol.24 , pp. 2821-2828
    • Ziff, R.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.