Time-property least-squares spectral method for population balance equations

Journal of Mathematical Chemistry

Volumn 46, Issue 3, 2009, Pages 770-780

  Dorao, C A ^a   Jakobsen, H A ^a  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

Least squares method; Population balance equation

Indexed keywords

EID: 70349482290     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10910-009-9546-0     Document Type: Article

References (21)

1. P. Bochev, Finite element methods based on least-squares and modified variational principles, Technical report, POSTECH (2001)
2. Chen M., Hwang C., Shih Y.: A wavelet-galerkin method for solving population balance equations. Comp. Chem. Eng. 20(2), 131-145 (1996)
3. Delves L.M., Mohamed J.L.: Computational methods for integral equations. Cambridge University Press, London (1985)
4. Deville M.O., Fischer P.F., Mund E.H.: High-order methods for incompressible fluid flow. Cambridge University Press, Cambridge (2002)
5. Dorao C.A., Jakobsen H.A.: Application of the least square method to population balance problems. Comp. Chem. Eng. 30(3), 535-547 (2005)
6. 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 & Process Industries. (SINTEF/NTNU Trondheim, Norway, 2005), 6-8 June 2005
7. d+1. Chem. Eng. Sci. 61(15), 5070-5081 (2005)
8. Dorao C.A., Jakobsen H.A.: A least squares method for solving advective population balance problems. J. Comp. Appl. Math. 201(1), 247-257 (2005)
9. Hackbusch W.: Integral equation: theory and numerical treatment. International series of numerical mathematics. vol. 120 Birkhauser Verlag, Basel (1995)
10. Jakobsen H.A., Lindborg H., Dorao C.A.: Modeling of bubble column reactors: progress and limitations. Ind. Eng. Chem. Res. 44(14), 5107-5151 (2005)
11. Jiang B.: The least-square finite element method: theory and applications in computational fluid dynamics and electromagnetics. Springer, New York (1998)
12. Liu Y., Cameron T.: A new wavelet-based method for the solution of the population balance equation. Chem. Eng. Sci. 56, 5283-5294 (2001)
13. De Maerschalck B. (2003) 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, Dept. of Aerospace Engineering, The Netherlands, 2003
14. Mantzaris N.V., Daoutidis P., Srienc F.: Numerical solution of multi-variable cell population balance models. II. Spectral methods. Comp. Chem. Eng. 25, 1441-1462 (2001)
15. Post D., Kendall R.: Software project management and quality engineering practices for comples, coupled multi-physics, massively parallel computational simulations: lessons learned from ASCI. Int. J. High Perform. Comp. Appl. 18(4), 399-416 (2003)
16. Proot M.M.J., Gerritsma M.I.: A least-squares spectral element formulation for stokes problem. J. Sci. Comp. 17(1-4), 285-296 (2002)
17. J.P. Pontaza, J.N. Reddy (2004) Spectral/hp least-squares finite element formulation for the incompressible Navier-Stokes equation. J. Comput. Phys. 190(2), 523-549 (2003)
18. Pontaza J.P., Reddy J.N.: Space-time coupled spectral/hp least squares finite element formulation for the incompressible Navier-Stokes equation. J. Comput. Phys. 190(2), 418-459 (2004)
19. Ramkrishna D.: Population balances, theory and applications to particulate systems in engineering. Academic Press, San Diego (2000)
20. Roy C.J.: Review of code and solution verification procedures for computational simulation. J. Comput. Phys. 205, 131-156 (2005)
21. Subramain G., Ramkrishna D.: On the solution of statistical models of cell populations. Math. Biosc. 10, 1-23 (1971)