REFERENCES
- Pontaza , J.P. ( 2006 ) J. Comput. Phys. , 217 : 563 – 588 .
- Pontaza , J.P. ( 2007 ) J. Comput. Phys. , 225 : 1590 – 1602 .
- Proot , M.M.J. and Gerritsma , M.I. ( 2006 ) J. Sci. Comput. , 27 : 389 – 401 .
- Chang , C.L. and Nelson , J.J. ( 1997 ) SIAM. J. Numer. Anal. , 34(2) : 480 – 489 .
- Gerritsma , M. I. , van der Bas , R. , De Maerschalck , B. , Koren , B. , and Deconinck , H. ( 2008 ) Int. J. Numer. Methods Fluids. 57 : 1371 – 1395 .
- Lin , W.H. ( 1998 ) J. Acoust. Soc. Am. , 104(5) : 3111 – 3114 .
- Lin , W.H. ( 2001 ) J. Acoust. Soc. Am. , 109(2) : 465 – 474 .
- Mazzarella , G. , Maggio , F. , and Pizianti , C. ( 2004 ) Int. J. Numer. Model. , 17 ( 6 ): 509 – 522 .
- Jakobsen , H.A. ( 2008 ) Chemical Reactor Modeling: Multiphase Reactive Flows ; Berlin : Springer .
- Jakobsen , H.A. , Lindborg , H. , and Dorao , C.A. ( 2005 ) Ind. Eng. Chem. Res. , 44 : 5107 – 5151 .
- Delnoij , E. ( 1998 ) Fluid dynamics of gas–liquid bubble columms: A theoretical and experimental study, Ph.D. thesis Twente University.
- Pfleger , D. , Gomes , S. , Gilbert , N. , and Wagner , H.-G. ( 1999 ) Chem. Eng. Sci. , 54 : 5091 – 5099 .
- Nayak , A.K. , Borka , Z. , Patruno , L.E. , Sporleder , F. , Dorao , C.A. , and Jakobsen , H.A. ( 2011 ) Ind. Eng. Chem. Res. , 50 : 1786 – 1798 .
- Shi , J. , Zwart , P. , Frank , T. , Rohde , U. , and Presser , H. ( 2004 ) Development of a multiple velocity multiple size group model for poly-dispersed multiphase flows, Tech Report. Institute of Safety Research. Forchungzentrum Rossendorf, Germany.
- Solsvik , J. , Becker , P.J. , Sheibat-Othman , N. , and Jakobsen , H.A. ( 2014 ) Can. J. Chem. Eng. , 92 : 250 – 265 .
- Jiang , B.-N. ( 1998 ) The Least-Squares Finite Element Method: Theory and Applications in Computational Fluid Dynamics and Electromagnetics ; Berlin : Springer .
- Dorao , C.A. ( 2006 ) High order methods for the solution of the population balance equation with applications to bubbly flows, Ph.D. thesis, Norwegian University of Science and Technology (NTNU).
- Zhu , Z. ( 2009 ) The least-squares spectral element method solution of the gas–liquid multi-fluid model coupled with the population balance equation, Ph.D. thesis, Norwegian University of Science and Technology (NTNU).
- Sporleder , F. ( 2011 ) Simulation of chemical reactors using the least-squards spectral element method, Ph.D. thesis, Norwegian University of Science and Technology (NTNU).
- Patruno , L.E. ( 2010 ) Experimental and numerical investigations of liquid fragmentation and droplet generation for gas processing at high pressures, Ph.D. thesis, Norwegian University of Science and Technology (NTNU).
- Sporleder , F. , Dorao , C.A. , and Jakobsen , H.A. (2011) Chem. Eng. Sci. , 66: 3133–3144.
- Borka , Z. and Jakobsen , H.A. ( 2012 ) Proc. Eng. , 42 : 1121 – 1132 .
- Borka , Z. and Jakobsen , H.A. ( 2012 ) Proc. Eng. , 42 : 623 – 633 .
- Rout , K.R. ( 2012 ) A study of the sorption-enhanced steam methane reforming process, Ph.D. thesis, Norwegian University of Science and Technology (NTNU).
- Sporleder , F. , Dorao , C.A. and Jakobsen , H.A. ( 2010 ) Chem. Eng. Sci. , 65 : 5146 – 5159 .
- Villadsen , J.V. and Steward , W.E. ( 1967 ) Chem. Eng. Sci. , 22 : 1482 – 1501 .
- Solsvik , J. , Tangen , S. , and Jakobsen , H.A. ( 2012 ) Ind. Eng. Chem. Res. , 51 ( 24 ): 8222 – 8236 .
- Patankar , S.V. ( 1980 ) Numerical Heat Transfer and Fluid Flow ; London: Hemisphere Publishing Corporation .
- Versteeg , H.K. and Malalasekera , W. ( 2007 ) An Introduction to Computational Fluid Dynamics: The Finite Volume Method, , 2nd Edition ; Harlow , England: Pearson Prentice Hall .
- Fan , R. , Marchisio , D.L. , and Fox , R.O. ( 2004 ) Powder Technol. , 139 : 7 – 20 .
- Marchisio , D.L. , Pikturna , J.T. , Fox , R.O. , Vivil , R.D. , and Barresi , A.A. ( 2003 ) AIChE. , 49 : 1266 – 1276 .
- Marchisio , D.L. , Vigil , R.D. , and Fox , R.O. ( 2003 ) J. Colloid and Interface Sci. , 258 : 322 – 334 .
- Dorao , C.A. and Jakobsen , H.A. ( 2006 ) J. Comput. and Appl. Math. , 196 : 619 – 633 .
- Zhu , Z. , Dorao , C.A. , and Jakobsen , H.A. ( 2008 ) Math. Comput. Simulat. , 79 : 716 – 727 .
- Solsvik , J. and Jakobsen , H.A. ( 2013 ) Ind. Eng. Chem. Res. , 52 : 15988 – 16013 .
- Solsvik , J. , Tangen , S. , and Jakobsen , H.A. ( 2013 ) Comp. Chem. Eng. , 58 : 223 – 259 .
- Kwakkel , M. and Gerritsma , M. I. ( 2006 ) European Conference on Computational Fluid Dynamics, ECCPMAS 2006, TU Delft, the Netherlands.
- Hoitinga , W. , de Groot , R. , Kwakkel , M. , and Gerritsma , M. I. ( 2008 ) J. Comput. Phys. , 227(4) : 2411 – 2429 .
- Hoitinga , W. ( 2004 ) Direct minimization of equation residuals in least-squares hp-finite element methods–A direct and iterative solution method, Ph.D. thesis, Delft University of Technology.
- Zhu , Z. , Dorao , C.A. , Lucas , D. , and Jakobsen , H.A. ( 2009 ) Ind. Eng. Chem. Res. , 48 : 7994 – 8006 .
- Zhu , Z. , Dorao , C.A. , and Jakobsen , H.A. ( 2009 ) Progre. Comput. Fluid Dynamics. , 9(6–7) : 436 – 446 .
- Ramkrishna , D. ( 2000 ) Population Balance: Theory and Applications to Particulate Systems in Engineering ; San Diego : Academic Press .
- Randolph , A.D. and Larson , M.A. ( 1998 ) Theory of Particulate Processes, Analysis and Techniques of Continuous Crystallization, , 2nd Edition ; San Diego : Academic Press .
- Sporleder , F. , Borka , Z. , Solsvik , J. , and Jakobsen , H.A. ( 2012 ) Rev. Chem. Eng. , 28 : 149 – 169 .
- Morel , C. , Ruyer , P. , Sedder , N. , and Lavièville , J.M. ( 2010 ) Int. J. Multiphase Flow. , 36 : 25 – 39 .
- Lasheras , J.C. , Eastwood , C. , Martínez-Bazán , C. , and Montañés , J.L. ( 2002 ) Int. J. Multiphase Flow. , 28 : 247 – 278 .
- Liao , Y. and Lucas , D. ( 2009 ) Chem. Eng. Sci. , 641 : 3389 – 3406 .
- Liao , Y. and Lucas , D. ( 2010 ) Chem. Eng. Sci. , 65 : 2851 – 2864 .
- Solsvik , J. , Tangen , S. , and Jakobsen , H.A. ( 2013 ) Rev. Chem. Eng. , 29 : 241 – 356 .
- Coulaloglou , C.A. and Tavlarides , L.L. ( 1977 ) Chem. Eng. Sci. , 32 : 1289 – 1297 .
- Diemer , R.B. and Olson , J.H. ( 2002 ) Chem. Eng. Sci. , 57(19) : 4787 – 4798 .
- Prince , M.J. and Blanch , H.W. ( 1990 ) AIChE J. , 36(10) : 1485 – 1499 .
- Maaß , S. , Gäbler , A. , Zaccone , A. , Paschedag , A.R. , and Kraume , M. ( 2007 ) Chemi. Eng. Res. Design , 85(A5) : 703 – 709 .
- Chatzi , E. and Lee , J.M. ( 1987 ) Ind. Eng. Chem. Res. , 26 : 2263 – 2267 .
- Konno , M. , Arai , K. , and Saito , S. ( 1983 ) J. Chem. Eng. Jpn. , 16(4) : 312 – 319 .
- Bahmanyar , H. and Slater , M.J. ( 1991 ) Chem. Eng. Technol. , 14(2) : 79 – 89 .
- Kuriyama , M. , Ono , M. , Tokanai , H. , Tokanai , H. , and Konno , H. ( 1995 ) J. Chem. Eng. Jpn. , 28 : 477 – 479 .
- Russo , F. and Fabre , J. ( 1998 ) J. Fluid Mech. , 372 : 323 – 355 .
- Martinez-Bazan , C. , Montanes , J.L. , and Lasheras , J.X. ( 1990 ) J. Fluid Mech. , 401 : 157 – 182 .
- Andersson , R. and Andersson , B. ( 2006 ) AIChE. J. , 52(6) : 2020 – 2030 .
- Solsvik , J. , Borka , Z. , Becker , P.J. , Sheibat-Othman , N. , and Jakobsen , H.A. ( 2014 ) Can. J. Chem. Eng. , 92 : 234 – 249 .
- Solsvik , J. and Jakonsen , H.A. ( 2013 ) Rev. Chem. Eng. , 29(2) : 63 – 98 .
- Solsvik , J. and Jakobsen , H. ( 2012 ) Comp. Chem. Eng. , 39 : 1 – 21 .
- Bochev , P.B. and Gunburger , M.D. ( 1998 ) SIAM Rev. , 40(4) : 789 – 837 .
- Bochev , P.B. ( 2001 ) Finite element methods based on least-squares and modified veriational princiokes, Technical report, POSTECH.
- Gunzbyrger , M.D. and Bochev , P.B. ( 2009 ) Least Squares Finite Element Methods, Volume 166 Applied Mathematical Science ; New York : Springer-Verlag .
- Proot , M.M.J. ( 2003 ) The least-squares spectral element method–Theory, implementation and application to incompressible flows, Ph.D. thesis, Delft University of Technology.
- Maerschalck , B.D. ( 2003 ) Space-time least-squares spectral element method for unsteady flows, Master's thesis, Delft University of Technology.
- Galerkin , B.G. ( 1915 ) Vestn. Inzh. Tech. , 19 : 897 – 908 .
- Lanczos , C. ( 1938 ) J. Meth. Phys. , 17 : 123 – 199 .
- Finlayson , B.A. ( 1972 ) The Method of Weighted Residuals and Veriational Principles, Volume 87 Mathematics in Science and Engineering ; New York : Academic Press .
- Rice , R.G. and Do , D.D. (1995) Applied Mathematics and Modelling for Chemical Engineers ; New York : John wiley & Sons.
- Villadsen , J. ( 1970 ) Selected Approximation Methods for Chemical Engineering Problems, København Danmarks Tekniske Højskole.
- Villadsen , J. and Michelsen , M.L. ( 1978 ) Solution of Differential Equation Models by Polynomial Approximation ; Englewood Cliffs , Nj : Prentice-Hall .
- Michelsen , M.L. and Villadsen , J. ( 1984 ) In R.S.H. Mah , W.D. Seider (Eds.) Foundations of Computer-Aided Chemical Process Design , New York : Engineering Foundation , pp. 341 – 368 .
- Szegö , G. ( 1939 ) Orthogonal Polynomials ; New York : American Mathematical Society .
- Ferziger , J.H. and Perić , M. ( 2002 ) Computational Methods for Fluid Dynamics; , 3rd ed. ; Berlin : Springer .
- Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/ldis.