Direct discretizations of bi-variate population balance systems with finite difference schemes of different order

Chemical Engineering Science - Tập 106 - Trang 39-52 - 2014
Volker John1,2, Carina Suciu1
1Weierstrass Institute for Applied Analysis and Stochastics, Leibniz Institute in Forschungsverbund Berlin e.V. (WIAS), Mohrenstr. 39, 10117 Berlin, Germany
2Free University of Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany

Tài liệu tham khảo

Borchert, C., 2012. Topics in crystal shape dynamics (Ph.D. thesis), Otto–von–Guericke–Universität Magdeburg. Borchert, 2011, Crystal aggregation in a flow tube, Chem. Eng. Technol., 34, 545, 10.1002/ceat.201000465 Bordás, 2013, Numerical methods for the simulation of a coalescence-driven droplet size distribution, Theor. Comput. Fluid Dyn., 27, 253, 10.1007/s00162-012-0275-9 Braatz, 2002, Identification of kinetic parameters in multidimensional crystallization processes, Int. J. Mod. Phys. B, 16, 367, 10.1142/S0217979202009883 Buffo, 2013, Multivariate quadrature-based moments methods for turbulent polydisperse gas–liquid systems, Int. J. Multiph. Flow, 50, 41, 10.1016/j.ijmultiphaseflow.2012.09.005 de Souza, 2010, Reconstruction of a distribution from a finite number of moments with an adaptive spline-based algorithm, Chem. Eng. Sci., 65, 2741, 10.1016/j.ces.2010.01.007 Ganesan, 2012, An operator-splitting Galerkin/SUPG finite element method for population balance equations, ESAIM Math. Model. Numer. Anal., 46, 1447, 10.1051/m2an/2012012 Ganesan, 2012, An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems, Chem. Eng. Sci., 69, 59, 10.1016/j.ces.2011.09.031 Gerstlauer, A., 1999. Herleitung und Reduktion populationsdynamischer Modelle am Beispiel der Flüssig-Flüssig-Extraktion, vol. 3, Verfahrenstechnik. VDI Verlag, Düsseldorf. Gresho, 2000 Hackbusch, 2012, A numerical method for the simulation of an aggregation-driven population balance system, Int. J. Numer. Methods Fluids, 69, 1646, 10.1002/fld.2656 Harten, 1987, uniformly high-order accurate essentially nonoscillatory schemes. III, J. Comput. Phys., 71, 231, 10.1016/0021-9991(87)90031-3 Hirsch, 1988 Hulburt, 1964, Some problems in particle technology, Chem. Eng. Sci., 19, 555, 10.1016/0009-2509(64)85047-8 John, 2007, Techniques for the reconstruction of a distribution from a finite number of its moments, Chem. Eng. Sci., 62, 2890, 10.1016/j.ces.2007.02.041 John, 2004, MooNMD—a program package based on mapped finite element methods, Comput. Vis. Sci., 6, 163, 10.1007/s00791-003-0120-1 John, 2009, Simulations of population balance systems with one internal coordinate using finite element methods, Chem. Eng. Sci., 64, 733, 10.1016/j.ces.2008.05.004 John, 2012, On (essentially) non-oscillatory discretizations of evolutionary convection-diffusion equations, J. Comput. Phys., 231, 1570, 10.1016/j.jcp.2011.10.025 John, 2010, On the impact of the scheme for solving the higher dimensional equation in coupled population balance systems, Int. J. Numer. Methods Eng., 82, 1450, 10.1002/nme.2830 John, 2010, Simulations of 3d/4d precipitation processes in a turbulent flow field, 479 John, 2008, Finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion, Comput. Methods Appl. Mech. Eng., 198, 475, 10.1016/j.cma.2008.08.016 John, Volker, Schmeyer, Ellen, 2009. On finite element methods for 3D time-dependent convection-diffusion-reaction equations with small diffusion. In: BAIL 2008—Boundary and Interior Layers, Lecture Notes in Computational Science and Engineering, vol. 69. Springer, Berlin, pp. 173–181. Kuzmin, 2009, Explicit and implicit FEM-FCT algorithms with flux linearization, J. Comput. Phys., 228, 2517, 10.1016/j.jcp.2008.12.011 Ma, 2001, Worst-case analysis of finite-time control policies, IEEE Trans. Cont. Syst. Technol., 9, 766, 10.1109/87.944471 Majumder, 2012, Lattice Boltzmann method for multi-dimensional population balance models in crystallization, Chem. Eng. Sci., 70, 121, 10.1016/j.ces.2011.04.041 Marchisio, 2005, Solution of population balance equations using the direct quadrature method of moments, J. Aerosol Sci., 36, 43, 10.1016/j.jaerosci.2004.07.009 McGraw, 1997, Description of aerosol dynamics by the quadrature method of moments, Aerosol Sci. Technol., 27, 255, 10.1080/02786829708965471 Shu, 2009, High order weighted essentially nonoscillatory schemes for convection dominated problems, SIAM Rev., 51, 82, 10.1137/070679065 Suciu, C., 2013. Numerical methods based on direct discretizations for uni- and bi-variate population balance systems (Ph.D. thesis), Freie Universität Berlin, Fachbereich Mathematik und Informatik. Togkalidou, 2001, Solute concentration prediction using chemometrics and ATR-FTIR spectroscopy, J. Cryst. Growth, 231, 534, 10.1016/S0022-0248(01)01518-4