16 Modeling, Simulation and Optimization of Process Chains
577
23. Gunawan, R., Fusman, I., Braatz, R.D.: High resolution algorithms for multidimensional population balance equations. AIChE J. 50(11), 2738–2749 (2004)
24. Chalons, C., Goatin, P., Villada, L.M.: High-order numerical schemes for onedimensional
nonlocal conservation laws. SIAM J. Sci. Comput. 40(1), A288–A305 (2018)
25. Friedrich, J., Kolb, O., Göttlich, S.: A Godunov type scheme for a class of LWR traffic flow
models with non-local flux. Netw. Heterog. Media NHM 13(4), 531–547 (2018)
26. Kumar, R., Kumar, J., Warnecke, G.: Moment preserving finite volume schemes for solving
population balance equations incorporating aggregation, breakage, growth and source terms.
Math. Models Methods Appl. Sci. 23(07), 1235–1273 (2013)
27. Eymard, R., Gallouët, T., Herbin, R.: Finite volume methods. In: Handbook of Numerical
Analysis, vol. 7, pp. 713–1018 (2000)
28. Qamar, S., Ashfaq, A., Warnecke, G., Angelov, I., Elsner, M.P., Seidel-Morgenstern, A.: Adaptive high-resolution schemes for multidimensional population balances in crystallization processes. Comput. Chem. Eng. 31(10), 1296–1311 (2007)
29. Pilon, L., Viskanta, R.: Modified method of characteristics for solving population balance
equations. Int. J. Numer. Methods Fluids 42(11), 1211–1236 (2003)
30. Févotte, F., Févotte, G.: A method of characteristics for solving population balance equations
(PBE) describing the adsorption of impurities during crystallization processes. Chem. Eng.
Sci. 65(10), 3191–3198 (2010)
31. Rehman, S.M., Qamar, S.: Application of the method of characteristics to population balance
models considering growth and nucleation phenomena. Appl. Math. 5(13), 1853 (2014)
32. De Souza, L.G.M., Janiga, G., John, V., Thévenin, D.: Reconstruction of a distribution from
a finite number of moments with an adaptive spline-based algorithm. Chem. Eng. Sci. 65(9),
2741–2750 (2010)
33. Qamar, S., Warnecke, G.: Numerical solution of population balance equations for nucleation,
growth and aggregation processes. Comput. Chem. Eng. 31(12), 1576–1589 (2007)
34. Ulbrich, S.: Adjoint-based derivative computations for the optimal control of discontinuous
solutions of hyperbolic conservation laws. Syst. Control Lett. 48(3–4), 313–328 (2003)
35. Ulbrich, M.: Optimization methods in Banach spaces. In: Optimization with PDE Constraints,
pp. 97–156. Springer (2009)
36. Gugat, M., Herty, M., Klar, A., Leugering, G.: Optimal control for traffic flownetworks. J. Opt.
Theory Appl. 126(3), 589–616 (2005). issn: 0022-3239. http://dx.doi.org/10.1007/s10957005-5499-z
37. Lang, Y.-D., Biegler, L.T.: A software environment for simultaneous dynamic optimization.
Comput. Chem. Eng. 31(8), 931–942 (2007)
38. Bück, A., Palis, S., Tsotsas, E.: Model-based control of particle properties in fluidised bed
spray granulation. Powder Technol. 270, 575–583 (2015)
39. Mantzaris, N.V., Daoutidis, P.: Cell population balance modeling and control in continuous
bioreactors. J. Process Control 14(7), 775–784 (2004)
40. Shi, D., El-Farra, N.H., Li, M., Mhaskar, P., Christofides, P.D.: Predictive control of particle
size distribution in particulate processes. Chem. Eng. Sci. 61(1), 268–281 (2006)
41. Madras, G., McCoy, B.J.: Temperature effects during Ostwald ripening. J. Chem. Phys. 119(3),
1683–1693 (2003)
42. Gröschel, M., Keimer, A., Leugering, G., Wang, Z.: Regularity theory and adjoint based optimality conditions for a nonlinear transport equation with nonlocal velocity. SIAM J. Control
Opt. 52(4), 2141–2163 (2014)
43. Peukert, W., Segets, D., Pflug, L., Leugering, G.: Unified design strategies for particulate
products. Adv. Chem. Eng. (2015)
44. Spinola, M., Keimer, A., Segets, D., Leugering, G., Pflug, L.: Model-based optimization of
ripening processes with feedback modules. Chem. Eng. Technol. 43, 896–903 (2020)
45. Dosta, M., Heinrich, S., Werther, J.: Fluidized bed spray granulation: analysis of the system
behaviour by means of dynamic flowsheet simulation. Powder Technol. (2010)
46. Keimer, A., Pflug, L., Spinola, M.: Existence, uniqueness and regularity of multidimensional
nonlocal balance laws with damping. J. Math. Anal. Appl. 466(1), 18–55 (2018)
577
23. Gunawan, R., Fusman, I., Braatz, R.D.: High resolution algorithms for multidimensional population balance equations. AIChE J. 50(11), 2738–2749 (2004)
24. Chalons, C., Goatin, P., Villada, L.M.: High-order numerical schemes for onedimensional
nonlocal conservation laws. SIAM J. Sci. Comput. 40(1), A288–A305 (2018)
25. Friedrich, J., Kolb, O., Göttlich, S.: A Godunov type scheme for a class of LWR traffic flow
models with non-local flux. Netw. Heterog. Media NHM 13(4), 531–547 (2018)
26. Kumar, R., Kumar, J., Warnecke, G.: Moment preserving finite volume schemes for solving
population balance equations incorporating aggregation, breakage, growth and source terms.
Math. Models Methods Appl. Sci. 23(07), 1235–1273 (2013)
27. Eymard, R., Gallouët, T., Herbin, R.: Finite volume methods. In: Handbook of Numerical
Analysis, vol. 7, pp. 713–1018 (2000)
28. Qamar, S., Ashfaq, A., Warnecke, G., Angelov, I., Elsner, M.P., Seidel-Morgenstern, A.: Adaptive high-resolution schemes for multidimensional population balances in crystallization processes. Comput. Chem. Eng. 31(10), 1296–1311 (2007)
29. Pilon, L., Viskanta, R.: Modified method of characteristics for solving population balance
equations. Int. J. Numer. Methods Fluids 42(11), 1211–1236 (2003)
30. Févotte, F., Févotte, G.: A method of characteristics for solving population balance equations
(PBE) describing the adsorption of impurities during crystallization processes. Chem. Eng.
Sci. 65(10), 3191–3198 (2010)
31. Rehman, S.M., Qamar, S.: Application of the method of characteristics to population balance
models considering growth and nucleation phenomena. Appl. Math. 5(13), 1853 (2014)
32. De Souza, L.G.M., Janiga, G., John, V., Thévenin, D.: Reconstruction of a distribution from
a finite number of moments with an adaptive spline-based algorithm. Chem. Eng. Sci. 65(9),
2741–2750 (2010)
33. Qamar, S., Warnecke, G.: Numerical solution of population balance equations for nucleation,
growth and aggregation processes. Comput. Chem. Eng. 31(12), 1576–1589 (2007)
34. Ulbrich, S.: Adjoint-based derivative computations for the optimal control of discontinuous
solutions of hyperbolic conservation laws. Syst. Control Lett. 48(3–4), 313–328 (2003)
35. Ulbrich, M.: Optimization methods in Banach spaces. In: Optimization with PDE Constraints,
pp. 97–156. Springer (2009)
36. Gugat, M., Herty, M., Klar, A., Leugering, G.: Optimal control for traffic flownetworks. J. Opt.
Theory Appl. 126(3), 589–616 (2005). issn: 0022-3239. http://dx.doi.org/10.1007/s10957005-5499-z
37. Lang, Y.-D., Biegler, L.T.: A software environment for simultaneous dynamic optimization.
Comput. Chem. Eng. 31(8), 931–942 (2007)
38. Bück, A., Palis, S., Tsotsas, E.: Model-based control of particle properties in fluidised bed
spray granulation. Powder Technol. 270, 575–583 (2015)
39. Mantzaris, N.V., Daoutidis, P.: Cell population balance modeling and control in continuous
bioreactors. J. Process Control 14(7), 775–784 (2004)
40. Shi, D., El-Farra, N.H., Li, M., Mhaskar, P., Christofides, P.D.: Predictive control of particle
size distribution in particulate processes. Chem. Eng. Sci. 61(1), 268–281 (2006)
41. Madras, G., McCoy, B.J.: Temperature effects during Ostwald ripening. J. Chem. Phys. 119(3),
1683–1693 (2003)
42. Gröschel, M., Keimer, A., Leugering, G., Wang, Z.: Regularity theory and adjoint based optimality conditions for a nonlinear transport equation with nonlocal velocity. SIAM J. Control
Opt. 52(4), 2141–2163 (2014)
43. Peukert, W., Segets, D., Pflug, L., Leugering, G.: Unified design strategies for particulate
products. Adv. Chem. Eng. (2015)
44. Spinola, M., Keimer, A., Segets, D., Leugering, G., Pflug, L.: Model-based optimization of
ripening processes with feedback modules. Chem. Eng. Technol. 43, 896–903 (2020)
45. Dosta, M., Heinrich, S., Werther, J.: Fluidized bed spray granulation: analysis of the system
behaviour by means of dynamic flowsheet simulation. Powder Technol. (2010)
46. Keimer, A., Pflug, L., Spinola, M.: Existence, uniqueness and regularity of multidimensional
nonlocal balance laws with damping. J. Math. Anal. Appl. 466(1), 18–55 (2018)