14 Numerical Methods for Coupled Population Balance Systems …
515
can be modeled appropriately only with very specific parameters and kernels sets,
the developed opportunity of big data acquisition within such a model experiment
can be of great interest to the community of crystallization process engineers. In
combination with the presented fast simulation methods for agglomeration and the
corresponding fluid flow calculations, one may even start to optimize flow geometries
in order to control the agglomeration in such crystallizers in the future.
Acknowledgements The work at this report was supported by the grants JO329/10-3, BO4141/13, and SU189/6-3 within the DFG priority programme 1679: Dynamic simulation of interconnected
solids processes.
References
1. Ahrens, R., Le Borne, S.: FFT-based evaluation of multivariate aggregation integrals in population balance equations on uniform tensor grids. J. Comput. Appl. Math. 338, 280–297 (2018)
2. Ahrens, R., Le Borne, S.: Tensor trains and moment conservation for multivariate aggregation
in population balance modeling. Appl. Numer. Math. 153, 473–491 (2020)
3. Anker, F., Ganesan, S., John, V., Schmeyer, E.: A comparative study of a direct discretization
and an operator-splitting solver for population balance systems. Comput. Chem. Eng. 75, 95–
104 (2015)
4. Bartsch, C.: A coupled stochastic-deterministic method for the numerical solution of population balance systems. Ph.D. Thesis, Freie Universität Berlin, Department of Mathematics and
Computer Science (2018)
5. Bartsch, C., John, V., Patterson, R.I.A.: Simulations of an ASA flow crystallizer with a coupled
stochastic-deterministic approach. Comput. Chem. Eng. 124, 350–363 (2019)
6. Bartsch, C., Wiedmeyer, V., Lakdawala, Z., Patterson, R.I.A., Voigt, A., Sundmacher, K., John,
V.: Stochastic-deterministic population balance modeling and simulation of a fluidized bed
crystallizer experiment. Chem. Eng. Sci. 208, 115102 (2019)
7. Berg, H.C.: Random Walks in Biology. Princeton University Press, Princeton, NJ (1983)
8. Bird, G.A.: Direct simulation and the Boltzmann equation. Phys. Fluids 13(11), 2676–2681
(1970)
9. Borchert, C., Sundmacher, K.: Efficient formulation of crystal shape evolution equations. Chem.
Eng. Sci. 84, 85–99 (2012)
10. Borchert, C., Sundmacher, K.: Morphology evolution of crystal populations: modeling and
observation analysis. Chem. Eng. Sci. 70, 87–98 (2012)
11. Borchert, C., Temmel, E., Eisenschmidt, H., Lorenz, H., Seidel-Morgenstern, A., Sundmacher,
K.: Image-based in situ identification of face specific crystal growth rates from crystal populations. Cryst. Growth Des. 14(3), 952–971 (2014)
12. Bordás, R., John, V., Schmeyer, E., Thévenin, D.: Measurement and simulation of a droplet
population in a turbulent flow field. Comput. Fluids 66, 52–62 (2012)
13. Bordás, R., John, V., Schmeyer, E., Thévenin, D.: Numerical methods for the simulation of a
coalescence-driven droplet size distribution. Theoret. Comput. Fluid Dyn. 27(3–4), 253–271
(2013)
14. Boris, J.P., Book, D.L.: Flux-corrected transport. I: SHASTA, a fluid transport algorithm that
works. J. Comput. Phys. 11, 38–69 (1973)
15. Le Borne, S., Eisenschmidt, H., Sundmacher, K.: Image-based analytical crystal shape computation exemplified for potassium dihydrogen phosphate (KDP). Chem. Eng. Sci. 139, 61–74
(2016)
16. Le Borne, S., Shahmuradyan, L., Sundmacher, K.: Fast evaluation of univariate aggregation
integrals on equidistant grids. Comput. Chem. Eng. 74, 115–127 (2015)
515
can be modeled appropriately only with very specific parameters and kernels sets,
the developed opportunity of big data acquisition within such a model experiment
can be of great interest to the community of crystallization process engineers. In
combination with the presented fast simulation methods for agglomeration and the
corresponding fluid flow calculations, one may even start to optimize flow geometries
in order to control the agglomeration in such crystallizers in the future.
Acknowledgements The work at this report was supported by the grants JO329/10-3, BO4141/13, and SU189/6-3 within the DFG priority programme 1679: Dynamic simulation of interconnected
solids processes.
References
1. Ahrens, R., Le Borne, S.: FFT-based evaluation of multivariate aggregation integrals in population balance equations on uniform tensor grids. J. Comput. Appl. Math. 338, 280–297 (2018)
2. Ahrens, R., Le Borne, S.: Tensor trains and moment conservation for multivariate aggregation
in population balance modeling. Appl. Numer. Math. 153, 473–491 (2020)
3. Anker, F., Ganesan, S., John, V., Schmeyer, E.: A comparative study of a direct discretization
and an operator-splitting solver for population balance systems. Comput. Chem. Eng. 75, 95–
104 (2015)
4. Bartsch, C.: A coupled stochastic-deterministic method for the numerical solution of population balance systems. Ph.D. Thesis, Freie Universität Berlin, Department of Mathematics and
Computer Science (2018)
5. Bartsch, C., John, V., Patterson, R.I.A.: Simulations of an ASA flow crystallizer with a coupled
stochastic-deterministic approach. Comput. Chem. Eng. 124, 350–363 (2019)
6. Bartsch, C., Wiedmeyer, V., Lakdawala, Z., Patterson, R.I.A., Voigt, A., Sundmacher, K., John,
V.: Stochastic-deterministic population balance modeling and simulation of a fluidized bed
crystallizer experiment. Chem. Eng. Sci. 208, 115102 (2019)
7. Berg, H.C.: Random Walks in Biology. Princeton University Press, Princeton, NJ (1983)
8. Bird, G.A.: Direct simulation and the Boltzmann equation. Phys. Fluids 13(11), 2676–2681
(1970)
9. Borchert, C., Sundmacher, K.: Efficient formulation of crystal shape evolution equations. Chem.
Eng. Sci. 84, 85–99 (2012)
10. Borchert, C., Sundmacher, K.: Morphology evolution of crystal populations: modeling and
observation analysis. Chem. Eng. Sci. 70, 87–98 (2012)
11. Borchert, C., Temmel, E., Eisenschmidt, H., Lorenz, H., Seidel-Morgenstern, A., Sundmacher,
K.: Image-based in situ identification of face specific crystal growth rates from crystal populations. Cryst. Growth Des. 14(3), 952–971 (2014)
12. Bordás, R., John, V., Schmeyer, E., Thévenin, D.: Measurement and simulation of a droplet
population in a turbulent flow field. Comput. Fluids 66, 52–62 (2012)
13. Bordás, R., John, V., Schmeyer, E., Thévenin, D.: Numerical methods for the simulation of a
coalescence-driven droplet size distribution. Theoret. Comput. Fluid Dyn. 27(3–4), 253–271
(2013)
14. Boris, J.P., Book, D.L.: Flux-corrected transport. I: SHASTA, a fluid transport algorithm that
works. J. Comput. Phys. 11, 38–69 (1973)
15. Le Borne, S., Eisenschmidt, H., Sundmacher, K.: Image-based analytical crystal shape computation exemplified for potassium dihydrogen phosphate (KDP). Chem. Eng. Sci. 139, 61–74
(2016)
16. Le Borne, S., Shahmuradyan, L., Sundmacher, K.: Fast evaluation of univariate aggregation
integrals on equidistant grids. Comput. Chem. Eng. 74, 115–127 (2015)