Application "Numerical methods for the simulation of population balance systems"
Population balance systems model particulate flows where the particles are represented by a particle size distribution (PSD). Mathematically, these are coupled systems consisting of the Navier-Stokes equations (flow), convection-diffusion-reaction equations (chemical reaction, transport of energy), and transport equations for the PSD. Population balance models are widely used in chemical engineering and they can be found also in meteorology (to model the behavior of droplets in clouds). The main difficulty for the numerical simulation is that the PSD depends on time, physical space (external coordinates), and properties of the particles (internal coordinates). Important processes, like the agglomeration (coalescence) of particles, are modeled with global integral operators. Altogether, one has to solve for the PSD a partial integro-differential equation in a high-dimensional domain.
The research focuses on the development of accurate and efficient numerical methods for the simulation of population balance systems. Main topics are the systematic assessment of numerical methods for uni-variate (one internal coordinate) PSDs and the development of direct discretizations for multi-variate PSDs on complex physical domains.
Contributing Groups of WIAS
Mathematical Context
- Numerical methods for coupled systems in computational fluid dynamics
- Solution of large sparse linear systems
- Systems of partial differential equations: modeling, numerical analysis and simulation
Related main application areas
Contact
Prof. Dr. John, Volker
Weierstrass Institute for Applied Analysis and StochasticsMohrenstrasse 39
10117 Berlin
tel: ++49 (0) 30 20372 561
fax: ++49 (0) 30 20372-303
e-mail: Volker.John@wias-berlin.de
Publications
Articles in Refereed Journals
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L.G.M. DE Souza, G. Janiga, V. John, D. Thévenin, Reconstruction of a distribution from a finite number of moments with an adaptive spline-based algorithm, Chem. Engng. Sci., 65 (2010) pp. 2741--2750.
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V. John, M. Roland, On the impact of the scheme for solving the higher-dimensional equation in coupled population balance systems, Internat. J. Numer. Methods Engrg., 82 (2010) pp. 1450--1474.
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V. John, T. Mitkova, M. Roland, K. Sundmacher, L. Tobiska, A. Voigt, Simulations of population balance systems with one internal coordinate using finite element methods, Chem. Engng. Sci., 64 (2009) pp. 733--741.
Contributions to Collected Editions
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V. John, M. Roland, Simulations of 3D/4D precipitation processes in a turbulent flow field, in: Numerical Mathematics and Advanced Applications 2009, G. Kreiss, P. Lötstedt, A. Målqvist, M. Neytcheva, eds., Springer, Heidelberg et al., 2010, pp. 479-- 487.
AbstractPrecipitation processes are modeled by population balance systems. A very expensive part of the simulation of population balance systems is the solution of the equation for the particle size distribution (PSD) since this equation is defined in a higher dimensional domain than the other equations in the system. This paper studies different approaches for the solution of this equation: two finite difference upwind schemes and a linear finite element flux--corrected transport method. It is shown that the different schemes lead to qualitatively different solutions for an output of interest.
Talks, Poster
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V. John, On the numerical simulation of population balance systems, Karlsruher Institut für Technologie, Fakultät für Mathematik, December 9, 2009.