Numerical reduction of a crystallizer model with internal and external coordinates by proper orthogonal decomposition

Krasnyk, Mykhaylo; Mangold, Michael; Ganesan, Sashikumaar; Tobiska, Lutz

doi:10.1016/j.ces.2011.05.053

Cited by 16 publications

(9 citation statements)

References 22 publications

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“…Its design is highly modular so that it can be easily extended to solve arbitrary PDEs. This package has been successfully applied, for example, in the solution of the steady state and time-dependent incompressible Navier-Stokes equations [33][34][35], large eddy simulations [36], free boundary value problems with capillary surfaces and ferrofluids [37,38], multiphase problems with and without surface active agents [39][40][41], population balance systems [42][43][44], and convection-diffusion equations by stabilized finite elements [45,46].…”

Section: Moonmdmentioning

confidence: 99%

Quantitative comparison of Taylor flow simulations based on sharp‐interface and diffuse‐interface models

Aland

Boden

Hahn³

et al. 2013

Numerical Methods in Fluids

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SUMMARYA pressure‐driven flow of elongated bullet‐shaped bubbles in a narrow channel is known as Taylor flow or bubble‐train flow. This process is of relevance in various applications of chemical engineering. In this paper, we describe a typical simplified experimental setting, with surface tension, density and viscosity as prescribed input parameters. We compare a sharp‐interface model based on a moving grid aligned with the bubble boundary (ALE coordinates) and a diffuse‐interface model where the bubble shape is implicitly given by a phase‐field function. Four independent implementations based on the two modeling approaches are introduced and described briefly. Besides the simulation of the bubble shapes, we compare some resulting quantities such as pressure difference and film widths within the implementations and to existing analytical and experimental results. The simulations were conducted in 2D and 3D (rotationally symmetric). Good accordance of the results indicate the applicability and the usability of all approaches. Differences between the models and their implementations are visible but in no contradiction to theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

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Section: Moonmdmentioning

confidence: 99%

Quantitative comparison of Taylor flow simulations based on sharp‐interface and diffuse‐interface models

Aland

Boden

Hahn³

et al. 2013

Numerical Methods in Fluids

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“…Later, this splitting scheme has been studied for different discretization and applications, see for example (Ahmed et al, 2013(Ahmed et al, , 2011Ganesan, 2012;Ganesan and Tobiska, 2013;Krasnyk et al, 2012). One of the main advantages, besides the splitting of a high-dimensional equation into a system of low-dimensional equations, is that the operator-splitting scheme allows to use different discretizations for each equation in the low-dimensional system.…”

Section: The Operator-splitting Schemementioning

confidence: 98%

A comparative study of a direct discretization and an operator-splitting solver for population balance systems

Anker

Ganesan

John

et al. 2015

Computers & Chemical Engineering

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“…Model reduction by proper orthogonal decomposition [10,11] is a promising candidate for automatic reduction of particle system models. It has been applied successfully to crystallization and granulation processes [12,13]. The new challenge of the fluidized bed crystallizer considered in this work lies in the feedback of the particle phase on the fluid flow, which causes a bidirectional coupling between continuous phase and particle phase.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear model reduction of a continuous fluidized bed crystallizer

Mangold

Feng

Khlopov

et al. 2015

Journal of Computational and Applied Mathematics

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Nonlinear model reduction of a continuous fluidized bed crystallizer, Journal of Computational and Applied Mathematics (2015), http://dx. AbstractThis work considers a system of a fluidized bed crystallizer and a ultrasonic attenuator, which separates an enantiomer from a liquid solution. A population balance model of the system shows autonomous oscillations over a wide range of operation conditions. Proper orthogonal decomposition is applied to obtain nonlinear reduced models of low order. An a posteriori error estimator is used to assess the quality of the reduced model during run time.

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Numerical reduction of a crystallizer model with internal and external coordinates by proper orthogonal decomposition

Cited by 16 publications

References 22 publications

Quantitative comparison of Taylor flow simulations based on sharp‐interface and diffuse‐interface models

Quantitative comparison of Taylor flow simulations based on sharp‐interface and diffuse‐interface models

A comparative study of a direct discretization and an operator-splitting solver for population balance systems

Nonlinear model reduction of a continuous fluidized bed crystallizer

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