Adaptive high-resolution schemes for multidimensional population balances in crystallization processes

Qamar, Shamsul; Ashfaq, Asia; Warnecke, Gerald; Angelov, I.; Elsner, M. P.; Seidel‐Morgenstern, A.

doi:10.1016/j.compchemeng.2006.10.014

Cited by 49 publications

(42 citation statements)

References 17 publications

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“…An alternative approach, high resolution finite volume method, was proposed [90,129,132] to provide high accuracy while avoiding the numerical diffusion (that is, smearing) and numerical dispersion (that is, nonphysical oscillations) associated with other finite difference and finite volume methods. This method has been shown to be a promising method and applied to various crystallisation systems [90,105,111,129,130] and further developed for effectively reducing the computation time using either an adaptive mesh technique [130] through redistributing the mesh by moving the spatial grid points iteratively and obtaining the corresponding numerical solution at the new grid points by solving a linear advection equation or a coordinate transformation technique [131] which utilizes a coordinate transformation technique to convert a size-dependent growth rate process into a size-independent growth rate problem with a larger time step to be allowed.…”

Section: Efficient Solution Of Pb Equationsmentioning

confidence: 99%

“…Monte Carlo simulations are most suitable for stochastic PB equations, especially for complex systems, but typically very computationally expensive. In the method of finite difference/volume discretisation, the PB equation is approximated by a finite difference scheme [90,127,[129][130][131]. Numerous discretisation methods for the PB equations with different orders of accuracy have been investigated and applied to various particulate systems (see for example [82,90,108,[129][130][131]).…”

Section: Efficient Solution Of Pb Equationsmentioning

confidence: 99%

“…In the method of finite difference/volume discretisation, the PB equation is approximated by a finite difference scheme [90,127,[129][130][131]. Numerous discretisation methods for the PB equations with different orders of accuracy have been investigated and applied to various particulate systems (see for example [82,90,108,[129][130][131]). An alternative approach, high resolution finite volume method, was proposed [90,129,132] to provide high accuracy while avoiding the numerical diffusion (that is, smearing) and numerical dispersion (that is, nonphysical oscillations) associated with other finite difference and finite volume methods.…”

Section: Efficient Solution Of Pb Equationsmentioning

confidence: 99%

“…Therefore, various numerical algorithms have been developed for solving PB equations such as method of moment [114][115][116][117], method of characteristics [108,[118][119][120][121], Monte Carlo techniques [122,123], and discretization methods including finite element technique [119,124,125], cell average methods [107], hierarchical solution strategy based on multilevel discretization [126], method of classes [82,95], fixed and moving pivot method [127,128], and finite difference/volume methods [90,119,[129][130][131]. Table 1 summarises these numerical solution methods with the further reviews below.…”

Section: Efficient Solution Of Pb Equationsmentioning

confidence: 99%

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Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

2016

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Crystal morphology is known to be of great importance to the end-use properties of the crystal product and affect the down-stream processing such as in filtration and drying, but was previously regarded as too challenging to achieve automatic closed-loop control. As a consequence, previous work has focused on control the crystal size distribution (CSD) where the size of a crystal is often defined as the diameter of a sphere that has the same volume of the crystal. This paper reviews very promising new advances made in recent years in morphological population balance models for modelling and simulation of crystal shape distribution (CShD), measurement and estimation of crystal facet growth kinetics, as well as in 2D and 3D imaging for on-line characterisation of crystal morphology and CShD. A framework is presented integrating various components in order to achieve the ultimate objective of model-based closed-loop control of CShD. The knowledge gaps and challenges that require further research are also identified.

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Section: Efficient Solution Of Pb Equationsmentioning

confidence: 99%

Section: Efficient Solution Of Pb Equationsmentioning

confidence: 99%

Section: Efficient Solution Of Pb Equationsmentioning

confidence: 99%

Section: Efficient Solution Of Pb Equationsmentioning

confidence: 99%

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Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

2016

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“…Qamar et al (2007) presented an adaptive mesh strategy making possible to reduce the mesh size maintaining the accuracy. Gunawan et al (2008) proposed parallelized solution using a master/slave structured CPU cluster.…”

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confidence: 99%

Graphical processing unit (GPU) acceleration for numerical solution of population balance models using high resolution finite volume algorithm

Szilágyi

Nagy

2016

Computers & Chemical Engineering

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Graphical Processing Unit (GPU) Acceleration for Numerical Solution of Population Balance Models Using High Resolution Finite Volume AlgorithmBotond Szilágyi 1 , Zoltán K. Nagy 2,3,* AbstractPopulation balance modeling is a widely used approach to describe crystallization processes.It can be extended to multivariate cases where more internal coordinates i.e. particle properties such as multiple characteristic sizes, composition, purity, etc. can be used. The current study presents highly efficient fully discretized parallel implementation of the high resolution finite volume technique implemented on graphical processing units (GPUs) for the solution of singleand multi-dimensional population balance models (PBMs). The proposed GPU-PBM is implemented using CUDA C++ code for GPU calculations and provides a generic Matlab interface for easy application for scientific computing. The case studies demonstrate that the code running on the GPU is between 2…40 times faster than the compiled C++ code and 50…250 times faster than the standard MatLab implementation. This significant improvement in computational time enables the application of model-based control approaches in real time even in case of multidimensional population balance models.

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Parallel high‐resolution finite volume simulation of particulate processes

2008

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in Wiley InterScience (www.interscience.wiley.com).Population balance models (PBMs) are widely used to describe the dynamics of particulate systems. The simulation of PBMs becomes challenging with increasing numbers of dimensions and integral terms associated with phenomena, such as coalescence and breakage, which has motivated efforts to develop more computationally efficient numerical algorithms. This article presents high-resolution finite-volume methods for the parallel simulation of PBMs that scale well to ;100 processors on a linux cluster. The high-resolution methods provide second-order accuracy with an accurate tracking of sharp fronts. The ParticleSolver software implementing these methods is verified by application to PBMs for (1) aerosol coagulation and condensation, (2) the formation of gold nanoparticles by nucleation, disproportionation, and coagulation, and (3) the nucleation and growth of inorganic crystals with a time-varying shape distribution.

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Adaptive high-resolution schemes for multidimensional population balances in crystallization processes

Cited by 49 publications

References 17 publications

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

Graphical processing unit (GPU) acceleration for numerical solution of population balance models using high resolution finite volume algorithm

Parallel high‐resolution finite volume simulation of particulate processes

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