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Journal articles on the topic 'Quadrature-based moment method'

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Author: Grafiati

Published: 14 March 2023

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1

Shiea, Mohsen, Antonio Buffo, Marco Vanni, and Daniele Marchisio. "Numerical Methods for the Solution of Population Balance Equations Coupled with Computational Fluid Dynamics." Annual Review of Chemical and Biomolecular Engineering 11, no. 1 (June 7, 2020): 339–66. http://dx.doi.org/10.1146/annurev-chembioeng-092319-075814.

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This review article discusses the solution of population balance equations, for the simulation of disperse multiphase systems, tightly coupled with computational fluid dynamics. Although several methods are discussed, the focus is on quadrature-based moment methods (QBMMs) with particular attention to the quadrature method of moments, the conditional quadrature method of moments, and the direct quadrature method of moments. The relationship between the population balance equation, in its generalized form, and the Euler-Euler multiphase flow models, notably the two-fluid model, is thoroughly discussed. Then the closure problem and the use of Gaussian quadratures to overcome it are analyzed. The review concludes with the presentation of numerical issues and guidelines for users of these modeling approaches.

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2

Heylmun, J. C., B. Kong, A. Passalacqua, and R. O. Fox. "A quadrature-based moment method for polydisperse bubbly flows." Computer Physics Communications 244 (November 2019): 187–204. http://dx.doi.org/10.1016/j.cpc.2019.06.005.

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3

Desjardins, O., R. O. Fox, and P. Villedieu. "A quadrature-based moment method for dilute fluid-particle flows." Journal of Computational Physics 227, no. 4 (February 2008): 2514–39. http://dx.doi.org/10.1016/j.jcp.2007.10.026.

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4

Vishnevsky, A., and A. Firsova. "Calculation of dipole magnetic moment from open-surface measurements." Transactions of the Krylov State Research Centre 1, no. 399 (March 15, 2022): 168–75. http://dx.doi.org/10.24937/2542-2324-2022-1-399-168-175.

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Object and purpose of research. This paper discusses a quadrature-based method of dipole magnetic moment (DMM) calculation as per magnetic field measurement data for the open surface encompassing magnetic field sources. The purpose of the study was to modify this method for the case when measurement data are not available for certain areas on the surface (in other words, when the surface is not closed). Materials and methods. The paper describes magnetic dipole calculation methods, as well as the publications discuss-ing their efficiency. The method suggested in this paper basically substitutes the lacking magnetic field data by the values for pre-defined type of source, thus giving the correction coefficients needed to take into account the contribution of lacking areas. Main results. The paper suggests the methods for taking into account the missing parts of the open measurement surface in quadrature-based DMM calculation procedure. Calculation errors of DMM components for magnetic fields of various structure are estimated as per the solution for a series of test problems. Conclusion. The quadrature method offered in this study offers more accurate DMM calculation. The expressions given in the paper could be used to calculate DMM components as per magnetic field measurements for the generatrices of cylindrical surface, and the approach suggested in this study could be applied to arbitrary open surfaces.

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5

Donde, Pratik, Heeseok Koo, and Venkat Raman. "A multivariate quadrature based moment method for LES based modeling of supersonic combustion." Journal of Computational Physics 231, no. 17 (July 2012): 5805–21. http://dx.doi.org/10.1016/j.jcp.2012.04.031.

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6

Deju, L., S. C. P. Cheung, G. H. Yeoh, and J. Tu. "Study of Isothermal Vertical Bubbly Flow Using Direct Quadrature Method of Moments." Journal of Computational Multiphase Flows 4, no. 1 (March 2012): 23–39. http://dx.doi.org/10.1260/1757-482x.4.1.23.

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In the numerical study, investigation of bubbly flow requires deep understanding of complex hydrodynamics under various flow conditions. In order to simulate the bubble behaviour in conjunction with suitable bubble coalescence and bubble breakage kernels, direct quadrature method of moments (DQMOM) has been applied and validated instead. To examine the predictive results from DQMOM model, the validation has been carried out against experimental data of Lucas et al. (2005) and Prasser et al. (2007) measured in the Forschungszentrum Dresden-Rossendorf FZD facility. Numerical results showed good agreement against experimental data for the local and axial void fraction, bubble size distribution and interfacial area concentration profiles. Encouraging results demonstrates the prospect of the DQMOM two-fluid model against flow conditions with wider range of bubble sizes and rigorous bubble interactions. Moreover, moment sensitivity study also has been carried out to carefully assess the performance of the model. In order to perform the moment sensitivity test three different moment criteria has chosen – as 4 moments, 6 moments and 8 moments. Close agreement between the predictions and measurement was found and it appeared that increasing the number of moments does not have much significance to improve the conformity with experimental data. Nonetheless, increasing the number of moments merely contribute to perform the calculation expensive in terms of computational resource and time. Based on the present study, this preliminary assessment has definitely served to demonstrate and exploit DQMOM model's capabilities to handle wider range of bubble sizes as well as moment resolution required to achieve moment independent solution.

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7

Fox, R. O. "A quadrature-based third-order moment method for dilute gas-particle flows." Journal of Computational Physics 227, no. 12 (June 2008): 6313–50. http://dx.doi.org/10.1016/j.jcp.2008.03.014.

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8

Madadi-Kandjani, E., and A. Passalacqua. "An extended quadrature-based moment method with log-normal kernel density functions." Chemical Engineering Science 131 (July 2015): 323–39. http://dx.doi.org/10.1016/j.ces.2015.04.005.

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9

Passalacqua, Alberto, Janine E. Galvin, Prakash Vedula, Christine M. Hrenya, and Rodney O. Fox. "A Quadrature-Based Kinetic Model for Dilute Non-Isothermal Granular Flows." Communications in Computational Physics 10, no. 1 (July 2011): 216–52. http://dx.doi.org/10.4208/cicp.020210.160910a.

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AbstractA moment method with closures based on Gaussian quadrature formulas is proposed to solve the Boltzmann kinetic equation with a hard-sphere collision kernel for mono-dispersed particles. Different orders of accuracy in terms of the moments of the velocity distribution function are considered, accounting for moments up to seventh order. Quadrature-based closures for four different models for inelastic collision-the Bhatnagar-Gross-Krook, ES-BGK, the Maxwell model for hard-sphere collisions, and the full Boltzmann hard-sphere collision integral-are derived and compared. The approach is validated studying a dilute non-isothermal granular flow of inelastic particles between two stationary Maxwellian walls. Results obtained from the kinetic models are compared with the predictions of molecular dynamics (MD) simulations of a nearly equivalent system with finite-size particles. The influence of the number of quadrature nodes used to approximate the velocity distribution function on the accuracy of the predictions is assessed. Results for constitutive quantities such as the stress tensor and the heat flux are provided, and show the capability of the quadrature-based approach to predict them in agreement with the MD simulations under dilute conditions.

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10

Afzalifar, Ali, Teemu Turunen-Saaresti, and Aki Grönman. "Non-realisability problem with the conventional method of moments in wet-steam flows." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 232, no. 5 (October 11, 2017): 473–89. http://dx.doi.org/10.1177/0957650917735955.

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The method of moments offers an efficient way to preserve the essence of particle size distribution, which is required in many engineering problems such as modelling wet-steam flows. However, in the context of the finite volume method, high-order transport algorithms are not guaranteed to preserve the moment space, resulting in so-called ‘non-realisable’ moment sets. Non-realisability poses a serious obstacle to the quadrature-based moment methods, since no size distribution can be identified for a non-realisable moment set and the moment-transport equations cannot be closed. On the other hand, in the case of conventional method of moments, closures to the moment-transport equations are directly calculated from the moments themselves; as such, non-realisability may not be a problem. This article describes an investigation of the effects of the non-realisability problem on the flow conditions and moment distributions obtained by the conventional method of moments through several one-dimensional test cases involving systems that exhibited similar characteristics to low-pressure wet-steam flows. The predictions of pressures and mean droplet sizes were not considerably disturbed due to non-realisability in any of the test cases. However, in one case that was characterised by strong temporal and spatial gradients, non-realisability did undermine the accuracy of the predictions of measures for the underlying size distributions, including the standard deviation and skewness.

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11

Bałdyga, Jerzy, Grzegorz Tyl, and Mounir Bouaifi. "Application of Gaussian cubature to model two-dimensional population balances." Chemical and Process Engineering 38, no. 3 (September 1, 2017): 393–409. http://dx.doi.org/10.1515/cpe-2017-0030.

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Abstract In many systems of engineering interest the moment transformation of population balance is applied. One of the methods to solve the transformed population balance equations is the quadrature method of moments. It is based on the approximation of the density function in the source term by the Gaussian quadrature so that it preserves the moments of the original distribution. In this work we propose another method to be applied to the multivariate population problem in chemical engineering, namely a Gaussian cubature (GC) technique that applies linear programming for the approximation of the multivariate distribution. Examples of the application of the Gaussian cubature (GC) are presented for four processes typical for chemical engineering applications. The first and second ones are devoted to crystallization modeling with direction-dependent two-dimensional and three-dimensional growth rates, the third one represents drop dispersion accompanied by mass transfer in liquid-liquid dispersions and finally the fourth case regards the aggregation and sintering of particle populations.

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12

Mukhtar, Sohaib, and Ahmad. "A Numerical Approach to Solve Volume-Based Batch Crystallization Model with Fines Dissolution Unit." Processes 7, no. 7 (July 15, 2019): 453. http://dx.doi.org/10.3390/pr7070453.

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In this article, a numerical study of a one-dimensional, volume-based batch crystallization model (PBM) is presented that is used in numerous industries and chemical engineering sciences. A numerical approximation of the underlying model is discussed by using an alternative Quadrature Method of Moments (QMOM). Fines dissolution term is also incorporated in the governing equation for improvement of product quality and removal of undesirable particles. The moment-generating function is introduced in order to apply the QMOM. To find the quadrature abscissas, an orthogonal polynomial of degree three is derived. To verify the efficiency and accuracy of the proposed technique, two test problems are discussed. The numerical results obtained by the proposed scheme are plotted versus the analytical solutions. Thus, these findings line up well with the analytical findings.

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13

Bruns, Morgan C., and Ofodike A. Ezekoye. "Development of a hybrid sectional quadrature-based moment method for solving population balance equations." Journal of Aerosol Science 54 (December 2012): 88–102. http://dx.doi.org/10.1016/j.jaerosci.2012.07.003.

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14

Zheng, Dan, Wei Zou, Chuanfeng Peng, Yuhang Fu, Jie Yan, and Fengzhen Zhang. "CFD-PBM Coupled Simulation of Liquid-Liquid Dispersions in Spray Fluidized Bed Extractor: Comparison of Three Numerical Methods." International Journal of Chemical Engineering 2019 (March 3, 2019): 1–13. http://dx.doi.org/10.1155/2019/4836213.

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A coupled numerical code of the Euler-Euler model and the population balance model (PBM) of the liquid-liquid dispersions in a spray fluidized bed extractor (SFBE) has been performed to investigate the hydrodynamic behavior. A classes method (CM) and two representatively numerical moment-based methods, namely, a quadrature method of moments (QMOM) and a direct quadrature method of moments (DQMOM), are used to solve the PBE for evaluating the effect of the numerical method. The purpose of this article is to compare the results achieved by three methods for solving population balance during liquid-liquid two-phase mixing in a SFBE. The predicted results reveal that the CM has the advantage of computing the droplet size distribution (DSD) directly, but it is computationally expensive if a large number of intervals are needed. The MOMs (QMOM and DQMOM) are preferable to coupling the PBE solution with CFD codes for liquid-liquid dispersions simulations due to their easy application, reasonable accuracy, and high reliability. Comparative results demonstrated the suitability of the DQMOM for modeling the spray fluidized bed extractor with simultaneous droplet breakage and aggregation. This work increases the understanding of the chemical engineering characteristics of multiphase systems and provides a theoretical basis for the quantitative design, scale-up, and optimization of multiphase devices.

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15

Passalacqua, A., R. O. Fox, R. Garg, and S. Subramaniam. "A fully coupled quadrature-based moment method for dilute to moderately dilute fluid–particle flows." Chemical Engineering Science 65, no. 7 (April 2010): 2267–83. http://dx.doi.org/10.1016/j.ces.2009.09.002.

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16

Mazzei, Luca, Daniele L. Marchisio, and Paola Lettieri. "New quadrature-based moment method for the mixing of inert polydisperse fluidized powders in commercial CFD codes." AIChE Journal 58, no. 10 (January 17, 2012): 3054–69. http://dx.doi.org/10.1002/aic.13714.

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17

Darvishan, Ehsan, Gholamreza Ghodrati Amiri, and Pedram Ghaderi. "A Study on Instantaneous Time-Frequency Methods for Damage Detection of Nonlinear Moment-Resisting Frames." Shock and Vibration 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/523675.

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Most of the civil structures exhibit nonlinear hysteresis behavior during earthquakes. However, detection of damage in these structures is a challenging issue due to successive change in structural characteristics during a seismic excitation. The current paper presents a promising approach for damage detection of nonlinear moment frames. First, several instantaneous time-frequency methods including Hilbert-Huang transform, direct quadrature, Teager energy operator, and higher-order energy operator are investigated as signal processing tools and the most appropriate method is selected using an outlier analysis. Next, a procedure is proposed based on time-frequency analysis in conjunction with clustering to find damage extension in moment frames under a seismic excitation using frequency, amplitude, and energy damage measures. A probabilistic approach is implemented to investigate capability of the procedure for different ground motion records using incremental dynamic analysis. Results show that frequency is not an appropriate feature to detect damage in nonlinear structures.

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18

Heylmun, Jeffrey C., Rodney O. Fox, and Alberto Passalacqua. "A quadrature-based moment method for the evolution of the joint size-velocity number density function of a particle population." Computer Physics Communications 267 (October 2021): 108072. http://dx.doi.org/10.1016/j.cpc.2021.108072.

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19

Basavarajappa, Manjunath, and Sanja Miskovic. "Investigation of gas dispersion characteristics in stirred tank and flotation cell using a corrected CFD-PBM quadrature-based moment method approach." Minerals Engineering 95 (September 2016): 161–84. http://dx.doi.org/10.1016/j.mineng.2016.06.026.

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20

Mirzaev, Sayibdjan, Majid Yusupov, Barna Rakhmankulova, Feruza Umarova, and Gulnaz Abdikayimova. "Vertical vibrations of traction engine with viscoelastic suspension." E3S Web of Conferences 365 (2023): 01022. http://dx.doi.org/10.1051/e3sconf/202336501022.

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The tasks of a traction engine with suspension elements and additional devices for converting movement (DCM) are considered. The object of protection, the estimated dynamic state, is solid with mass M and moment of inertia J relative to the center of gravity. To account the suspension material's rheological properties, the Boltzmann-Volterra principle is used. Mathematical models of the problem under consideration are obtained, which are described by the systems of integro-differential equations. A solution method based on quadrature formulas is developed, and a computer program is compiled based on its basis, the results of which are reflected in the graphs. The influence of DCM and rheological properties of the suspension material on the shape of the vertical vibrations of the object is investigated.

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21

Li, Zerun, Qinglin Wang, Yufei Zhu, and Zuocheng Xing. "Automatic Modulation Classification for MASK, MPSK, and MQAM Signals Based on Hierarchical Self-Organizing Map." Sensors 22, no. 17 (August 26, 2022): 6449. http://dx.doi.org/10.3390/s22176449.

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Automatic modulation classification (AMC) plays a fundamental role in common communication systems. Existing clustering models typically handle fewer modulation types with lower classification accuracies and more computational resources. This paper proposes a hierarchical self-organizing map (SOM) based on a feature space composed of high-order cumulants (HOC) and amplitude moment features. This SOM with two stacked layers can identify intrinsic differences among samples in the feature space without the need to set thresholds. This model can roughly cluster the multiple amplitude-shift keying (MASK), multiple phase-shift keying (MPSK), and multiple quadrature amplitude keying (MQAM) samples in the root layer and then finely distinguish the samples with different orders in the leaf layers. We creatively implement a discrete transformation method based on modified activation functions. This method causes MQAM samples to cluster in the leaf layer with more distinct boundaries between clusters and higher classification accuracies. The simulation results demonstrate the superior performance of the proposed hierarchical SOM on AMC problems when compared with other clustering models. Our proposed method can manage more categories of modulation signals and obtain higher classification accuracies while using fewer computational resources.

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22

Et. al., Masharipov Otaboy Matyoqubovich,. "On A Methods Of Using Weighted Simulation Improving Reliability To Redundant Fiber Optic Communication Systems." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 5 (April 11, 2021): 1538–50. http://dx.doi.org/10.17762/turcomat.v12i5.2125.

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The article describes the methodology of weighted modelling to increase the reliability of redundant fibre-optic communication systems. In a specific example, a network graph of a many-node fibre-optic communication system is considered. Applying general ideas to determine the reliability characteristics of systems consisting of a large number of different types of elements with different functional relationships between them is quite a difficult task. The materials presented in this article are intended to solve this problem. Along with their relative simplicity, they are highly accurate. The numerical examples in this chapter show that the use of these methods for highly reliable systems can reduce the variance of the estimate by several orders of magnitude compared to the direct modelling method, and thus reduce the time required for calculations on electronic computers by several orders of magnitude. The purpose of the study is to increase the reliability of fibre-optic communication systems. The research methodology is based on models with a limited number of monotonous failure chains, which is available for visual enumeration of the reliability of highly reliable systems. As a result, it is proposed to obtain an approximate formula for assessing the reliability of a highly reliable system, both by modelling and analytically, and calculations using it can be performed using the quadrature method or moment methods. This allows you to build a model according to the block principle, including full-scale blocks or records of the results of their tests, simplifies the interpretation of the results, and creates convenience in software implementation.

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23

Bryngelson, Spencer H., Tim Colonius, and Rodney O. Fox. "QBMMlib: A library of quadrature-based moment methods." SoftwareX 12 (July 2020): 100615. http://dx.doi.org/10.1016/j.softx.2020.100615.

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24

Pollack, Martin, Michele Pütz, Daniele L. Marchisio, Michael Oevermann, and Christian Hasse. "Zero-flux approximations for multivariate quadrature-based moment methods." Journal of Computational Physics 398 (December 2019): 108879. http://dx.doi.org/10.1016/j.jcp.2019.108879.

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25

Fox, R. O. "Higher-order quadrature-based moment methods for kinetic equations." Journal of Computational Physics 228, no. 20 (November 2009): 7771–91. http://dx.doi.org/10.1016/j.jcp.2009.07.018.

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26

Chowdhary, K., M. Salloum, B. Debusschere, and V. E. Larson. "Quadrature Methods for the Calculation of Subgrid Microphysics Moments." Monthly Weather Review 143, no. 7 (July 1, 2015): 2955–72. http://dx.doi.org/10.1175/mwr-d-14-00168.1.

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Abstract Many cloud microphysical processes occur on a much smaller scale than a typical numerical grid box can resolve. In such cases, a probability density function (PDF) can act as a proxy for subgrid variability in these microphysical processes. This method is known as the assumed PDF method. By placing a density on the microphysical fields, one can use samples from this density to estimate microphysics averages. In the assumed PDF method, the calculation of such microphysical averages has primarily been done using classical Monte Carlo methods and Latin hypercube sampling. Although these techniques are fairly easy to implement and ubiquitous in the literature, they suffer from slow convergence rates as a function of the number of samples. This paper proposes using deterministic quadrature methods instead of traditional random sampling approaches to compute the microphysics statistical moments for the assumed PDF method. For smooth functions, the quadrature-based methods can achieve much greater accuracy with fewer samples by choosing tailored quadrature points and weights instead of random samples. Moreover, these techniques are fairly easy to implement and conceptually similar to Monte Carlo–type methods. As a prototypical microphysical formula, Khairoutdinov and Kogan’s autoconversion and accretion formulas are used to illustrate the benefit of using quadrature instead of Monte Carlo or Latin hypercube sampling.

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27

Xu, Yunjun, and Prakash Vedula. "A quadrature-based method of moments for nonlinear filtering." Automatica 45, no. 5 (May 2009): 1291–98. http://dx.doi.org/10.1016/j.automatica.2009.01.015.

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28

Huang, Qian, Shuiqing Li, and Wen-An Yong. "Stability Analysis of Quadrature-Based Moment Methods for Kinetic Equations." SIAM Journal on Applied Mathematics 80, no. 1 (January 2020): 206–31. http://dx.doi.org/10.1137/18m1231845.

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29

Vikas, V., C. Yuan, Z. J. Wang, and R. O. Fox. "Modeling of bubble-column flows with quadrature-based moment methods." Chemical Engineering Science 66, no. 14 (July 2011): 3058–70. http://dx.doi.org/10.1016/j.ces.2011.03.009.

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30

Vikas, V., Z. J. Wang, A. Passalacqua, and R. O. Fox. "Realizable high-order finite-volume schemes for quadrature-based moment methods." Journal of Computational Physics 230, no. 13 (June 2011): 5328–52. http://dx.doi.org/10.1016/j.jcp.2011.03.038.

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31

Otten, Dustin L., and Prakash Vedula. "A quadrature based method of moments for nonlinear Fokker–Planck equations." Journal of Statistical Mechanics: Theory and Experiment 2011, no. 09 (September 30, 2011): P09031. http://dx.doi.org/10.1088/1742-5468/2011/09/p09031.

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32

Upadhyay, R. R., and O. A. Ezekoye. "Treatment of size-dependent aerosol transport processes using quadrature based moment methods." Journal of Aerosol Science 37, no. 7 (July 2006): 799–819. http://dx.doi.org/10.1016/j.jaerosci.2005.06.002.

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33

Li, Dongyue, Zhipeng Li, and Zhengming Gao. "Quadrature-based moment methods for the population balance equation: An algorithm review." Chinese Journal of Chemical Engineering 27, no. 3 (March 2019): 483–500. http://dx.doi.org/10.1016/j.cjche.2018.11.028.

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34

Mazzei, Luca. "Limitations of quadrature-based moment methods for modeling inhomogeneous polydisperse fluidized powders." Chemical Engineering Science 66, no. 16 (August 2011): 3628–40. http://dx.doi.org/10.1016/j.ces.2011.04.038.

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35

Buffo, A., M. Vanni, D. L. Marchisio, and R. O. Fox. "Multivariate Quadrature-Based Moments Methods for turbulent polydisperse gas–liquid systems." International Journal of Multiphase Flow 50 (April 2013): 41–57. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2012.09.005.

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36

Kariwala, Vinay, Yi Cao, and Zoltan K. Nagy. "Automatic differentiation-based quadrature method of moments for solving population balance equations." AIChE Journal 58, no. 3 (May 18, 2011): 842–54. http://dx.doi.org/10.1002/aic.12613.

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37

Ilgun, A. D., R. O. Fox, and A. Passalacqua. "Solution of the first-order conditional moment closure for multiphase reacting flows using quadrature-based moment methods." Chemical Engineering Journal 405 (February 2021): 127020. http://dx.doi.org/10.1016/j.cej.2020.127020.

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38

Santos, Fabio P., Paulo L. C. Lage, Jovani L. Favero, and Inanc Senocak. "GPU‐accelerated simulation of polydisperse multiphase flows using dual‐quadrature‐based moment methods." Canadian Journal of Chemical Engineering 98, no. 5 (January 21, 2020): 1211–24. http://dx.doi.org/10.1002/cjce.23697.

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39

Nikkhoo, Ali, and Hassan Kananipour. "Numerical solution for dynamic analysis of semicircular curved beams acted upon by moving loads." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 228, no. 13 (January 7, 2014): 2314–22. http://dx.doi.org/10.1177/0954406213518908.

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The present study proposes a dynamic numerical solution for deflections of curved beam structures. In order to extract characteristic equations of an arch under an in-plane constant moving load, an analysis procedure based on the Euler–Bernoulli beam theory considering polar system is conducted. A prismatic semicircular arch with uniform cross section, in various boundary conditions, is assumed. Radial and tangential displacements, as well as bending moments are obtained using differential quadrature method as a well-known numerical method. In addition to parametric studies, a curved steel bridge as an actual application is analyzed by the mentioned method. By using this differential quadrature technique, the function values and some partial derivatives are approximated by weighting coefficients. Convergence study is carried out to demonstrate the stability of the present method. In order to confirm the high level of accuracy of this approach, some comparisons are made between the results obtained by selected methods such as differential quadrature method, Galerkin method, and finite element method. The results show that in the structural problems with specific geometry, using differential quadrature method, which is independent of domain discretization, is proven to be efficient.

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40

Santos, F. P., P. L. C. Lage, and C. E. Fontes. "Numerical aspects of direct quadrature-based moment methods for solving the population balance equation." Brazilian Journal of Chemical Engineering 30, no. 3 (September 2013): 643–56. http://dx.doi.org/10.1590/s0104-66322013000300021.

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41

Frances, Christine, and Alain Liné. "Comminution process modeling based on the monovariate and bivariate direct quadrature method of moments." AIChE Journal 60, no. 5 (February 6, 2014): 1621–31. http://dx.doi.org/10.1002/aic.14358.

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42

Chandrawat, Rajesh Kumar, Varun Joshi, and O. Anwar Bég. "Numerical Study of Interface Tracking for the Unsteady Flow of Two Immiscible Micropolar and Newtonian Fluids Through a Horizontal Channel with an Unstable Interface." Journal of Nanofluids 10, no. 4 (December 1, 2021): 552–63. http://dx.doi.org/10.1166/jon.2021.1805.

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The dynamics of the interaction between immiscible fluids is relevant to numerous complex flows in nature and industry, including lubrication and coating processes, oil extraction, physicochemical separation techniques, etc. One of the most essential components of immiscible flow is the fluid interface, which must be consistently monitored. In this article, the unsteady flow of two immiscible fluids i.e., an Eringen micropolar and Newtonian liquid is considered in a horizontal channel. Despite the no-slip and hyper-stick shear stress condition at the channel edge, it is accepted that the liquid interface is dynamic, migrating from one position to the next and possibly get absolute change; as a result, The CS (continuum surface) model is integrated with the single moment equation based on the VOF (volume of fluid) approach to trace the interface. The immiscible fluids are considered to flow under three applied pressure gradients (constant, decaying, and periodic) and flow is analyzed under seamless shear stress over the entire interface. The modified cubic b-spline differential quadrature method (MCB-DQM) is used to solve the modeled coupled partial differential equations for the fluid interface evolution. The advection and tracking of the interface with time, wave number, and amplitude are illustrated through graphs. It is observed that the presence of micropolar parameters affects the interface with time. The novelty of the current study is that previous studies (which considered the smooth and unstable movement of the micropolar fluid, the steady stream of two immiscible fluids, and interface monitoring through different modes) are extended and generalized to consider the time-dependent flow of two immiscible fluids namely Eringen micropolar and Newtonian with a moving interface in a horizontal channel. For the decaying pressure gradient case, which requires more time to achieve the steady-state, the peak of the waves resembles those for the constant pressure gradient case. The interface becomes steady for a more extensive time when a constant pressure gradient is applied. The interface becomes stable quickly with time as the micropolar parameter is decreased for the constant pressure gradient case i.e., weaker micropolar fluids encourage faster stabilization of the interface. With periodic pressure gradient, the interface takes more time to stabilize, and the crest of the waves is significantly higher in amplitude compared to the constant and decaying pressure cases. The simulations demonstrate the excellent ability of MCB-DQM to analyze complex interfacial immiscible flows.

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Shiea, Mohsen, Antonio Buffo, Marco Vanni, and Daniele L. Marchisio. "A novel finite-volume TVD scheme to overcome non-realizability problem in quadrature-based moment methods." Journal of Computational Physics 409 (May 2020): 109337. http://dx.doi.org/10.1016/j.jcp.2020.109337.

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Vikas, V., Z. J. Wang, and R. O. Fox. "Realizable high-order finite-volume schemes for quadrature-based moment methods applied to diffusion population balance equations." Journal of Computational Physics 249 (September 2013): 162–79. http://dx.doi.org/10.1016/j.jcp.2013.05.002.

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Gumprich, W. W., B. Synek, and Amsini Sadiki. "ASSESSMENT OF THE DIRECT QUADRATURE-BASED SECTIONAL METHOD OF MOMENTS FOR THE SIMULATION OF EVAPORATING POLYDISPERSE SPRAYS." Atomization and Sprays 26, no. 2 (2016): 163–86. http://dx.doi.org/10.1615/atomizspr.2014010635.

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Komatsu, Yosuke, and Takashi Yamamoto. "Stochastic multiscale simulation of porous sound absorbing material based on adaptive bayesian quadrature." Journal of the Acoustical Society of America 152, no. 4 (October 2022): A186. http://dx.doi.org/10.1121/10.0015977.

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This presentation proposes a method to analyze porous sound absorbing materials by multiscale simulation with the adaptive Bayesian quadrature method. The homogenization method calculates equivalent physical acoustic properties from the microstructure of a porous material. This method is powerful in designing new porous materials because it can predict acoustic properties from arbitrary microstructures. On the other hand, it is difficult to consider the randomness of actual materials because of the assumption of periodic microstructures. We propose a method for quantifying uncertainty in acoustic properties by incorporating a Bayesian perspective into Gaussian process regression. Assuming the microscopic structure of porous material as random variables, the response obtained by the homogenization method is approximated by Gaussian process regression. Bayesian quadrature is used to calculate the statistical moments of the integral of the characteristic functions.An additional integration point that minimizes the variance of the integral is adaptively selected, and further responses are obtained using the homogenization method. Repeating this process shows that the integral of characteristic functions can be calculated accurately and efficiently, and their uncertainties can be quantitatively evaluated.

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Walters, Gage, Andrew Wixom, and Sheri Martinelli. "Comparison of quadrature and regression based generalized polynomial chaos expansions for structural acoustics." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 263, no. 6 (August 1, 2021): 863–74. http://dx.doi.org/10.3397/in-2021-1670.

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This work performs a direct comparison between generalized polynomial chaos (GPC) expansion techniques applied to structural acoustic problems. Broadly, the GPC techniques are grouped in two categories: , where the stochastic sampling is predetermined according to a quadrature rule; and , where an arbitrary selection of points is used as long as they are a representative sample of the random input. As a baseline comparison, Monte Carlo type simulations are also performed although they take many more sampling points. The test problems considered include both canonical and more applied cases that exemplify the features and types of calculations commonly arising in vibrations and acoustics. A range of different numbers of random input variables are considered. The primary point of comparison between the methods is the number of sampling points they require to generate an accurate GPC expansion. This is due to the general consideration that the most expensive part of a GPC analysis is evaluating the deterministic problem of interest; thus the method with the fewest sampling points will often be the fastest. Accuracy of each GPC expansion is judged using several metrics including basic statistical moments as well as features of the actual reconstructed probability density function.

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Yeoh, G. H., Sherman C. P. Cheung, and J. Y. Tu. "On the Prediction of Bubble Size Distribution and Void Fraction in Vertical Gas-Liquid Flows." Journal of Computational Multiphase Flows 4, no. 1 (March 2012): 1–22. http://dx.doi.org/10.1260/1757-482x.4.1.1.

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Two-fluid modeling approach is considered as one of the most practical and accurate macroscopic formulation of handling bubbly flow systems. Nevertheless, in order to rigorously account for bubble-bubble interactions, the population balance equation (PBE) must be solved alongside with the continuity and momentum balance equations. Class method typified by the MUltiple SIze Group (MUSIG) model appears to be one of the most direct methods to solve the PBE using a finite series of discrete classes. In this paper, an alternative approach based on the direct quadrature method of moments (DQMOM) is investigated. In contrast to MUSIG model which requires a large number of classes to resolve the bubble distribution, the main advantage of DQMOM is that the number of moments to be solved is generally very small. Validation and assessment of the two population balance models are carried out against measurements of vertical bubbly flows for a range of flow conditions. Based on the present study, preliminary computed results have been found to compare very well against the experimental data as well as the numerical results predicted through the MUSIG model.

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Gupta, Kapil, and Rachna Mehta. "Moment-Generating Function Based Symbol Error Probability Comparison of M-ary Modulation Techniques in Fading Environment." Journal of Computational and Theoretical Nanoscience 17, no. 11 (November 1, 2020): 5085–90. http://dx.doi.org/10.1166/jctn.2020.9344.

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This paper analyses and compare Symbol Error Probability (SEP) of M-ary modulation in different fading environment. Maximal ratio combining (MRC) technique with N branch receiver diversity is taken into consideration for the analysis. Expression for probability of symbol error for M-ary frequency shift keying/M-ary phase shift keying/M-ary differential phase shift key/and M-Level Quadrature Amplitude Modulation are obtained through moment-generating function (MGF) approach. Conventional integration process has probability of uncertainty and erroneousness because of composite mathematical calculations and infinite integration bounds. MGF method is used to avoid complex numerical computation for calculation of SEP. Comparison of SEP for diverse values of Rician factor “K”, Nakagami-M factor, modulation order “M” and diversity order “N” has been carried out.

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Sun, Dan, Andrew Garmory, and Gary J. Page. "Simulation of inertial behavior of dilute particle flow in horizontal channel with Eulerian method of velocity-reassociated quadrature-based method of moments." Powder Technology 304 (December 2016): 157–63. http://dx.doi.org/10.1016/j.powtec.2016.09.035.

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