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Academic literature on the topic 'Quadrature method of moment'

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Published: 14 March 2023

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Journal articles on the topic "Quadrature method of moment"

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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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Fox, Rodney O. "Optimal Moment Sets for Multivariate Direct Quadrature Method of Moments." Industrial & Engineering Chemistry Research 48, no. 21 (November 4, 2009): 9686–96. http://dx.doi.org/10.1021/ie801316d.

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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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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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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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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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Su, Junwei, Wang Le, Zhaolin Gu, and Chungang Chen. "Local Fixed Pivot Quadrature Method of Moments for Solution of Population Balance Equation." Processes 6, no. 11 (October 31, 2018): 209. http://dx.doi.org/10.3390/pr6110209.

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A local fixed pivot quadrature method of moments (LFPQMOM) is proposed for the solution of the population balance equation (PBE) for the aggregation and breakage process. First, the sectional representation for aggregation and breakage is presented. The continuous summation of the Dirac Delta function is adopted as the discrete form of the continuous particle size distribution in the local section as performed in short time Fourier transformation (STFT) and the moments in local sections are tracked successfully. Numerical simulation of benchmark test cases including aggregation, breakage, and aggregation breakage combined processes demonstrate that the new method could make good predictions for the moments along with particle size distribution without further assumption. The accuracy in the numerical results of the moments is comparable to or higher than the quadrature method of moment (QMOM) in most of the test cases. In theory, any number of moments can be tracked with the new method, but the computational expense can be relatively large due to many scalar equations that may be included.
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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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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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Su, Junwei, Zhaolin Gu, Yun Li, Shiyu Feng, and X. Yun Xu. "An adaptive direct quadrature method of moment for population balance equations." AIChE Journal 54, no. 11 (November 2008): 2872–87. http://dx.doi.org/10.1002/aic.11599.

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Dissertations / Theses on the topic "Quadrature method of moment"

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Ali, Shaukat. "Direct quadrature conditional moment closure for turbulent non-premixed combustion." Thesis, Queen Mary, University of London, 2014. http://qmro.qmul.ac.uk/xmlui/handle/123456789/7868.

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The accurate description of the turbulence chemistry interactions that can determine chemical conversion rates and flame stability in turbulent combustion modelling is a challenging research area. This thesis presents the development and implementation of a model for the treatment of fluctuations around the conditional mean (i.e., the auto-ignition and extinction phenomenon) of realistic turbulence-chemistry interactions in computational fluid dynamics (CFD) software. The wider objective is to apply the model to advanced combustion modelling and extend the present analysis to larger hydrocarbon fuels and particularly focus on the ability of the model to capture the effects of particulate formation such as soot. A comprehensive approach for modelling of turbulent combustion is developed in this work. A direct quadrature conditional moment closure (DQCMC) method for the treatment of realistic turbulence-chemistry interactions in computational fluid dynamics (CFD) software is described. The method which is based on the direct quadrature method of moments (DQMOM) coupled with the Conditional Moment Closure (CMC) equations is in simplified form and easily implementable in existing CMC formulation for CFD code. The observed fluctuations of scalar dissipation around the conditional mean values are captured by the treatment of a set of mixing environments, each with its pre-defined weight. In the DQCMC method the resulting equations are similar to that of the first-order CMC, and the “diffusion in the mixture fraction space” term is strictly positive and no correction factors are used. Results have been presented for two mixing environments, where the resulting matrices of the DQCMC can be inverted analytically. Initially the DQCMC is tested for a simple hydrogen flame using a multi species chemical scheme containing nine species. The effects of the fluctuations around the conditional means are captured qualitatively and the predicted results are in very good agreement with observed trends from direct numerical simulations (DNS). To extend the analysis further and validate the model for larger hydrocarbon fuel, the simulations have been performed for n-heptane flame using detailed multi species chemical scheme containing 67 species. The hydrocarbon fuel showed improved results in comparison to the simple hydrogen flame. It suggests that higher hydrocarbons are more sensitive to local scalar dissipation rate and the fluctuations around the conditional means than the hydrogen. Finally, the DQCMC is coupled with a semi-empirical soot model to study the effects of particulate formation such as soot. The modelling results show to predict qualitatively the trends from DNS and are in very good agreement with available experimental data from a shock tube concerning ignition delays time. Furthermore, the findings suggest that the DQCMC approach is a promising framework for soot modelling.
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Pollack, Martin [Verfasser]. "Quadrature based moment methods for sprays and turbulent premixed combustion / Martin Pollack." München : Verlag Dr. Hut, 2021. http://d-nb.info/1232847070/34.

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Hubrich, Simeon [Verfasser]. "The hierarchical finite cell method for nonlinear problems: moment fitting quadratures, basis function removel, and remeshing / Simeon Hubrich." Hamburg : Universitätsbibliothek der Technischen Universität Hamburg-Harburg, 2021. http://d-nb.info/1236991451/34.

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Friedrich, Markus [Verfasser]. "Modellierung und numerische Simulation der Diesel-Direkteinspritzung auf Basis einer Eulerschen Beschreibung des Kraftstoffsprays unter Verwendung der Direct Quadrature Method of Moments / Markus Friedrich." München : Verlag Dr. Hut, 2012. http://d-nb.info/102582119X/34.

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Chen, Heli. "The quadrature discretization method and its applications." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0002/NQ34540.pdf.

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Su, Haozhe. "Advancing the quadrature method in option pricing." Thesis, University of Nottingham, 2018. http://eprints.nottingham.ac.uk/53505/.

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This thesis advances the research on the quadrature (QUAD) method. We aim to make it more computationally efficient, apply it to different underlying processes and even develop a new breed of QUAD method. QUAD is efficient in many ways except when it comes to options with early exercise opportunities such as Bermudan or American options. We develop a series of acceleration techniques for the QUAD method to improve its implementation. After that, we show how to apply the accelerated QUAD method to pricing American options under lognormal jump diffusion and stochastic volatility jump diffusion processes. QUAD is more efficient in dealing with jump processes compared with other numerical techniques such as the finite difference method and the Monte Carlo method, as long as the transition probability density of those processes are known. When the transition probability density is not known in closed-form, this thesis explores a new approach by combining the finite difference method with QUAD (FD-QUAD) - since density can be calculated numerically using the finite difference methods. Overall, this thesis greatly improves and advances the quadrature method in option pricing.
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Wunsch, Dirk. "Theoretical and numerical study of collision and coalescence - Statistical modeling approaches in gas-droplet turbulent flows." Thesis, Toulouse, INPT, 2009. http://www.theses.fr/2009INPT031H/document.

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Ce travail consiste en une étude des phénomènes de coalescence dans un nuage de gouttes, par la simulation numérique directe d'un écoulement turbulent gazeux, couplée avec une approche de suivi Lagrangien pour la phase dispersée. La première étape consiste à développer et valider une méthode de détection des collisions pour une phase polydispersée. Elle est ensuite implémentée dans un code couplé de simulation directe et de suivi Lagrangien existant. Des simulations sont menées pour une turbulence homogène isotrope de la phase continue et pour des phases dispersées en équilibre avec le fluide. L'influence de l'inertie des gouttes et de la turbulence sur le taux de coalescence des gouttes est discutée dans un régime de coalescence permanente. Un aperçu est donné de la prise en compte d'autres régimes de collision et de coalescence entre gouttes. Ces simulations sont la base de développement et de validation des approches utilisées dans les calculs à l'échelle industrielle. En particulier, les résultats des simulations sont comparés avec les prédictions d'une approche Lagrangienne de type Monte-Carlo et de l'approche Eulerienne 'Direct Quadrature Method of Moments' (DQMOM). Différents types de fermeture des termes de coalescence sont validés. Les uns sont basés sur l'hypothèse de chaos-moléculaire, les autres sont capables de prendre en compte des corrélations de vitesses des gouttes avant la collision. Il est montré que cette derniere approche prédit beaucoup mieux le taux de coalescence par comparaison avec les résultats des simulations déterministes
Coalescence in a droplet cloud is studied in this work by means of direct numerical simulation of the turbulent gas flow, which is coupled with a Lagrangian tracking of the disperse phase. In a first step, a collision detection algorithm is developed and validated, which can account for a polydisperse phase. This algorithm is then implemented into an existing code for direct numerical simulations coupled with a Lagrangian tracking scheme. Second, simulations are performed for the configuration of homogeneous isotropic turbulence of the fluid phase and a disperse phase in local equilibrium with the fluid. The influence of both droplet inertia and turbulence intensity on the coalescence rate of droplets is discussed in a pure permanent coalescence regime. First results are given, if other droplet collision outcomes than permanent coalescence (i.e. stretching and reflexive separation) are considered. These results show a strong dependence on the droplet inertia via the relative velocity of the colliding droplets at the moment of collision. The performed simulations serve also as reference data base for the development and validation of statistical modeling approaches, which can be used for simulations of industrial problems. In particular, the simulation results are compared to predictions from a Lagrangian Monte-Carlo type approach and the Eulerian 'Direct Quadrature Method of Moments' (DQMOM) approach. Different closures are validated for the coalescence terms in these approaches, which are based either on the assumption of molecular-chaos, or based on a formulation, which allows to account for the correlation of droplet velocities before collision by the fluid turbulence. It is shown that the latter predicts much better the coalescence rates in comparison with results obtained by the performed deterministic simulations
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Akman, Makbule. "Differential Quadrature Method For Time-dependent Diffusion Equation." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/1224559/index.pdf.

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This thesis presents the Differential Quadrature Method (DQM) for solving time-dependent or heat conduction problem. DQM discretizes the space derivatives giving a system of ordinary differential equations with respect to time and the fourth order Runge Kutta Method (RKM) is employed for solving this system. Stabilities of the ordinary differential equations system and RKM are considered and step sizes are arranged accordingly. The procedure is applied to several time dependent diffusion problems and the solutions are presented in terms of graphics comparing with the exact solutions. This method exhibits high accuracy and efficiency comparing to the other numerical methods.
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Collowald, Mathieu. "Problèmes multivariés liés aux moments : applications de la reconstruction de formes linéaires sur l'anneau des polynômes." Thesis, Nice, 2015. http://www.theses.fr/2015NICE4139/document.

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Cette thèse porte sur la reconstruction de formes linéaires sur l'anneau des polynômes dans le cas multivarié et ses applications. Nous proposons des outils théoriques et algorithmiques permettant de résoudre des problèmes liés aux moments : la reconstruction de polytopes convexes à partir de leurs moments et la recherche de cubatures. L'algorithme numérique proposé pour reconstruire des polytopes utilise des méthodes numériques utilisées précédemment pour le cas des polygones, ainsi que les identités de Brion reliant moments directionnels et sommets projetés. Un polyèdre à 57 sommets - la coupe d'un diamant - est ainsi reconstruit. Pour la recherche de cubatures, nous adaptons la méthode de Prony univariée en une méthode multivariée à l'aide des opérateurs de Hankel. Un problème de complétion de matrices est aussi résolu grâce au théorème d'extension plate de Curto-Fialkow. Nous expliquons ainsi la recherche de cubatures à l'aide des matrices de moments, connue dans la littérature. La symétrie, qui est ici un élément naturel, réduit la complexité algorithmique. Nous prouvons qu'une diagonalisation par blocs des matrices concernées est alors possible. De ces blocs et à l'aide de la matrice de multiplicités d'un groupe fini, des conditions nécessaires à l'existence de cubatures sont obtenues. Pour une mesure, un degré et un nombre de nœuds donnés, notre algorithme certifie tout d'abord l'existence de cubatures et ensuite calcule ses poids et nœuds. De nouvelles cubatures ont ainsi été trouvées : soit en complétant celles connues pour une mesure et un degré donnés, soit en ajoutant des cubatures de degrés supérieurs pour une mesure donnée
This thesis deals with the reconstruction of linear forms on the polynomial ring and its applications. We propose theoretical and algorithmic tools to solve multivariate moment problems: the reconstruction of convex polytopes from their moments (shape-from-moments) and the search for cubatures. The numerical algorithm we propose to reconstruct polytopes uses numerical methods previously known in the case of polygons, and also Brion's identities that relate directional moments and projected vertices. A polyhedron with 57 vertices – a diamond cut – is thus reconstructed. Concerning the search for cubatures, we adapt the univariate Prony's method into a multivariate method thanks to Hankel operators. A matrix completion problem is then solved with a basis-free version of Curto-Fialkow's flat extension theorem. We explain thus the moment matrix approach to cubatures, known in the litterature. Symmetry is here a natural ingredient and reduces the algorithmic complexity. We show that a block diagonalisation of the involved matrices is possible. Those blocs and the matrix of multiplicities of a finite group provide necessary conditions on the existence of cubatures. Given a measure, a degree and a number of nodes, our algorithm first certify the existence of cubatures and then compute the weights and nodes. New cubatures have been found: either by completing the ones known for a given measure and degree, or by adding cubatures with a higher degree for a given measure
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Tekin, Íbrahim. "Moment method solution for junction problems /." The Ohio State University, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487948807586872.

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Books on the topic "Quadrature method of moment"

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Gottlieb, David. Quadrature imposition of compatability conditions in Chebyshev methods. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1990.

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Chi-Wang, Shu, and Langley Research Center, eds. Quadrature-free implementation of discontinuous Galerkin method for hyperbolic equations. Hampton, Va: National Aeronautics and Space Administration , Langley Research Center, 1996.

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Chi-Wang, Shu, and Langley Research Center, eds. Quadrature-free implementation of discontinuous Galerkin method for hyperbolic equations. Hampton, Va: National Aeronautics and Space Administration , Langley Research Center, 1996.

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Chi-Wang, Shu, and Langley Research Center, eds. Quadrature-free implementation of discontinuous Galerkin method for hyperbolic equations. Hampton, Va: National Aeronautics and Space Administration , Langley Research Center, 1996.

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Atkins, H. L. Quadrature-free implementation of discontinuous Galerkin method for hyperbolic equations. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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Q, Pan J., and United States. National Aeronautics and Space Administration., eds. Frequency analysis via the method of moment functionals. [Washington, D.C: National Aeronautics and Space Administration, 1990.

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Center, Langley Research, ed. Moment method analysis of linearly tapered slot antennas. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1993.

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C, Hansen Robert, ed. Moment methods in antennas and scattering. Boston: Artech House, 1990.

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Hohmann, Andreas. Inexact Gauss Newton methods for parameter dependent nonlinear problems. Aachen: Shaker, 1994.

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Bancroft, Randy. Understanding electromagnetic scattering using the moment method: A practical approach. Boston: Artech House, 1996.

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Book chapters on the topic "Quadrature method of moment"

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Fox, Rodney O. "Quadrature-Based Moment Methods for Polydisperse Multiphase Flows." In Stochastic Methods in Fluid Mechanics, 87–136. Vienna: Springer Vienna, 2014. http://dx.doi.org/10.1007/978-3-7091-1622-7_3.

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Schanz, Martin. "Convolution quadrature method." In Wave Propagation in Viscoelastic and Poroelastic Continua, 7–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-540-44575-3_2.

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Peterson, Andrew F., and Malcolm M. Bibby. "Classical Quadrature Rules." In An Introduction to the Locally-Corrected Nyström Method, 7–17. Cham: Springer International Publishing, 2010. http://dx.doi.org/10.1007/978-3-031-01710-0_2.

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Peterson, Andrew F., and Malcolm M. Bibby. "Generalized Gaussian Quadrature." In An Introduction to the Locally-Corrected Nyström Method, 59–68. Cham: Springer International Publishing, 2010. http://dx.doi.org/10.1007/978-3-031-01710-0_5.

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Struchtrup, Henning. "Grad’s moment method." In Macroscopic Transport Equations for Rarefied Gas Flows, 87–107. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/3-540-32386-4_6.

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Podder, Debabrata, and Santanu Chatterjee. "Moment Distribution Method." In Introduction to Structural Analysis, 327–52. Boca Raton: CRC Press, 2021. http://dx.doi.org/10.1201/9781003081227-22.

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Shu, Chang. "Miscellaneous Applications of Differential Quadrature Method." In Differential Quadrature and Its Application in Engineering, 224–44. London: Springer London, 2000. http://dx.doi.org/10.1007/978-1-4471-0407-0_8.

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Gautschi, Walter, and Sotirios E. Notaris. "Newton’s Method and Gauss-Kronrod Quadrature." In International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, 60–71. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-6398-8_6.

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Spencer, W. J. "The Moment Distribution Method." In Fundamental Structural Analysis, 119–46. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4757-2006-8_5.

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Jukna, Stasys. "The Second Moment Method." In Texts in Theoretical Computer Science. An EATCS Series, 303–12. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-17364-6_21.

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Conference papers on the topic "Quadrature method of moment"

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Afzalifar, Ali, Teemu Turunen-Saaresti, and Aki Grönman. "Non-Realizability Problem With Quadrature Method of Moments in Wet-Steam Flows and Solution Techniques." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-57796.

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The quadrature method of moments (QMOM) has recently attracted much attention in representing the size distribution of liquid droplets in wet-steam flows using the n-point Gaussian quadrature. However, solving transport equations of moments using high-order advection schemes is bound to corrupt the moment set, which is then termed a non-realizable moment set. The problem is that the failure and success of the Gaussian quadrature is unconditionally dependent on the realizability of the moment set. First, this article explains the non-realizability problem with the QMOM. Second, it compares two solutions to preserve realizability of the moment sets. The first solution applies a so-called “quasi-high-order” advection scheme specifically proposed for the QMOM to preserve realizability. However, owing to the fact that wet-steam models are usually built on existing numerical solvers, in many cases modifying the available advection schemes is either impossible or not desired. Therefore, the second solution considers correction techniques directly applied to the non-realizable moment sets instead of the advection scheme. These solutions are compared in terms of accuracy in representing the droplet size distribution. It is observed that a quasi-high-order scheme can be reliably applied to guarantee realizability. However, as with all numerical models in an Eulerian reference frame, in general its results are also sensitive to the grid resolution. In contrast, the corrections applied to moments either fail in identifying and correcting the invalid moment sets, or distorts the shape of the droplet size distribution after the correction.
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Donde, Pratik, Heeseok Koo, and Venkat Raman. "A multivariate quadrature based moment method for supersonic combustion modeling." In 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2011. http://dx.doi.org/10.2514/6.2011-322.

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Koellermeier, J., and M. Torrilhon. "Hyperbolic moment equations using quadrature-based projection methods." In PROCEEDINGS OF THE 29TH INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4902651.

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Koo, Heeseok, Pratik Donde, and Venkatramanan Raman. "Supersonic Cavity Flame Stabilization Studies using a Multivariate Quadrature based Moment Method." In 40th Fluid Dynamics Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2010. http://dx.doi.org/10.2514/6.2010-5009.

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Le Lostec, Nechtan, Philippe Villedieu, and Olivier Simonin. "Comparison Between Grad’s and Quadrature-Based Methods of Moments for the Numerical Simulation of Unsteady Particle-Laden Flows." In ASME 2009 Fluids Engineering Division Summer Meeting. ASMEDC, 2009. http://dx.doi.org/10.1115/fedsm2009-78360.

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We present here a new method of moments for the numerical simulation of particle-laden flows. The closure needed in Eulerian methods relies on writing the kinetic descriptor, the velocity destribution function, as a sum of delta-functions instead of the one-delta-function or close-to-Maxwellian assumption in existing methods. The closure velocity distribution function parameters are computed from the transported moments using a quadrature method. Simulation results are compared to those of a close-to-Maxwellian-based Eulerian method and those of a reference Lagrangian simulation, considering only transport and drag of particles in a Taylor-Green fluid flow. For a particular Stokes number of 1 the velocity distribution function is far from equilibrium and particle trajectory crossing is an important feature. We find that the quadrature-based method performs better than the close-to-equilibrium-based method, giving moment profiles closer to those of the Lagrangian reference simulation. However significant differences still remain between quadrature-based and Lagrangian methods results.
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Vikas, V., Z. J. Wang, Rodney O. Fox, and Alberto Passalacqua. "Development of High-Order Realizable Finite-Volume Schemes for Quadrature-Based Moment Method." In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2010. http://dx.doi.org/10.2514/6.2010-1080.

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Dunn, D. M., and K. D. Squires. "Modeling Dilute Gas-Solid Turbulent Boundary Layers Using Moment Methods." In ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting collocated with the ASME 2014 12th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/fedsm2014-21693.

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The specific focus of the current effort is on modeling dilute particle-laden turbulent boundary layers in which the gas-phase carrier flow is populated with a second phase of small, dispersed solid particles possessing material densities much larger than that of the carrier flow. A novel approach known as the conditional quadrature method of moments (CQMOM) developed by Yuan and Fox [1], derived from the quadrature-based method of moments (QMOM) developed originally by McGraw [2], is being implemented to model the dispersed particles as an Eulerian phase. Both enabled and disabled inter-particle collision treatments are included in the model for a dispersed phase coupled to the fluid via a drag force acting on the particles. Simulations are conducted with a Reynolds number of 2800 based on the boundary layer thickness at the inlet to the domain. The full 3-D mesh contains 800×128×98 structured cells with overall dimensions in terms of the inlet boundary layer thickness of 80×6 ×4 in the streamwise, spanwise, and wall-normal directions, respectively. The gas-phase carrier flow is computed using Direct Numerical Simulation of the incompressible Navier-Stokes equations. The boundary layer develops spatially from a turbulent inflow condition and drives the particulate phase via drag and collisions. Comparisons are made against simulations performed using Lagrangian-based discrete particle simulation (DPS) of the dispersed phase and demonstrate the utility of the Eulerian moment method approach. Both instantaneous and time-averaged quantities are presented.
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Xu, Yunjun, and Prakash Vedula. "A Quadrature Based Method of Moments for Nonlinear Filtering." In AIAA/AAS Astrodynamics Specialist Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2008. http://dx.doi.org/10.2514/6.2008-6602.

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McGraw, Robert. "Sparse aerosol models beyond the quadrature method of moments." In NUCLEATION AND ATMOSPHERIC AEROSOLS: 19th International Conference. AIP, 2013. http://dx.doi.org/10.1063/1.4803355.

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Hughes, Fiona R., Jörg Starzmann, Alexander J. White, and John B. Young. "A Comparison of Modelling Techniques for Polydispersed Droplet Spectra in Steam Turbines." In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/gt2015-42589.

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Within steam turbine flows, condensation phenomena give rise to complex droplet spectra that can span more than two orders of magnitude in size. To predict the behaviour of the two-phase flow and the resulting losses, the interactions between the vapour phase and droplets of all sizes must be accurately calculated. The estimation of thermodynamic losses and droplet deposition rates, in particular, depend on the size range and shape of the droplet spectrum. These calculations become computationally burdensome when a large number of droplet groups are present, and it is therefore advantageous to capture the complete droplet spectrum in a compressed form. This paper compares several methods for reducing the complexity of the droplet spectrum: a single representative droplet size (equivalent monodispersion), the moment method (including various growth rate approximations), the quadrature method of moments, and spectrum pruning. In spectrum pruning, droplet groups are individually nucleated, but their number is subsequently reduced by combining groups together in a manner that preserves droplet number, wetness fraction, and the shape of the initial spectrum. The various techniques are compared within a Lagrangian framework by tracking the two-phase behaviour along predefined pressure-time trajectories. Primary and secondary nucleation, droplet evaporation, and a representative turbomachinery case are modelled. The calculations are compared in terms of speed, accuracy, and robustness. It is shown that both the moment methods and spectrum pruning provide an appreciable improvement in accuracy over the use of an ‘equivalent’ monodispersion without compromising calculation speed. Although all the examined methods are adequate for primary nucleation and droplet growth calculations, spectrum pruning and the quadrature method of moments are most accurate over the range of conditions considered.
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Reports on the topic "Quadrature method of moment"

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Lyness, J. N., and L. M. Delves. On the implementation of a modified Sag-Szekeres quadrature method. Office of Scientific and Technical Information (OSTI), July 1997. http://dx.doi.org/10.2172/505380.

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Burke, G. J. Evaluation of the discrete complex-image method for a NEC-like moment-method solution. Office of Scientific and Technical Information (OSTI), January 1996. http://dx.doi.org/10.2172/201799.

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ORLOV, Y. F., W. M. MORSE, and Y. K. SEMERTZIDIS. RESONANCE METHOD OF ELECTRIC-DIPOLE-MOMENT MEASUREMENTS IN STORAGE RINGS. Office of Scientific and Technical Information (OSTI), May 2006. http://dx.doi.org/10.2172/884642.

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Butler, Chalmers M. Analysis and Design of Antenna Structures - Diakoptic Theory and the Moment Method. Fort Belvoir, VA: Defense Technical Information Center, November 1990. http://dx.doi.org/10.21236/ada230838.

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Endeve, Eirik, Ran Chu, Anthony Mezzacappa, and Bronson Messer II. Towards a Discontinuous Galerkin Method for the Multi-Group Two-Moment Model of Neutrino Transport. Office of Scientific and Technical Information (OSTI), January 2018. http://dx.doi.org/10.2172/1513431.

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Chuang, C. W., and T. H. Lee. Microwave Antenna Technology: Calculation of Fields Radiated by Rotationally Symmetric Horn Antennas Using Moment Method. Fort Belvoir, VA: Defense Technical Information Center, May 1987. http://dx.doi.org/10.21236/ada298930.

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Newman, E. H., and M. Kragalott. Moment Method Analysis of the Electric Shielding Factor of a Conducting TM Shield at ELF. Fort Belvoir, VA: Defense Technical Information Center, April 1995. http://dx.doi.org/10.21236/ada309645.

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Glushko, E. Ya, and A. N. Stepanyuk. New perspectives to improve accuracy of the molar gas constant using pneumatic photonic structures. [б. в.], December 2018. http://dx.doi.org/10.31812/123456789/2873.

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In this work, a method is proposed to determine the molar constant R with the relative standard uncertainty near 10^-10 that is based on an extra accurate volume controlling and high sensitive pressure measurements in the framework of scale echeloning procedure. An essential moment of the method is uniting of results for two measurement scales with increased relative standard uncertainty (10^-5) to obtain the higher precise level. The gas-filled 1D elastic pneumatic photonic crystal is proposed as an optical indicator of pressure which can unite several pressure scales of magnitude.
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Wang, Yao, Jeehee Lim, Rodrigo Salgado, Monica Prezzi, and Jeremy Hunter. Pile Stability Analysis in Soft or Loose Soils: Guidance on Foundation Design Assumptions with Respect to Loose or Soft Soil Effects on Pile Lateral Capacity and Stability. Purdue University, 2022. http://dx.doi.org/10.5703/1288284317387.

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The design of laterally loaded piles is often done in practice using the p-y method with API p-y curves representing the behavior of soil at discretized points along the pile length. To account for pile-soil-pile interaction in pile groups, AASHTO (2020) proposes the use of p-multipliers to modify the p-y curves. In this research, we explored, in depth, the design of lateral loaded piles and pile groups using both the Finite Element (FE) method and the p-y method to determine under what conditions pile stability problems were likely to occur. The analyses considered a wide range of design scenarios, including pile diameters ranging from 0.36 m (14.17 inches) to 1.0 m (39.37 inches), pile lengths ranging from 10 m (32.81 ft) to 20 m (65.62 ft), uniform and multilayered soil profiles containing weak soil layers of loose sand or normally consolidated (NC) clay, lateral load eccentricity ranging from 0 m to 10 m (32.81 ft), combined axial and lateral loads, three different pile group configurations (1×5, 2×5, and 3×5), pile spacings ranging from 3 to 5 times the pile diameter, two different load directions (“strong” direction and “weak” direction), and two different pile cap types (free-standing and soil-supported pile caps). Based on the FEA results, we proposed new p-y curve equations for clay and sand. We also examined the behavior of the individual piles in the pile groups and found that the moment applied to the pile cap is partly transferred to the individual piles as moments, which is contrary to the assumption often made that moments are fully absorbed by axial loads on the group piles. This weakens the response of the piles to lateral loading because a smaller lateral pressure is required to produce a given deflection when moments are transferred to the head of the piles as moments. When the p-y method is used without consideration of the transferred moments, unconservative designs result. Based on the FEA results, we proposed both a new set of p-multipliers and a new method to use when moment distribution between piles is not known, using pile efficiency instead to calculate the total capacity of pile groups.
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Warrick, Arthur W., Gideon Oron, Mary M. Poulton, Rony Wallach, and Alex Furman. Multi-Dimensional Infiltration and Distribution of Water of Different Qualities and Solutes Related Through Artificial Neural Networks. United States Department of Agriculture, January 2009. http://dx.doi.org/10.32747/2009.7695865.bard.

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The project exploits the use of Artificial Neural Networks (ANN) to describe infiltration, water, and solute distribution in the soil during irrigation. It provides a method of simulating water and solute movement in the subsurface which, in principle, is different and has some advantages over the more common approach of numerical modeling of flow and transport equations. The five objectives were (i) Numerically develop a database for the prediction of water and solute distribution for irrigation; (ii) Develop predictive models using ANN; (iii) Develop an experimental (laboratory) database of water distribution with time; within a transparent flow cell by high resolution CCD video camera; (iv) Conduct field studies to provide basic data for developing and testing the ANN; and (v) Investigate the inclusion of water quality [salinity and organic matter (OM)] in an ANN model used for predicting infiltration and subsurface water distribution. A major accomplishment was the successful use of Moment Analysis (MA) to characterize “plumes of water” applied by various types of irrigation (including drip and gravity sources). The general idea is to describe the subsurface water patterns statistically in terms of only a few (often 3) parameters which can then be predicted by the ANN. It was shown that ellipses (in two dimensions) or ellipsoids (in three dimensions) can be depicted about the center of the plume. Any fraction of water added can be related to a ‘‘probability’’ curve relating the size of the ellipse (or ellipsoid) that contains that amount of water. The initial test of an ANN to predict the moments (and hence the water plume) was with numerically generated data for infiltration from surface and subsurface drip line and point sources in three contrasting soils. The underlying dataset consisted of 1,684,500 vectors (5 soils×5 discharge rates×3 initial conditions×1,123 nodes×20 print times) where each vector had eleven elements consisting of initial water content, hydraulic properties of the soil, flow rate, time and space coordinates. The output is an estimate of subsurface water distribution for essentially any soil property, initial condition or flow rate from a drip source. Following the formal development of the ANN, we have prepared a “user-friendly” version in a spreadsheet environment (in “Excel”). The input data are selected from appropriate values and the output is instantaneous resulting in a picture of the resulting water plume. The MA has also proven valuable, on its own merit, in the description of the flow in soil under laboratory conditions for both wettable and repellant soils. This includes non-Darcian flow examples and redistribution and well as infiltration. Field experiments were conducted in different agricultural fields and various water qualities in Israel. The obtained results will be the basis for the further ANN models development. Regions of high repellence were identified primarily under the canopy of various orchard crops, including citrus and persimmons. Also, increasing OM in the applied water lead to greater repellency. Major scientific implications are that the ANN offers an alternative to conventional flow and transport modeling and that MA is a powerful technique for describing the subsurface water distributions for normal (wettable) and repellant soil. Implications of the field measurements point to the special role of OM in affecting wettability, both from the irrigation water and from soil accumulation below canopies. Implications for agriculture are that a modified approach for drip system design should be adopted for open area crops and orchards, and taking into account the OM components both in the soil and in the applied waters.
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