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Academic literature on the topic 'Quadrature-based moment method'

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Published: 14 March 2023

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

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Quadrature-based moment method"

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ICARDI, MATTEO. "Computational models for the simulation of turbulent poly-dispersed flows: Large Eddy Simulation and Quadrature-Based Moment Method." Doctoral thesis, Politecnico di Torino, 2012. http://hdl.handle.net/11583/2496099.

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This work focuses on the development of efficient computational tools for the simulation of turbulent multiphase polydispersed flows. In terms of methodologies we focus here on the use of Large Eddy Simulation (LES) and Quadrature-Based Methods of Moments (QBMM). In terms of applications the work is finalised, in order to be applied in the future, to particle production processes (precipitation and crystallisation in particular). An important part of the work concerns the study of the flow field in a Confined Impinging Jets Reactor (CIJR), frequently used in particle production processes. The first part is limited to the comparison and analysis of micro Particle Image Velocimetry (μPIV) experiments, carried out in a previous work, and Direct Numerical Simulation (DNS), carried out in this thesis. In particular the effects of boundary and operating conditions are studied and the numerical simulations are used to understand the experimental predictions and demonstrate the importance of unavoidable fluctuations in the experimental inlets. This represents a preparatory work for the LES modelling of the CIJR. Before investigating the accuracy of LES predictions for this particular application, the model and the implementation are studied in a more general context, represented by a well-known test case such as the periodic turbulent channel flow: the LES model implementation in TransAT, the code used in this work, is compared with DNS data and with predictions of other codes. LES simulations for the CIJR, provided with the proper boundary conditions obtained by the previous DNS/μPIV study, are then performed and compared with experiments, validating the model in a more realistic test case. Since particle precipitation and crystallization often result in complex interactions between particles and the continuous phase, in the second part of the work particular attention has been paid in the modelling of the momentum transfer and the resulting velocity of the particles (relative to the fluid). In particular the possibility of describing poly-disperse fluid-solid systems with QBMM together with LES and Equilibrium Eulerian Model (EEM) is assessed. The study is performed by comparing our predictions with DNS Lagrangian data in the turbulent channel flow previously described, seeded with particles corresponding to a realistic Particle Size Distribution (PSD). The last part of the work deals with particle collisions, extending QBMM to the investigation of non-equilibrium flows governed by the Boltzmann Equation with a hard-sphere collision kernel. The evolution of the particle velocity distribution is predicted and compared with other methods for kinetic equations such as Lattice Boltzmann Method (LBM), Discrete Velocity Method (DVM) and Grad’s Moment Method (GM). The overall results of this thesis can be extended to a broad range of other applications of single-phase, dispersed multiphase and non-equilibrium flows.
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SHIEA, MOHSEN. "Simulation of polydisperse bubbly flows: An investigation on physical and numerical aspects." Doctoral thesis, Politecnico di Torino, 2020. http://hdl.handle.net/11583/2823958.

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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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Upadhyay, Rochan Raj. "Simulation of population balance equations using quadrature based moment methods." Thesis, 2006. http://hdl.handle.net/2152/2943.

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Donde, Pratik Prakash. "LES/PDF approach for turbulent reacting flows." 2012. http://hdl.handle.net/2152/19481.

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The probability density function (PDF) approach is a powerful technique for large eddy simulation (LES) based modeling of turbulent reacting flows. In this approach, the joint-PDF of all reacting scalars is estimated by solving a PDF transport equation, thus providing detailed information about small-scale correlations between these quantities. The objective of this work is to further develop the LES/PDF approach for studying flame stabilization in supersonic combustors, and for soot modeling in turbulent flames. Supersonic combustors are characterized by strong shock-turbulence interactions which preclude the application of conventional Lagrangian stochastic methods for solving the PDF transport equation. A viable alternative is provided by quadrature based methods which are deterministic and Eulerian. In this work, it is first demonstrated that the numerical errors associated with LES require special care in the development of PDF solution algorithms. The direct quadrature method of moments (DQMOM) is one quadrature-based approach developed for supersonic combustion modeling. This approach is shown to generate inconsistent evolution of the scalar moments. Further, gradient-based source terms that appear in the DQMOM transport equations are severely underpredicted in LES leading to artificial mixing of fuel and oxidizer. To overcome these numerical issues, a new approach called semi-discrete quadrature method of moments (SeQMOM) is formulated. The performance of the new technique is compared with the DQMOM approach in canonical flow configurations as well as a three-dimensional supersonic cavity stabilized flame configuration. The SeQMOM approach is shown to predict subfilter statistics accurately compared to the DQMOM approach. For soot modeling in turbulent flows, an LES/PDF approach is integrated with detailed models for soot formation and growth. The PDF approach directly evolves the joint statistics of the gas-phase scalars and a set of moments of the soot number density function. This LES/PDF approach is then used to simulate a turbulent natural gas flame. A Lagrangian method formulated in cylindrical coordinates solves the high dimensional PDF transport equation and is coupled to an Eulerian LES solver. The LES/PDF simulations show that soot formation is highly intermittent and is always restricted to the fuel-rich region of the flow. The PDF of soot moments has a wide spread leading to a large subfilter variance. Further, the conditional statistics of soot moments conditioned on mixture fraction and reaction progress variable show strong correlation between the gas phase composition and soot moments.
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Books on the topic "Quadrature-based moment method"

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Gautschi, Walter. Orthogonal Polynomials. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198506720.001.0001.

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This is the first book on constructive methods for, and applications of orthogonal polynomials, and the first available collection of relevant Matlab codes. The book begins with a concise introduction to the theory of polynomials orthogonal on the real line (or a portion thereof), relative to a positive measure of integration. Topics which are particularly relevant to computation are emphasized. The second chapter develops computational methods for generating the coefficients in the basic three-term recurrence relation. The methods are of two kinds: moment-based methods and discretization methods. The former are provided with a detailed sensitivity analysis. Other topics addressed concern Cauchy integrals of orthogonal polynomials and their computation, a new discussion of modification algorithms, and the generation of Sobolev orthogonal polynomials. The final chapter deals with selected applications: the numerical evaluation of integrals, especially by Gauss-type quadrature methods, polynomial least squares approximation, moment-preserving spline approximation, and the summation of slowly convergent series. Detailed historic and bibliographic notes are appended to each chapter. The book will be of interest not only to mathematicians and numerical analysts, but also to a wide clientele of scientists and engineers who perceive a need for applying orthogonal polynomials.
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Book chapters on the topic "Quadrature-based moment method"

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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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Passalacqua, Alberto, and Rodney O. Fox. "Quadrature-based moment methods for particle-laden flows." In Modeling Approaches and Computational Methods for Particle-Laden Turbulent Flows, 419–47. Elsevier, 2023. http://dx.doi.org/10.1016/b978-0-32-390133-8.00021-9.

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Fox, Rodney O. "Quadrature-Based Moment Methods for Multiphase Chemically Reacting Flows." In Bridging Scales in Modelling and Simulation of Non-Reacting and Reacting Flows. Part I, 1–50. Elsevier, 2018. http://dx.doi.org/10.1016/bs.ache.2018.01.001.

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Voigt, Andreas, Wolfram Heineken, Dietrich Flockerzi, and Kai Sundmacher. "Dimension reduction of two-dimensional population balances based on the quadrature method of moments." In Computer Aided Chemical Engineering, 913–18. Elsevier, 2008. http://dx.doi.org/10.1016/s1570-7946(08)80158-7.

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Conference papers on the topic "Quadrature-based moment method"

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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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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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Sun, Dan, Andrew Garmory, Gary Page, and Indi Tristanto. "Simulation of Particle flow in Inertial Particle Separator with Eulerian Method of Velocity Re-associated Two-node Quadrature-based Method of Moment." In 54th AIAA Aerospace Sciences Meeting. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2016. http://dx.doi.org/10.2514/6.2016-1641.

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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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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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Yoon, Jangho, Yunjun Xu, and Praksh Vedula. "Enhanced Direct Quadrature Based Method of Moments for Nonlinear Filtering." In AIAA Guidance, Navigation, and Control Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2009. http://dx.doi.org/10.2514/6.2009-6086.

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Synek, B., W. W. Gumprich, and Amsini Sadiki. "Evaluation of evaporation models using the Direct Quadrature-based Sectional Method of Moments." In THMT-15. Proceedings of the Eighth International Symposium On Turbulence Heat and Mass Transfer. Connecticut: Begellhouse, 2015. http://dx.doi.org/10.1615/ichmt.2015.thmt-15.1290.

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