Conditional quadrature method of moments for kinetic equations
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Yuan and Fox's moment-inversion algorithm yields a quadrature without iterations.
“Besides, it yields a quadrature without iterations.”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [325]
Yuan and Fox proposed a moment-inversion algorithm based on well-defined Vandermonde matrices that always produces non-negative weights when the moments are realizable at a reasonable computational cost.
“Yuan and Fox [325] proposed a novel moment-inversion algorithm based on welldefined Vandermonde matrices that produce always non-negative weights when the moments are realizable at a reasonable computational cost.”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [325]
Cites
Bhatnagar, P. L., Gross, E. P., & Krook, M. (1954) · Physical Review · doi:10.1103/physrev.94.511 · Cited by 8,663 · see citing works
Molecular Gas Dynamics And The Direct Simulation Of Gas Flows
Bird, G. A. (1994) · doi:10.1093/oso/9780198561958.001.0001 · Cited by 7,269 · see citing works
Finite Volume Methods for Hyperbolic Problems
(2002) · doi:10.1017/cbo9780511791253 · Cited by 6,386 · see citing works
The mathematical theory of non-uniform gases
Budden, K. G. (1971) · Journal of Atmospheric and Terrestrial Physics · doi:10.1016/0021-9169(71)90189-9 · Cited by 3,593 · see citing works
The Boltzmann Equation and Its Applications
Cercignani, C. (1988) · Applied Mathematical Sciences · doi:10.1007/978-1-4612-1039-9 · Cited by 3,130 · see citing works
On the kinetic theory of rarefied gases
Grad, H. (1949) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160020403 · Cited by 2,689 · see citing works
Numerical recipes in FORTRAN: the art of scientific computing
(1993) · Choice Reviews Online · doi:10.5860/choice.30-5638a · Cited by 2,500 · see citing works
Lallemand, P., & Luo, L. (2000) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.61.6546 · Cited by 2,292 · see citing works
Approximate Calculation of Multiple Integrals
G., W., & Stroud, A. H. (1973) · Mathematics of Computation · doi:10.2307/2005635 · Cited by 1,494 · see citing works
A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles
Jenkins, J. T., & Savage, S. B. (1983) · Journal of Fluid Mechanics · doi:10.1017/s0022112083001044 · Cited by 1,393 · see citing works
VII. On stresses in rarified gases arising from inequalities of temperature
Maxwell, J. C. (1879) · Philosophical Transactions of the Royal Society of London · doi:10.1098/rstl.1879.0067 · Cited by 1,291 · see citing works
On the approximate calculation of multiple integrals
Bakhvalov, N. S. (2015) · Journal of Complexity · doi:10.1016/j.jco.2014.12.003 · Cited by 1,265 · see citing works
Description of aerosol dynamics by the quadrature method of moments
McGraw, R. (1997) · Aerosol Science and Technology · doi:10.1080/02786829708965471 · Cited by 1,128 · see citing works
Moment closure hierarchies for kinetic theories
Levermore, C. D. (1996) · Journal of Statistical Physics · doi:10.1007/bf02179552 · Cited by 939 · see citing works
Computational Models for Turbulent Reacting Flows
Fox, R. O. (2003) · Cambridge University Press eBooks · doi:10.1017/cbo9780511610103 · Cited by 922 · see citing works
Self-citationLattice gas hydrodynamics in two and three dimensions
Frisch, U., d’Humières, D., Hasslacher, B., et al. (1986) · University of North Texas Digital Library (University of North Texas) · Cited by 903 · see citing works
On Stresses in Rarified Gases arising from Inequalities of Temperature
Maxwell, J. C. (2011) · Cambridge University Press eBooks · doi:10.1017/cbo9780511710377.068 · Cited by 807 · see citing works
Solution of population balance equations using the direct quadrature method of moments
Marchisio, D. L., & Fox, R. O. (2005) · Journal of Aerosol Science · doi:10.1016/j.jaerosci.2004.07.009 · Cited by 803 · see citing works
Self-citationGoldhirsch, I. (2002) · Annual Review of Fluid Mechanics · doi:10.1146/annurev.fluid.35.101101.161114 · Cited by 799 · see citing works
New Statistical Models for Kinetic Theory: Methods of Construction
Holway, L. H. (1966) · The Physics of Fluids · doi:10.1063/1.1761920 · Cited by 581 · see citing works
Theory of the lattice Boltzmann method: Acoustic and thermal properties in two and three dimensions
Lallemand, P., & Luo, L. (2003) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.68.036706 · Cited by 471 · see citing works
Macroscopic Transport Equations for Rarefied Gas Flows
Struchtrup, H. (2005) · Interaction of mechanics and mathematics · doi:10.1007/3-540-32386-4 · Cited by 463 · see citing works
Error Bounds in Equilibrium Statistical Mechanics
Gordon, R. G. (1968) · Journal of Mathematical Physics · doi:10.1063/1.1664624 · Cited by 453 · see citing works
Chen, G., & Liu, H. (2003) · SIAM Journal on Mathematical Analysis · doi:10.1137/s0036141001399350 · Cited by 386 · see citing works
SMALL AMPLITUDE PROCESSES IN CHARGED AND NEUTRAL ONE-COMPONENT SYSTEMS
Bhatnagar, P. L., Gross, E., & Krook, M. (1954) · Cited by 385 · see citing works
Spray Combustion and Atomization
Williams, F. A. (1958) · The Physics of Fluids · doi:10.1063/1.1724379 · Cited by 380 · see citing works
Shock Structure in a Simple Discrete Velocity Gas
Broadwell, J. E. (1964) · The Physics of Fluids · doi:10.1063/1.1711368 · Cited by 369 · see citing works
Macroscopic transport equations for rarefied gas flows
Struchtrup, H. (2005) · Interaction of mechanics and mathematics · doi:10.1007/3-540-32386-4_9 · Cited by 306 · see citing works
Kinetic-Theoretic Description of the Formation of a Shock Wave
Chu, C. K. (1965) · The Physics of Fluids · doi:10.1063/1.1761077 · Cited by 285 · see citing works
Hadjiconstantinou, N. G. (2006) · Physics of Fluids · doi:10.1063/1.2393436 · Cited by 243 · see citing works
The Theory of Canonical Moments with Applications in Statistics, Probability and Analysis
Rukhin, A. L., Dette, H., & Studden, W. J. (1998) · Journal of the American Statistical Association · doi:10.2307/2670071 · Cited by 239 · see citing works
Regularized 13-moment equations: shock structure calculations and comparison to Burnett models
Torrilhon, M., & Struchtrup, H. (2004) · Journal of Fluid Mechanics · doi:10.1017/s0022112004009917 · Cited by 237 · see citing works
A quadrature-based moment method for dilute fluid-particle flows
Desjardins, O., Fox, R. O., & Villedieu, P. (2007) · Journal of Computational Physics · doi:10.1016/j.jcp.2007.10.026 · Cited by 197 · see citing works
Self-citationModified moments and Gaussian quadratures
Wheeler, J. C. (1974) · Rocky Mountain Journal of Mathematics · doi:10.1216/rmj-1974-4-2-287 · Cited by 190 · see citing works
Second-Order Boltzmann Schemes for Compressible Euler Equations in One and Two Space Dimensions
Benoît Perthame, B. (1992) · SIAM Journal on Numerical Analysis · doi:10.1137/0729001 · Cited by 185 · see citing works
Cercignani, C. (2000) · Cited by 161 · see citing works
A quadrature-based third-order moment method for dilute gas-particle flows
Fox, R. O. (2008) · Journal of Computational Physics · doi:10.1016/j.jcp.2008.03.014 · Cited by 149 · see citing works
Self-citationTruncated K-moment problems in several variablesPreprint
Curto, R. E., & Fialkow, L. A. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0507067 · Cited by 139 · see citing works
Fox, R. O., Laurent, F., & Massot, M. (2007) · Journal of Computational Physics · doi:10.1016/j.jcp.2007.10.028 · Cited by 133 · see citing works
Self-citationNumerical Approximations of Pressureless and Isothermal Gas Dynamics
Bouchut, F., Jin, S., & Li, X. (2003) · SIAM Journal on Numerical Analysis · doi:10.1137/s0036142901398040 · Cited by 128 · see citing works
Benamou, J. (1996) · Journal of Computational Physics · doi:10.1006/jcph.1996.0224 · Cited by 98 · see citing works
Realizable high-order finite-volume schemes for quadrature-based moment methods
Vikas, V., Wang, Z. J., Passalacqua, A., & Fox, R. O. (2011) · Journal of Computational Physics · doi:10.1016/j.jcp.2011.03.038 · Cited by 98 · see citing works
Self-citationMulti-phase computations in geometrical optics
Engquist, B. E., & Runborg, O. (1996) · Journal of Computational and Applied Mathematics · doi:10.1016/0377-0427(96)00023-4 · Cited by 97 · see citing works
A kinetic formulation for multi-branch entropy solutions of scalar conservation laws
Brenier, Y., & Corrias, L. (1998) · Annales de l Institut Henri Poincaré C Analyse Non Linéaire · doi:10.1016/s0294-1449(97)89298-0 · Cited by 91 · see citing works
Higher-order quadrature-based moment methods for kinetic equations
Fox, R. O. (2009) · Journal of Computational Physics · doi:10.1016/j.jcp.2009.07.018 · Cited by 84 · see citing works
Self-citationComputing multivalued physical observables for the semiclassical limit of the Schrödinger equation
Jin, S., Liu, H., Osher, S., et al. (2004) · Journal of Computational Physics · doi:10.1016/j.jcp.2004.11.008 · Cited by 84 · see citing works
Jin, S., & Li, X. (2003) · Physica D Nonlinear Phenomena · doi:10.1016/s0167-2789(03)00124-6 · Cited by 82 · see citing works
Mathematical Models and Numerical Methods for High Frequency Waves
Runborg, O. (2007) · Communications in Computational Physics · doi:10.4208/cicp.2007.v2.p827 · Cited by 80 · see citing works
A fully coupled quadrature-based moment method for dilute to moderately dilute fluid–particle flows
Passalacqua, A., Fox, R. O., Garg, R., & Subramaniam, S. (2009) · Chemical Engineering Science · doi:10.1016/j.ces.2009.09.002 · Cited by 74 · see citing works
Self-citationKinetic Modeling of Nanoprecipitation using CFD Coupled with a Population Balance
Cheng, J. C., & Fox, R. O. (2010) · Industrial & Engineering Chemistry Research · doi:10.1021/ie100558n · Cited by 68 · see citing works
Self-citationOptimal Moment Sets for Multivariate Direct Quadrature Method of Moments
Fox, R. O. (2008) · Industrial & Engineering Chemistry Research · doi:10.1021/ie801316d · Cited by 62 · see citing works
Self-citationHyperbolic Moment Equations in Kinetic Gas Theory Based on Multi-Variate Pearson-IV-Distributions
Torrilhon, M. (2009) · Communications in Computational Physics · doi:10.4208/cicp.2009.09.049 · Cited by 60 · see citing works
Positivity of Riesz functionals and solutions of quadratic and quartic moment problems
Fialkow, L. A., & Nie, J. (2009) · Journal of Functional Analysis · doi:10.1016/j.jfa.2009.09.015 · Cited by 59 · see citing works
TWO MOMENT SYSTEMS FOR COMPUTING MULTIPHASE SEMICLASSICAL LIMITS OF THE SCHRÖDINGER EQUATION
Gosse, L., Jin, S., & Li, X. (2003) · Mathematical Models and Methods in Applied Sciences · doi:10.1142/s0218202503003082 · Cited by 59 · see citing works
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Cheng, J. C., Vigil, R. D., & Fox, R. O. (2010) · Journal of Colloid and Interface Science · doi:10.1016/j.jcis.2010.07.066 · Cited by 57 · see citing works
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Fox, R. O. (2006) · Journal of Aerosol Science · doi:10.1016/j.jaerosci.2006.03.005 · Cited by 56 · see citing works
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Gosse, L. (2002) · Journal of Computational Physics · doi:10.1006/jcph.2002.7085 · Cited by 55 · see citing works
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Beylich, A. E. (2000) · Physics of Fluids · doi:10.1063/1.870322 · Cited by 55 · see citing works
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Kah, D., Laurent, F., Fréret, L., et al. (2010) · Flow Turbulence and Combustion · doi:10.1007/s10494-010-9286-z · Cited by 49 · see citing works
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Fox, R. O., & Vedula, P. (2009) · Industrial & Engineering Chemistry Research · doi:10.1021/ie9013138 · Cited by 47 · see citing works
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de Chaisemartin, S., Fréret, L., Kah, D., et al. (2009) · Comptes Rendus Mécanique · doi:10.1016/j.crme.2009.06.016 · Cited by 47 · see citing works
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Runborg, O. (2000) · ESAIM Mathematical Modelling and Numerical Analysis · doi:10.1051/m2an:2000124 · Cited by 46 · see citing works
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Hrenya, C. M., Galvin, J. E., & Wildman, R. D. (2008) · Journal of Fluid Mechanics · doi:10.1017/s0022112007000079 · Cited by 37 · see citing works
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Passalacqua, A., & Fox, R. O. (2010) · Applied Mathematical Modelling · doi:10.1016/j.apm.2010.09.038 · Cited by 35 · see citing works
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Passalacqua, A., Galvin, J. E., Vedula, P., et al. (2011) · Communications in Computational Physics · doi:10.4208/cicp.020210.160910a · Cited by 34 · see citing works
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Galvin, J. E., Hrenya, C. M., & Wildman, R. D. (2007) · Journal of Fluid Mechanics · doi:10.1017/s0022112007006489 · Cited by 34 · see citing works
Li, X., Wohlbier, J. G., Jin, S., et al. (2004) · Physical Review E · doi:10.1103/physreve.70.016502 · Cited by 32 · see citing works
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Fialkow, L. A., & Petrovic, S. (2005) · Integral Equations and Operator Theory · doi:10.1007/s00020-003-1334-9 · Cited by 18 · see citing works
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Wohlbier, J. G., Jin, S., & Sengele, S. (2005) · Physics of Plasmas · doi:10.1063/1.1851990 · Cited by 11 · see citing works
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Self-citation
- Authors
- Yuan, C., & Fox, R. O.
- Affiliations
- Iowa State University (US)
- Corresponding author
- Fox, R.O.
- ORCID
- Fox, R.O.
- Venue
- Journal of Computational Physics
- Publisher
- Elsevier BV
- Published
- 2011-09
- Volume
- 230
- Issue
- 22
- Pages
- 8216-8246
- ISSN
- 0021-9991 (ISSN-L)
- OpenAlex
- W1971818437
- Cited by
- 232
- References
- 75
- Citations by year
- 2026: 8 · 2025: 12 · 2024: 12 · 2023: 8 · 2022: 23 · 2021: 16 · 2020: 15 · 2019: 25 · 2018: 17 · 2017: 13 · 2016: 19 · 2015: 13 · 2014: 18 · 2013: 14 · 2012: 10
- FWCI
- 26.34
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Computational Physics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Gas Dynamics and Kinetic Theory
- Physical Sciences › Engineering › Ocean Engineering › Particle Dynamics in Fluid Flows
- Physical Sciences › Engineering › Computational Mechanics › Radiative Heat Transfer Studies
- Keywords
- quadrature-based moment methods, kinetic equations, moment closure, adaptive quadrature, truncated moment problem, multivalued solutions, collisionless Boltzmann equation, particle-particle collisions, inelastic collisions, fluid drag, volume averaging
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