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Convergence rate for the method of moments with linear closure relations
1. | Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Ave, Ottawa, Ontario, Canada |
2. | Laboratoire J.-A. Dieudonné, Université de Nice - Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, France |
3. | CSCAMM and Department of Mathematics, University of Maryland, College Park, MD 20742-4015, United States |
References:
[1] |
P. L. Bhatnagar, E. P. Gross and M. Krook, A model for collision processes in gases. I. small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94 (1954), 511-525.
doi: 10.1103/PhysRev.94.511. |
[2] |
G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flow, Oxford Engineering Science Series, 42. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1995. |
[3] |
A. V. Bobylev, The Chapman-Enskog and Grad methods for solving the Boltzmann equation, Dokl. Akad. Nauk SSSR, 262 (1982), 71-75. |
[4] |
F. Brini, Hyperbolicity region in extended thermodynamics with 14 moments, Continuum Mech. Thermodyn., 13 (2001), 1-8.
doi: 10.1007/s001610100036. |
[5] |
Z. Cai, Y. Fan and R. Li, Globally hyperbolic regularization of Grad's moment system in one dimensional space, Commun. Math. Sci., 11 (2013), 547-571. arXiv:1111.3409, 2012.
doi: 10.4310/CMS.2013.v11.n2.a12. |
[6] |
Z. Cai and R. Li, Numerical regularized moment method of arbitrary order for Boltzmann-BGK equation, SIAM J. Sci. Comput., 32 (2010), 2875-2907.
doi: 10.1137/100785466. |
[7] |
Z. Cai, R. Li and Y. Wang, An efficient NRxx method for Boltzmann-BGK equation, J. Sci. Comput., 50 (2012), 103-119.
doi: 10.1007/s10915-011-9475-5. |
[8] |
S. Chandrasekhar, Stochastic problems in physics and astronomy, Rev. Mod. Phys. 15 (1943), 1-89.
doi: 10.1103/RevModPhys.15.1. |
[9] |
L. Desvillettes, Some applications of the method of moments for the homogeneous Boltzmann and Kac equations, Archive Rat. Mech. Anal. 123 (1993), 387-404.
doi: 10.1007/BF00375586. |
[10] |
H. Grad, On the kinetic theory of rarefied gases, Comm. Pure Appl. Math., 2 (1949), 331-407.
doi: 10.1002/cpa.3160020403. |
[11] |
P. Le Tallec and J. P. Perlat, Numerical Analysis of Levermore's Moment System, Rapport de recherche 3124, INRIA Rocquencourt, March 1997. |
[12] |
C. D. Levermore, Moment closure hierarchy for kinetic theories, J. Statist. Phys., 83 (1996), 1021-1065.
doi: 10.1007/BF02179552. |
[13] |
C. D. Levermore and W. J. Morokoff, The Gaussian moment closure for gas dynamics, SIAM J. Appl. Math., 59 (1999), 72-96.
doi: 10.1137/S0036139996299236. |
[14] |
H. G. Othmer and S. R. Dunbar and W. Alt, Models of dispersal in biological systems, J. Math. Biol., 26 (1988), 263-298.
doi: 10.1007/BF00277392. |
[15] |
B. Perthame, Boltzmann type schemes for gas dynamics and the entropy property, SIAM J. Numer. Anal., 27 (1990), 1405-1421.
doi: 10.1137/0727081. |
[16] |
J. Shen and T. Tang, Spectral and High-Order Methods with Applications, volume 3 of Mathematics Monograph Series, Science Press, Beijing, P. R. China, 2006. |
[17] |
H. Struchtrup, Macroscopic Transport Equations for Rarefied Gas Flows: Approximation Methods in Kinetic Theory, Springer, 2005. |
[18] |
H. Struchtrup and M. Torrilhon, Regularization of Grad's 13 moment equations: Derivation and linear analysis, Phys. Fluids, 15 (2003), 2668-2680.
doi: 10.1063/1.1597472. |
[19] |
E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, A Practical Introduction, 3rd edition, Springer, 2009.
doi: 10.1007/b79761. |
[20] |
M. Torrilhon, Two dimensional bulk microflow simulations based on regularized Grad's 13-moment equations, SIAM Multiscale Model. Simul., 5 (2006), 695-728.
doi: 10.1137/050635444. |
[21] |
M. Torrilhon, Hyperbolic moment equations in kinetic gas theory based on multivariate Pearson-IV-distributions, Commun. Comput. Phys., 7 (2010), 639-673.
doi: 10.4208/cicp.2009.09.049. |
[22] |
D. Vernon Widder, The Laplace Transform, Princeton University Press, 1941. |
[23] |
G. M. Wing, An Introduction to Transport Theory, New-York, Wiley, 1962. |
show all references
References:
[1] |
P. L. Bhatnagar, E. P. Gross and M. Krook, A model for collision processes in gases. I. small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94 (1954), 511-525.
doi: 10.1103/PhysRev.94.511. |
[2] |
G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flow, Oxford Engineering Science Series, 42. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1995. |
[3] |
A. V. Bobylev, The Chapman-Enskog and Grad methods for solving the Boltzmann equation, Dokl. Akad. Nauk SSSR, 262 (1982), 71-75. |
[4] |
F. Brini, Hyperbolicity region in extended thermodynamics with 14 moments, Continuum Mech. Thermodyn., 13 (2001), 1-8.
doi: 10.1007/s001610100036. |
[5] |
Z. Cai, Y. Fan and R. Li, Globally hyperbolic regularization of Grad's moment system in one dimensional space, Commun. Math. Sci., 11 (2013), 547-571. arXiv:1111.3409, 2012.
doi: 10.4310/CMS.2013.v11.n2.a12. |
[6] |
Z. Cai and R. Li, Numerical regularized moment method of arbitrary order for Boltzmann-BGK equation, SIAM J. Sci. Comput., 32 (2010), 2875-2907.
doi: 10.1137/100785466. |
[7] |
Z. Cai, R. Li and Y. Wang, An efficient NRxx method for Boltzmann-BGK equation, J. Sci. Comput., 50 (2012), 103-119.
doi: 10.1007/s10915-011-9475-5. |
[8] |
S. Chandrasekhar, Stochastic problems in physics and astronomy, Rev. Mod. Phys. 15 (1943), 1-89.
doi: 10.1103/RevModPhys.15.1. |
[9] |
L. Desvillettes, Some applications of the method of moments for the homogeneous Boltzmann and Kac equations, Archive Rat. Mech. Anal. 123 (1993), 387-404.
doi: 10.1007/BF00375586. |
[10] |
H. Grad, On the kinetic theory of rarefied gases, Comm. Pure Appl. Math., 2 (1949), 331-407.
doi: 10.1002/cpa.3160020403. |
[11] |
P. Le Tallec and J. P. Perlat, Numerical Analysis of Levermore's Moment System, Rapport de recherche 3124, INRIA Rocquencourt, March 1997. |
[12] |
C. D. Levermore, Moment closure hierarchy for kinetic theories, J. Statist. Phys., 83 (1996), 1021-1065.
doi: 10.1007/BF02179552. |
[13] |
C. D. Levermore and W. J. Morokoff, The Gaussian moment closure for gas dynamics, SIAM J. Appl. Math., 59 (1999), 72-96.
doi: 10.1137/S0036139996299236. |
[14] |
H. G. Othmer and S. R. Dunbar and W. Alt, Models of dispersal in biological systems, J. Math. Biol., 26 (1988), 263-298.
doi: 10.1007/BF00277392. |
[15] |
B. Perthame, Boltzmann type schemes for gas dynamics and the entropy property, SIAM J. Numer. Anal., 27 (1990), 1405-1421.
doi: 10.1137/0727081. |
[16] |
J. Shen and T. Tang, Spectral and High-Order Methods with Applications, volume 3 of Mathematics Monograph Series, Science Press, Beijing, P. R. China, 2006. |
[17] |
H. Struchtrup, Macroscopic Transport Equations for Rarefied Gas Flows: Approximation Methods in Kinetic Theory, Springer, 2005. |
[18] |
H. Struchtrup and M. Torrilhon, Regularization of Grad's 13 moment equations: Derivation and linear analysis, Phys. Fluids, 15 (2003), 2668-2680.
doi: 10.1063/1.1597472. |
[19] |
E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, A Practical Introduction, 3rd edition, Springer, 2009.
doi: 10.1007/b79761. |
[20] |
M. Torrilhon, Two dimensional bulk microflow simulations based on regularized Grad's 13-moment equations, SIAM Multiscale Model. Simul., 5 (2006), 695-728.
doi: 10.1137/050635444. |
[21] |
M. Torrilhon, Hyperbolic moment equations in kinetic gas theory based on multivariate Pearson-IV-distributions, Commun. Comput. Phys., 7 (2010), 639-673.
doi: 10.4208/cicp.2009.09.049. |
[22] |
D. Vernon Widder, The Laplace Transform, Princeton University Press, 1941. |
[23] |
G. M. Wing, An Introduction to Transport Theory, New-York, Wiley, 1962. |
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