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Optimal prediction for radiative transfer: A new perspective on moment closure
Non--local macroscopic models based on Gaussian closures for the Spizer-Härm regime
1. | Project-Team SIMPAF–INRIA Lille Nord Europe, Park Plazza, 40 avenue Halley, F-59650 Villeneuve d’Ascq cedex, France, France |
References:
[1] |
F. Alouani Bibi and J.-P. Matte, Nonlocal electron heat transport and electronion energy transfer in the presence of strong collisional heating, Laser and Particle Beams, 22 (2004), 103-108. |
[2] |
E. M. Epperlein and R. Short, A practical nonlocal model for electron heat transport in laser plasmas, Phys. Fluids B, 3 (1991), 3092-3098.
doi: 10.1063/1.859789. |
[3] |
M. Frank, D. Levermore and M. Shäfer, Diffusive corrections to $\mathbb P_N$ approximations, Multiscale Model. Simul., 9 (2011), 1-28. |
[4] |
T. Goudon and M. Parisot, On the Spitzer-Härm regime and non-local approximations: modeling, analysis and numerical simulations, SIAM Multiscale Model. Simul., (2011), To appear. |
[5] |
B. Graille, "Modélisation de Mélanges Gazeux Réactifs Ionisés Dissipatifs," Ph.D. thesis, Ecole Polytechnique, 2004. |
[6] |
Y. Guo, The Landau equation in a periodic box, Comm. Math. Phys., 231 (2002), 391-434.
doi: 10.1007/s00220-002-0729-9. |
[7] |
D. Levermore, "Boundary Conditions for Moment Closures," IPAM KT 2009, UCLA, CA, 2009. |
[8] |
D. Levermore, "Kinetic Theory, Gaussian Moment Closures, and Fluid Approximations," IPAM KT 2009, Culminating Retreat, Lake Arrowhead, CA, 2009. |
[9] |
T.-P.Liu and Y. Zeng, Large time behavior of solutions for general quasilinear hyperbolic-parabolic systems of conservation laws, Mem. Amer. Math. Soc., 125 (1997), viii+120. |
[10] |
J.-F. Luciani and P. Mora, Resummation methods of the Chapman-Enskog expansion for a strongly inhomogeneous plasma, J. Stat. Phys., 43 (1986), 281-302.
doi: 10.1007/BF01010582. |
[11] |
J.-F. Luciani and P. Mora, Nonlocal electron transport in laser created plasmas, Laser and Particle Beams, 12 (1994), 387-400.
doi: 10.1017/S0263034600008247. |
[12] |
J.-F. Luciani, P. Mora and R. Pellat, Quasistatic heat front and delocalized heat flux, Phys. Fluids, 28 (1985), 835-845.
doi: 10.1063/1.865052. |
[13] |
P. Nicolaï, J.-L. Feugeas and G. Schurtz, A practical nonlocal model for heat transport in magnetized laser plasmas, Phys. of Plasmas, 13 (2006), 032701-1/032701-13. |
[14] |
M. Parisot, Finite volume schemes on unstructured grids for generalized Spitzer-Härm model, Tech. Rep., INRIA, 2011, In preparation. |
[15] |
E. J. Routh, "A Treatise on the Stability of a Given State of Motion," Macmillan and Co., 1877. |
[16] |
G. P. Schurtz, P. Nicolaï and M. Busquet, A nonlocal electron conduction model for multidimensional radiation hydrodynamics codes, Physics of Plasmas, 7 (2000), 4238-4250.
doi: 10.1063/1.1289512. |
[17] |
I. P. Shkarofsky, Cartesian tensor expansion of the Fokker-Planck equation, Can. J. Phys., 41 (1963), 1753-1775.
doi: 10.1139/p63-179. |
[18] |
L. Spitzer and R. Härm, Transport phenomena in a completely ionized gas, Phys. Rev., 89 (1953), 977-981.
doi: 10.1103/PhysRev.89.977. |
show all references
References:
[1] |
F. Alouani Bibi and J.-P. Matte, Nonlocal electron heat transport and electronion energy transfer in the presence of strong collisional heating, Laser and Particle Beams, 22 (2004), 103-108. |
[2] |
E. M. Epperlein and R. Short, A practical nonlocal model for electron heat transport in laser plasmas, Phys. Fluids B, 3 (1991), 3092-3098.
doi: 10.1063/1.859789. |
[3] |
M. Frank, D. Levermore and M. Shäfer, Diffusive corrections to $\mathbb P_N$ approximations, Multiscale Model. Simul., 9 (2011), 1-28. |
[4] |
T. Goudon and M. Parisot, On the Spitzer-Härm regime and non-local approximations: modeling, analysis and numerical simulations, SIAM Multiscale Model. Simul., (2011), To appear. |
[5] |
B. Graille, "Modélisation de Mélanges Gazeux Réactifs Ionisés Dissipatifs," Ph.D. thesis, Ecole Polytechnique, 2004. |
[6] |
Y. Guo, The Landau equation in a periodic box, Comm. Math. Phys., 231 (2002), 391-434.
doi: 10.1007/s00220-002-0729-9. |
[7] |
D. Levermore, "Boundary Conditions for Moment Closures," IPAM KT 2009, UCLA, CA, 2009. |
[8] |
D. Levermore, "Kinetic Theory, Gaussian Moment Closures, and Fluid Approximations," IPAM KT 2009, Culminating Retreat, Lake Arrowhead, CA, 2009. |
[9] |
T.-P.Liu and Y. Zeng, Large time behavior of solutions for general quasilinear hyperbolic-parabolic systems of conservation laws, Mem. Amer. Math. Soc., 125 (1997), viii+120. |
[10] |
J.-F. Luciani and P. Mora, Resummation methods of the Chapman-Enskog expansion for a strongly inhomogeneous plasma, J. Stat. Phys., 43 (1986), 281-302.
doi: 10.1007/BF01010582. |
[11] |
J.-F. Luciani and P. Mora, Nonlocal electron transport in laser created plasmas, Laser and Particle Beams, 12 (1994), 387-400.
doi: 10.1017/S0263034600008247. |
[12] |
J.-F. Luciani, P. Mora and R. Pellat, Quasistatic heat front and delocalized heat flux, Phys. Fluids, 28 (1985), 835-845.
doi: 10.1063/1.865052. |
[13] |
P. Nicolaï, J.-L. Feugeas and G. Schurtz, A practical nonlocal model for heat transport in magnetized laser plasmas, Phys. of Plasmas, 13 (2006), 032701-1/032701-13. |
[14] |
M. Parisot, Finite volume schemes on unstructured grids for generalized Spitzer-Härm model, Tech. Rep., INRIA, 2011, In preparation. |
[15] |
E. J. Routh, "A Treatise on the Stability of a Given State of Motion," Macmillan and Co., 1877. |
[16] |
G. P. Schurtz, P. Nicolaï and M. Busquet, A nonlocal electron conduction model for multidimensional radiation hydrodynamics codes, Physics of Plasmas, 7 (2000), 4238-4250.
doi: 10.1063/1.1289512. |
[17] |
I. P. Shkarofsky, Cartesian tensor expansion of the Fokker-Planck equation, Can. J. Phys., 41 (1963), 1753-1775.
doi: 10.1139/p63-179. |
[18] |
L. Spitzer and R. Härm, Transport phenomena in a completely ionized gas, Phys. Rev., 89 (1953), 977-981.
doi: 10.1103/PhysRev.89.977. |
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