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On the gain of regularity for the positive part of Boltzmann collision operator associated with soft-potentials
Kinetic/fluid micro-macro numerical schemes for Vlasov-Poisson-BGK equation using particles
1. | INRIA-Nancy Grand Est, CALVI Project, and IRMA, Université de Strasbourg, 67084, STRASBOURG, France |
2. | INRIA-Rennes Bretagne Atlantique, IPSO Project, and IRMAR (Université de Rennes 1), 35042 RENNES, France |
3. | CNRS and IRMAR (Université de Rennes 1), and INRIA-Rennes Bretagne Atlantique, IPSO Project, 35042 RENNES, France |
References:
[1] |
C. Bardos, F. Golse and D. Levermore, Fluid dynamic limits of kinetic equations I. Formal derivation, J. Statist. Phys., 63 (1991), 323-344.
doi: 10.1007/BF01026608. |
[2] |
C. K. Birdsall and A. B. Langdon, Plasma physics via computer simulation, Institute of Physics (IOP), Series in Plasma Physics 2004. |
[3] |
M. Bennoune, M. Lemou and L. Mieussens, Uniformly stable numerical schemes for the Boltzmann equation preserving the compressible Navier-Stokes asymptotics, J. Comput. Phys., 227 (2008), 3781-3803.
doi: 10.1016/j.jcp.2007.11.032. |
[4] |
S. Brunner, E. Valeo and J. A. Krommes, Collisional delta-f scheme with evolving background for transport time scale simulations, Phys. of Plasmas, 12 (1999). |
[5] |
S. Brunner, E. Valeo and J. A. Krommes, Linear delta-f simulations of nonlocal electron heat transport, Phys. of Plasmas, 7 (2000). |
[6] |
J.-M. Coron and B. Perthame, Numerical passage from kinetic to fluid equations, SIAM J. Numer. Anal., 28 (1991), 26-42. |
[7] |
G.-H. Cottet and P.-A. Raviart, On particle-in-cell methods for the one-dimensional Vlasov-Poisson equations, SIAM J. of Numer. Anal., 21 (1984), 52-76. |
[8] |
N. Crouseilles, P. Degond and M. Lemou, A hybrid kinetic/fluid model for solving the gas dynamics Boltzmann-BGK equation, J. Comput. Phys., 199 (2004), 776-808.
doi: 10.1016/j.jcp.2004.03.007. |
[9] |
N. Crouseilles and M. Lemou, An asymptotic preserving scheme based on a micro-macro decomposition for collisional Vlasov equations: Diffusion and high-field scaling limits, Kin. Rel. Models, 4 (2011), 441-477. |
[10] |
N. Crouseilles, M. Mehrenberger and E. Sonnendrücker, Conservative semi-Lagrangian schemes for the Vlasov equation, J. Comput. Phys., 229 (2010), 1927-1953.
doi: 10.1016/j.jcp.2009.11.007. |
[11] |
P. Degond and F. J. Mustieles, A deterministic approximation of diffusion equations using particles, SIAM J. on Scientific and Statistical Computing, 11 (1990), 293-310.
doi: 10.1137/0911018. |
[12] |
P. Degond and G. Dimarco, Fluid simulations with localized Boltzmann upscaling by direct simulation Monte-Carlo, J. Comput. Phys., 231 (2012), 2414-2437.
doi: 10.1016/j.jcp.2011.11.030. |
[13] |
P. Degond, G. Dimarco and L. Pareschi, The moment guided Monte Carlo method, International Journal for Numerical Methods in Fluids, 67 (2011), 189-213.
doi: 10.1002/fld.2345. |
[14] |
P. Degond, S. Jin and L. Mieussens, A smooth transition model between kinetic and hydrodynamic equations, J. Comput. Phys., 209 (2005), 665-694.
doi: 10.1016/j.jcp.2005.03.025. |
[15] |
P. Degond and S. Mas-Gallic, The weighted particle method for convection-diffusion equations, Part 2: The anisotropic case, Math. Comput., 53 (1989), 509-525.
doi: 10.1090/S0025-5718-1989-0983560-5. |
[16] |
F. Delaurens and F. J. Mustieles, A deterministic particle method for solving kinetic transport equations: The semiconductor Boltzmann equation case, SIAM J. Appl. Math., 52 (1991), 973-988.
doi: 10.1137/0152056. |
[17] |
F. Filbet and S. Jin, A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources, J. Comp. Phys., 229 (2010), 7625-7648.
doi: 10.1016/j.jcp.2010.06.017. |
[18] |
F. Filbet and S. Jin, An asymptotic preserving scheme for the ES-BGK model for the Boltzmann equation, J. Sci. Computing, 46 (2011), 204-224.
doi: 10.1007/s10915-010-9394-x. |
[19] |
E. Gabetta, L. Pareschi and G. Toscani, Relaxation schemes for nonlinear kinetic equations, SIAM J. Numer. Anal., 34 (1997), 2168-2194.
doi: 10.1137/S0036142995287768. |
[20] |
D. Issautier, Convergence of a weighted particle method for solving the Boltzmann (BGK) equation, SIAM J. Numer. Anal., 33 (1994), 2099-2119.
doi: 10.1137/S0036142994266856. |
[21] |
S. Jin, Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations, SIAM J. Sci. Comput., 21 (1999), 441-454.
doi: 10.1137/S1064827598334599. |
[22] |
M. Lemou, Relaxed micro-macro schemes for kinetic equations, Comptes Rendus Math\'ematique, 348 (2010), 455-460. |
[23] |
M. Lemou and L. Mieussens, A new asymptotic preserving scheme based on micro-macro formulation for linear kinetic equations in the diffusion limit, SIAM J. Sci. Comp., 31 (2008), 334-368.
doi: 10.1137/07069479X. |
[24] |
R. J. LeVeque, "Numerical Methods for Conservation Laws," Lectures in Mathematics Birkhauser Verlag, Basel, 1992. |
[25] |
L. Mieussens, Discrete velocity model and implicit scheme for the BGK equation of rarefied gas dynamics, Math. Models and Meth. Appl. Sci., 8 (2000), 1121-1149. |
[26] |
B. Niclot, P. Degond and F. Poupaud, Deterministic particle simulations of the Boltzmann transport equation of semiconductors, J. Comput. Phys., 78 (1988), 313-349.
doi: 10.1016/0021-9991(88)90053-8. |
[27] |
L. Pareschi and G. Russo, Asymptotic preserving Monte Carlo methods for the Boltzmann equation, Trans. Theo. Stat. Phys., 29 (2000), 415-430.
doi: 10.1080/00411450008205882. |
[28] |
L. Pareschi and G. Russo, Time relaxed Monte Carlo methods for the Boltzmann equation, SIAM J. Sci. Comput., 23 (2001), 1253-1273.
doi: 10.1137/S1064827500375916. |
[29] |
P.-A. Raviart, "An Analysis of Particle Methods in Numerical Methods in Fluid Dynamics," Lecture Notes in Math. 1127, F. Brezzi ed., Springer-Verlag, Berlin, 1985. |
[30] |
E. Sonnendrücker, Mathematical models for fusion,, Lecture Notes, ().
|
[31] |
B. Yan and S. Jin, A successive penalty-based asymptotic-preserving scheme for kinetic equations,, submitted., ().
|
show all references
References:
[1] |
C. Bardos, F. Golse and D. Levermore, Fluid dynamic limits of kinetic equations I. Formal derivation, J. Statist. Phys., 63 (1991), 323-344.
doi: 10.1007/BF01026608. |
[2] |
C. K. Birdsall and A. B. Langdon, Plasma physics via computer simulation, Institute of Physics (IOP), Series in Plasma Physics 2004. |
[3] |
M. Bennoune, M. Lemou and L. Mieussens, Uniformly stable numerical schemes for the Boltzmann equation preserving the compressible Navier-Stokes asymptotics, J. Comput. Phys., 227 (2008), 3781-3803.
doi: 10.1016/j.jcp.2007.11.032. |
[4] |
S. Brunner, E. Valeo and J. A. Krommes, Collisional delta-f scheme with evolving background for transport time scale simulations, Phys. of Plasmas, 12 (1999). |
[5] |
S. Brunner, E. Valeo and J. A. Krommes, Linear delta-f simulations of nonlocal electron heat transport, Phys. of Plasmas, 7 (2000). |
[6] |
J.-M. Coron and B. Perthame, Numerical passage from kinetic to fluid equations, SIAM J. Numer. Anal., 28 (1991), 26-42. |
[7] |
G.-H. Cottet and P.-A. Raviart, On particle-in-cell methods for the one-dimensional Vlasov-Poisson equations, SIAM J. of Numer. Anal., 21 (1984), 52-76. |
[8] |
N. Crouseilles, P. Degond and M. Lemou, A hybrid kinetic/fluid model for solving the gas dynamics Boltzmann-BGK equation, J. Comput. Phys., 199 (2004), 776-808.
doi: 10.1016/j.jcp.2004.03.007. |
[9] |
N. Crouseilles and M. Lemou, An asymptotic preserving scheme based on a micro-macro decomposition for collisional Vlasov equations: Diffusion and high-field scaling limits, Kin. Rel. Models, 4 (2011), 441-477. |
[10] |
N. Crouseilles, M. Mehrenberger and E. Sonnendrücker, Conservative semi-Lagrangian schemes for the Vlasov equation, J. Comput. Phys., 229 (2010), 1927-1953.
doi: 10.1016/j.jcp.2009.11.007. |
[11] |
P. Degond and F. J. Mustieles, A deterministic approximation of diffusion equations using particles, SIAM J. on Scientific and Statistical Computing, 11 (1990), 293-310.
doi: 10.1137/0911018. |
[12] |
P. Degond and G. Dimarco, Fluid simulations with localized Boltzmann upscaling by direct simulation Monte-Carlo, J. Comput. Phys., 231 (2012), 2414-2437.
doi: 10.1016/j.jcp.2011.11.030. |
[13] |
P. Degond, G. Dimarco and L. Pareschi, The moment guided Monte Carlo method, International Journal for Numerical Methods in Fluids, 67 (2011), 189-213.
doi: 10.1002/fld.2345. |
[14] |
P. Degond, S. Jin and L. Mieussens, A smooth transition model between kinetic and hydrodynamic equations, J. Comput. Phys., 209 (2005), 665-694.
doi: 10.1016/j.jcp.2005.03.025. |
[15] |
P. Degond and S. Mas-Gallic, The weighted particle method for convection-diffusion equations, Part 2: The anisotropic case, Math. Comput., 53 (1989), 509-525.
doi: 10.1090/S0025-5718-1989-0983560-5. |
[16] |
F. Delaurens and F. J. Mustieles, A deterministic particle method for solving kinetic transport equations: The semiconductor Boltzmann equation case, SIAM J. Appl. Math., 52 (1991), 973-988.
doi: 10.1137/0152056. |
[17] |
F. Filbet and S. Jin, A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources, J. Comp. Phys., 229 (2010), 7625-7648.
doi: 10.1016/j.jcp.2010.06.017. |
[18] |
F. Filbet and S. Jin, An asymptotic preserving scheme for the ES-BGK model for the Boltzmann equation, J. Sci. Computing, 46 (2011), 204-224.
doi: 10.1007/s10915-010-9394-x. |
[19] |
E. Gabetta, L. Pareschi and G. Toscani, Relaxation schemes for nonlinear kinetic equations, SIAM J. Numer. Anal., 34 (1997), 2168-2194.
doi: 10.1137/S0036142995287768. |
[20] |
D. Issautier, Convergence of a weighted particle method for solving the Boltzmann (BGK) equation, SIAM J. Numer. Anal., 33 (1994), 2099-2119.
doi: 10.1137/S0036142994266856. |
[21] |
S. Jin, Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations, SIAM J. Sci. Comput., 21 (1999), 441-454.
doi: 10.1137/S1064827598334599. |
[22] |
M. Lemou, Relaxed micro-macro schemes for kinetic equations, Comptes Rendus Math\'ematique, 348 (2010), 455-460. |
[23] |
M. Lemou and L. Mieussens, A new asymptotic preserving scheme based on micro-macro formulation for linear kinetic equations in the diffusion limit, SIAM J. Sci. Comp., 31 (2008), 334-368.
doi: 10.1137/07069479X. |
[24] |
R. J. LeVeque, "Numerical Methods for Conservation Laws," Lectures in Mathematics Birkhauser Verlag, Basel, 1992. |
[25] |
L. Mieussens, Discrete velocity model and implicit scheme for the BGK equation of rarefied gas dynamics, Math. Models and Meth. Appl. Sci., 8 (2000), 1121-1149. |
[26] |
B. Niclot, P. Degond and F. Poupaud, Deterministic particle simulations of the Boltzmann transport equation of semiconductors, J. Comput. Phys., 78 (1988), 313-349.
doi: 10.1016/0021-9991(88)90053-8. |
[27] |
L. Pareschi and G. Russo, Asymptotic preserving Monte Carlo methods for the Boltzmann equation, Trans. Theo. Stat. Phys., 29 (2000), 415-430.
doi: 10.1080/00411450008205882. |
[28] |
L. Pareschi and G. Russo, Time relaxed Monte Carlo methods for the Boltzmann equation, SIAM J. Sci. Comput., 23 (2001), 1253-1273.
doi: 10.1137/S1064827500375916. |
[29] |
P.-A. Raviart, "An Analysis of Particle Methods in Numerical Methods in Fluid Dynamics," Lecture Notes in Math. 1127, F. Brezzi ed., Springer-Verlag, Berlin, 1985. |
[30] |
E. Sonnendrücker, Mathematical models for fusion,, Lecture Notes, ().
|
[31] |
B. Yan and S. Jin, A successive penalty-based asymptotic-preserving scheme for kinetic equations,, submitted., ().
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