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A numerical model of the Boltzmann equation related to the discontinuous Galerkin method
1. | Dipartimento di Matematica e Informatica, Viale A. Doria 6, 95125 Catania, Italy |
References:
[1] |
V. V. Aristov, "Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows,'', Kluwer Academic Publishers, (2001).
|
[2] |
L. L. Baker and N. G. Hadjiconstantinou, Variance-reduced Monte Carlo solutions of the Boltzmann equation for low-speed gas flows: A discontinuous Galerkin formulation,, Int. J. Numer. Meth. Fluids, 58 (2008), 381.
doi: 10.1002/fld.1724. |
[3] |
J. A. Carrillo, I. M. Gamba, A. Majorana and C.-W. Shu, A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices. Performance and comparisons with Monte Carlo methods,, Journal of Computational Physics, 184 (2003), 498.
doi: 10.1016/S0021-9991(02)00032-3. |
[4] |
J. A. Carrillo, I. M. Gamba, A. Majorana and C.-W. Shu, 2D semiconductor device simulations by WENO-Boltzmann schemes: Efficiency, boundary conditions and comparison to Monte Carlo methods,, Journal of Computational Physics, 214 (2006), 55.
doi: 10.1016/j.jcp.2005.09.005. |
[5] |
C. Cercignani, "The Boltzmann Equation and its Applications,'', Springer, (1988).
|
[6] |
C. Cercignani, "Mathematical Methods in Kinetic Theory,'', Plenum, (1990).
|
[7] |
Y. Cheng, I. M. Gamba, A. Majorana and C.-W. Shu, A discontinuous Galerkin solver for Boltzmann-Poisson systems for semiconductor devices,, Computer Methods in Applied Mechanics and Engineering, 198 (2009), 3130.
doi: 10.1016/j.cma.2009.05.015. |
[8] |
B. Cockburn and C.-W. Shu, Runge-Kutta discontinuous Galerkin methods for convection-dominated problems,, Journal of Scientific Computing, 16 (2001), 173.
doi: 10.1023/A:1012873910884. |
[9] |
F. Rogier and J. Schneider, A direct method for solving the Boltzmann equation,, Transport Theory Statist. Phys., 23 (1994), 313.
doi: 10.1080/00411459408203868. |
[10] |
Y. Sone, T. Ohwada and K. Aoki, Temperature jump and Knudsen layer in a rarefied gas over a plane wall: Numerical analysis of the linearized Boltzmann equation for hard-sphere molecules,, Physics of Fluids A, 1 (1989), 363.
doi: 10.1063/1.857457. |
show all references
References:
[1] |
V. V. Aristov, "Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows,'', Kluwer Academic Publishers, (2001).
|
[2] |
L. L. Baker and N. G. Hadjiconstantinou, Variance-reduced Monte Carlo solutions of the Boltzmann equation for low-speed gas flows: A discontinuous Galerkin formulation,, Int. J. Numer. Meth. Fluids, 58 (2008), 381.
doi: 10.1002/fld.1724. |
[3] |
J. A. Carrillo, I. M. Gamba, A. Majorana and C.-W. Shu, A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices. Performance and comparisons with Monte Carlo methods,, Journal of Computational Physics, 184 (2003), 498.
doi: 10.1016/S0021-9991(02)00032-3. |
[4] |
J. A. Carrillo, I. M. Gamba, A. Majorana and C.-W. Shu, 2D semiconductor device simulations by WENO-Boltzmann schemes: Efficiency, boundary conditions and comparison to Monte Carlo methods,, Journal of Computational Physics, 214 (2006), 55.
doi: 10.1016/j.jcp.2005.09.005. |
[5] |
C. Cercignani, "The Boltzmann Equation and its Applications,'', Springer, (1988).
|
[6] |
C. Cercignani, "Mathematical Methods in Kinetic Theory,'', Plenum, (1990).
|
[7] |
Y. Cheng, I. M. Gamba, A. Majorana and C.-W. Shu, A discontinuous Galerkin solver for Boltzmann-Poisson systems for semiconductor devices,, Computer Methods in Applied Mechanics and Engineering, 198 (2009), 3130.
doi: 10.1016/j.cma.2009.05.015. |
[8] |
B. Cockburn and C.-W. Shu, Runge-Kutta discontinuous Galerkin methods for convection-dominated problems,, Journal of Scientific Computing, 16 (2001), 173.
doi: 10.1023/A:1012873910884. |
[9] |
F. Rogier and J. Schneider, A direct method for solving the Boltzmann equation,, Transport Theory Statist. Phys., 23 (1994), 313.
doi: 10.1080/00411459408203868. |
[10] |
Y. Sone, T. Ohwada and K. Aoki, Temperature jump and Knudsen layer in a rarefied gas over a plane wall: Numerical analysis of the linearized Boltzmann equation for hard-sphere molecules,, Physics of Fluids A, 1 (1989), 363.
doi: 10.1063/1.857457. |
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