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Full-Text Articles in Physical Sciences and Mathematics
A Direct Simulation Monte Carlo Method For The Uehling-Uhlenbeck-Boltzmann Equation, Alejandro Garcia, Wolfgang Wagner
A Direct Simulation Monte Carlo Method For The Uehling-Uhlenbeck-Boltzmann Equation, Alejandro Garcia, Wolfgang Wagner
Alejandro Garcia
In this paper we describe a direct simulation Monte Carlo algorithm for the Uehling-Uhlenbeck-Boltzmann equation in terms of Markov processes. This provides a unifying framework for both the classical Boltzmann case as well as the Fermi-Dirac and Bose-Einstein cases. We establish the foundation of the algorithm by demonstrating its link to the kinetic equation. By numerical experiments we study its sensitivity to the number of simulation particles and to the discretization of the velocity space, when approximating the steady-state distribution.
Inverted Velocity Profile In The Cylindrical Couette Flow Of A Rarefied Gas, Alejandro Garcia, K. Aoki, H. Yoshida, T. Nakanishi
Inverted Velocity Profile In The Cylindrical Couette Flow Of A Rarefied Gas, Alejandro Garcia, K. Aoki, H. Yoshida, T. Nakanishi
Alejandro Garcia
The cylindrical Couette flow of a rarefied gas is investigated, under the diffuse-specular reflection condition of Maxwell’s type on the cylinders, in the case where the inner cylinder is rotating whereas the outer cylinder is at rest. The inverted velocity profile for small accommodation coefficients, pointed out by Tibbs, Baras, and Garcia [Phys. Rev. E 56, 2282 (1997)] on the basis of a Monte Carlo simulation, is investigated extensively by means of a systematic asymptotic analysis for small Knudsen numbers as well as the direct numerical analysis of the Boltzmann equation, and the parameter range in which the phenomenon appears …
Inverted Velocity Profile In The Cylindrical Couette Flow Of A Rarefied Gas, Alejandro Garcia, K. Aoki, H. Yoshida, T. Nakanishi
Inverted Velocity Profile In The Cylindrical Couette Flow Of A Rarefied Gas, Alejandro Garcia, K. Aoki, H. Yoshida, T. Nakanishi
Faculty Publications
The cylindrical Couette flow of a rarefied gas is investigated, under the diffuse-specular reflection condition of Maxwell’s type on the cylinders, in the case where the inner cylinder is rotating whereas the outer cylinder is at rest. The inverted velocity profile for small accommodation coefficients, pointed out by Tibbs, Baras, and Garcia [Phys. Rev. E 56, 2282 (1997)] on the basis of a Monte Carlo simulation, is investigated extensively by means of a systematic asymptotic analysis for small Knudsen numbers as well as the direct numerical analysis of the Boltzmann equation, and the parameter range in which the phenomenon appears …
A Direct Simulation Monte Carlo Method For The Uehling-Uhlenbeck-Boltzmann Equation, Alejandro Garcia, W. Wagner
A Direct Simulation Monte Carlo Method For The Uehling-Uhlenbeck-Boltzmann Equation, Alejandro Garcia, W. Wagner
Faculty Publications
In this paper we describe a direct simulation Monte Carlo algorithm for the Uehling-Uhlenbeck-Boltzmann equation in terms of Markov processes. This provides a unifying framework for both the classical Boltzmann case as well as the Fermi-Dirac and Bose-Einstein cases. We establish the foundation of the algorithm by demonstrating its link to the kinetic equation. By numerical experiments we study its sensitivity to the number of simulation particles and to the discretization of the velocity space, when approximating the steady-state distribution.