Theory of collision algorithms for gases and plasmas based on the Boltzmann equation and the Landau-Fokker-Planck equation

2000 ◽  
Vol 61 (4) ◽  
pp. 4576-4586 ◽  
Author(s):  
A. V. Bobylev ◽  
K. Nanbu
Keyword(s):  
Boltzmann Equation ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
The Boltzmann Equation ◽  
Fokker Planck

A Particle Fokker-Planck Algorithm with Multiscale Temporal Discretization for Rarefied and Continuum Gas Flows

2017 ◽  
Vol 22 (2) ◽  
pp. 338-374 ◽  
Author(s):  
Fei Fei ◽  
Zhaohui Liu ◽  
Jun Zhang ◽  
Chuguang Zheng
Keyword(s):  
Boltzmann Equation ◽  
Planck Equation ◽  
Benchmark Problems ◽  
Integration Scheme ◽  
Gas Flows ◽  
Time Step ◽  
Langevin Model ◽  
Temporal Discretization ◽  
The Boltzmann Equation ◽  
Fokker Planck

AbstractFor gas flows with moderate and low Knudsen numbers, pair-wise collisions in the Boltzmann equation can be approximated by the Langevin model corresponding to the Fokker-Planck equation. Using this simplified collision model, particle numerical schemes, e.g. the Fokker-Planck model (FPM) method, can simulate low Knudsen number gas flows more efficient than those based on the Boltzmann equation, such as the Direct Simulation Monte Carlo (DSMC) method. However, as analyzed in this paper, the transport properties of the FPM method deviate from the physical values as the time step increases, and this problem affects its computational accuracy and efficiency for the simulation of multi-scale flows. Herewe propose a particle Fokker-Planck algorithm with multiscale temporal discretization (MTD-FPM) to overcome the drawbacks of the original FPM method. In the MTD-FPM method, the molecular motion is tracked following the integration scheme of the Langevin model in analogy to the original FPM method. However, to ensure consistent transport coefficients for arbitrary temporal discretization, a time step dependent friction coefficient has been implemented. Several benchmark problems, including Couette, thermal Couette, Poiseuille, and Sod tube flows, are simulated to validate the proposed MTD-FPM method.

Grad–Fokker–Planck plasma equations. Part 1. Coffision moments

1982 ◽  
Vol 27 (3) ◽  
pp. 437-452 ◽  
Author(s):  
K. A. Broughan
Keyword(s):  
Boltzmann Equation ◽  
Planck Equation ◽  
Computer Language ◽  
Collision Term ◽  
Moment Equations ◽  
Species Pair ◽  
Collision Integrals ◽  
Fokker Planck Equation ◽  
Hot Plasma ◽  
Fokker Planck

Thirteen moments are taken of the collision term in the Boltzmann–Fokker– Planck equation for a multi-species, multi-temperature, hot plasma, following the method first developed by Grad for neutral gases. The collision integrals are evaluated for each colliding species pair. These integrals give, in particular, the rate of exchange of momentum and energy produced by collisions. The set of integrals may be combined with moments of the remaining terms in the Boltzmann equation to give thirteen moment equations for each species of particle. To complete the calculation, extensive use was made of the symbolic computer language REDUCE.

AN APPLICATION OF FOKKER–PLANCK EQUATION TO JOSEPHSON JUNCTION

1989 ◽  
Vol 9 (1) ◽  
pp. 109-120
Author(s):  
G. Liao ◽  
A.F. Lawrence ◽  
A.T. Abawi
Keyword(s):  
Josephson Junction ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

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