scholarly journals Direct simulation of second sound in graphene by solving the phonon Boltzmann equation via a multiscale scheme

2019 ◽  
Vol 100 (15) ◽  
Author(s):  
Xiao-Ping Luo ◽  
Yang-Yu Guo ◽  
Mo-Ran Wang ◽  
Hong-Liang Yi
Keyword(s):  
Boltzmann Equation ◽  
Second Sound ◽  
Direct Simulation ◽  
Phonon Boltzmann Equation

A high-order Monte Carlo algorithm for the direct simulation of Boltzmann equation

2012 ◽  
Vol 231 (14) ◽  
pp. 4578-4596 ◽  
Author(s):  
Pouyan Jahangiri ◽  
Amir Nejat ◽  
Jila Samadi ◽  
Ali Aboutalebi
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
High Order ◽  
Monte Carlo Algorithm ◽  
Direct Simulation

scholarly journals Thermal transport at the nanoscale: A Fourier's law vs. phonon Boltzmann equation study

2017 ◽  
Vol 121 (4) ◽  
pp. 044302 ◽  
Author(s):  
J. Kaiser ◽  
T. Feng ◽  
J. Maassen ◽  
X. Wang ◽  
X. Ruan ◽  
...  
Keyword(s):  
Boltzmann Equation ◽  
Thermal Transport ◽  
Fourier’S Law ◽  
Phonon Boltzmann Equation ◽  
Fourier's Law

Hydrodynamic approximation to the phonon Boltzmann equation

1974 ◽  
Vol 10 (8) ◽  
pp. 3546-3551 ◽  
Author(s):  
Robert J. Hardy ◽  
Dennis L. Albers
Keyword(s):  
Boltzmann Equation ◽  
Hydrodynamic Approximation ◽  
Phonon Boltzmann Equation

Simulation of Nanoscale Multidimensional Transient Heat Conduction Problems Using Ballistic-Diffusive Equations and Phonon Boltzmann Equation

2005 ◽  
Vol 127 (3) ◽  
pp. 298-306 ◽  
Author(s):  
Ronggui Yang ◽  
Gang Chen ◽  
Marine Laroche ◽  
Yuan Taur
Keyword(s):  
Heat Conduction ◽  
Boltzmann Equation ◽  
Boundary Conditions ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Computational Time ◽  
Discrete Ordinates ◽  
Fourier Law ◽  
Phonon Boltzmann Equation

Heat conduction in micro- and nanoscale and in ultrafast processes may deviate from the predictions of the Fourier law, due to boundary and interface scattering, the ballistic nature of the transport, and the finite relaxation time of heat carriers. The transient ballistic-diffusive heat conduction equations (BDE) were developed as an approximation to the phonon Boltzmann equation (BTE) for nanoscale heat conduction problems. In this paper, we further develop BDE for multidimensional heat conduction, including nanoscale heat source term and different boundary conditions, and compare the simulation results with those obtained from the phonon BTE and the Fourier law. The numerical solution strategies for multidimensional nanoscale heat conduction using BDE are presented. Several two-dimensional cases are simulated and compared to the results of the transient phonon BTE and the Fourier heat conduction theory. The transient BTE is solved using the discrete ordinates method with a two Gauss-Legendre quadratures. Special attention has been paid to the boundary conditions. Compared to the cases without internal heat generation, the difference between the BTE and BDE is larger for the case studied with internal heat generation due to the nature of the ballistic-diffusive approximation, but the results from BDE are still significantly better than those from the Fourier law. Thus we conclude that BDE captures the characteristics of the phonon BTE with much shorter computational time.

DSMC: Fast direct simulation Monte Carlo solver for the Boltzmann equation by Multi-Chain Markov Chain and multicore programming

2016 ◽  
Vol 07 (02) ◽  
pp. 1650009
Author(s):  
Di Zhao ◽  
Haiwu He
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Boltzmann Equation ◽  
Direct Simulation Monte Carlo ◽  
Collision Term ◽  
Direct Simulation ◽  
Multicore Programming ◽  
The Boltzmann Equation ◽  
Simulation Monte Carlo

Direct Simulation Monte Carlo (DSMC) solves the Boltzmann equation with large Knudsen number. The Boltzmann equation generally consists of three terms: the force term, the diffusion term and the collision term. While the first two terms of the Boltzmann equation can be discretized by numerical methods such as the finite volume method, the third term can be approximated by DSMC, and DSMC simulates the physical behaviors of gas molecules. However, because of the low sampling efficiency of Monte Carlo Simulation in DSMC, this part usually occupies large portion of computational costs to solve the Boltzmann equation. In this paper, by Markov Chain Monte Carlo (MCMC) and multicore programming, we develop Direct Simulation Multi-Chain Markov Chain Monte Carlo (DSMC3): a fast solver to calculate the numerical solution for the Boltzmann equation. Computational results show that DSMC3 is significantly faster than the conventional method DSMC.

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