Title  A fastconverging scheme for the phonon Boltzmann equation with dual relaxation times 
Author  
Corresponding Author  Su，Wei 
Publication Years  20221015

DOI  
Source Title  
ISSN  00219991

EISSN  10902716

Volume  467 
Abstract  The phonon Boltzmann transport equation with dual relaxation times is often used to describe the heat conduction in semiconductor materials when the classical Fourier's law is no longer valid. For practical engineering designs, accurate and efficient numerical methods are highly demanded to solve the equation. At a large Knudsen number (i.e., the ratio of the phonon mean free path to a characteristic system length), steadystate solutions can be obtained via the conventional iterative scheme (CIS) within a few iterations. However, when the Knudsen number becomes small, i.e., when the phonon transport occurs in the diffusive or hydrodynamic regime, thousands of iterations are required to obtain converged results. In this work, a general synthetic iterative scheme (GSIS) is proposed to tackle the inefficiency of CIS. The key ingredient of the GSIS is that a set of macroscopic synthetic equations, which is exactly derived from the Boltzmann transport equation, is simultaneously solved with the kinetic equation to obtain the temperature and heat flux. During the iteration, the macroscopic quantities are used to evaluate the equilibria in the scattering terms of the kinetic equation, thus guiding the evolution of the phonon distribution function, while the distribution function, in turn, provides closures to the synthetic equations. The Fourier stability analysis is conducted to reveal the superiority of the GSIS over the CIS in terms of fast convergence in periodic systems. It is shown that the convergence rate of the GSIS can always be maintained under 0.2 so that only two iterations are required to reduce the iterative error by one order of magnitude. Numerical results in wallbounded systems are presented to demonstrate further the efficiency of GSIS, where the CPU time is reduced by up to three orders of magnitude, especially in both the diffusive and hydrodynamic regimes where the Knudsen number is small. 
Keywords  
URL  [Source Record] 
Indexed By  
Language  English

SUSTech Authorship  First

Funding Project  National Natural Science Foundation of China[11871414];National Natural Science Foundation of China[12147122];China Postdoctoral Science Foundation[2021M701565];

WOS Research Area  Computer Science
; Physics

WOS Subject  Computer Science, Interdisciplinary Applications
; Physics, Mathematical

WOS Accession No  WOS:000917225500010

Publisher  
EI Accession Number  20222912385452

EI Keywords  Boltzmann equation
; Distribution functions
; Fourier transforms
; Heat conduction
; Heat flux
; Hydrodynamics
; Integral equations
; Iterative methods
; Kinetic energy
; Kinetic theory
; Kinetics
; Numerical methods
; Phonons
; Semiconductor materials

ESI Classification Code  Fluid Flow, General:631.1
; Heat Transfer:641.2
; Semiconducting Materials:712.1
; Calculus:921.2
; Mathematical Transformations:921.3
; Numerical Methods:921.6
; Statistical Methods:922
; Probability Theory:922.1
; Classical Physics; Quantum Theory; Relativity:931

ESI Research Field  PHYSICS

Scopus EID  2s2.085134326965

Data Source  Scopus

Citation statistics 
Cited Times [WOS]:1

Document Type  Journal Article 
Identifier  http://kc.sustech.edu.cn/handle/2SGJ60CL/359516 
Department  Department of Mechanics and Aerospace Engineering 
Affiliation  1.Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen,518055,China 2.School of Mathematics and Computational Science,Xiangtan University,Xiangtan,411105,China 3.School of Engineering,The University of Edinburgh,Edinburgh,EH9 3FD,United Kingdom 
First Author Affilication  Department of Mechanics and Aerospace Engineering 
First Author's First Affilication  Department of Mechanics and Aerospace Engineering 
Recommended Citation GB/T 7714 
Liu，Jia,Zhang，Chuang,Yuan，Haizhuan,et al. A fastconverging scheme for the phonon Boltzmann equation with dual relaxation times[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2022,467.

APA 
Liu，Jia,Zhang，Chuang,Yuan，Haizhuan,Su，Wei,&Wu，Lei.(2022).A fastconverging scheme for the phonon Boltzmann equation with dual relaxation times.JOURNAL OF COMPUTATIONAL PHYSICS,467.

MLA 
Liu，Jia,et al."A fastconverging scheme for the phonon Boltzmann equation with dual relaxation times".JOURNAL OF COMPUTATIONAL PHYSICS 467(2022).

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