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A fast synthetic iterative scheme for the stationary phonon Boltzmann transport equation

机译：固定声子Boltzmann传输方程的快速合成迭代方案

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摘要

The heat transfer in solid materials at the micro- and nano-scale can be described by the mesoscopic phonon Boltzmann transport equation (BTE), rather than the macroscopic Fourier's heat conduction equation that works only in the diffusive regime. The implicit discrete ordinate method (DOM) is efficient to find steady-state solutions to the BTE for highly non-equilibrium heat transfer problems, but converges extremely slowly in the near-diffusive regime. In this paper, a fast synthetic iterative scheme is developed to expedite convergence for the implicit DOM. The key innovative point of the present scheme is the introduction of a macroscopic diffusion-type equation for the temperature variation, which is exactly derived from the phonon BTE and valid for all Knudsen numbers. The synthetic equation, which is asymptomatically preserving to Fourier's heat conduction equation in the diffusive regime, contains a term related to Fourier's law and a term determined by the second-order moment of the distribution function that reflects the non-Fourier heat transfer. The mesoscopic kinetic equation and macroscopic diffusion-type equations are tightly coupled, because the macroscopic equation provides the temperature for the BTE, while the BTE provides a high-order moment to the diffusion-type equation. This synthetic iterative scheme strengthens the coupling of phonons with different wave vectors in the phase space to facilitate fast convergence from the diffusive to ballistic regimes. Typical numerical tests in one-, two-, and three-dimensional problems demonstrate that our scheme can describe the multiscale heat transfer problems accurately and efficiently. For all test cases, the present convergence is one to three orders of magnitude faster than the traditional implicit DOM in the near-diffusive regime.
机译：微型和纳米级的固体材料中的热传递可以由介于镜片声子螺栓玻璃传送方程（BTE）描述，而不是仅在扩散制度中起作用的宏观傅里叶的热传导方程。隐式离散纵坐标方法（DOM）有效地寻找对BTE的稳态解决方案，以实现高度平衡的传热问题，但在近扩散的制度中会聚得非常缓慢。在本文中，开发了一种快速的合成迭代方案以加快隐式DOM的收敛。本方案的关键创新点是引入温度变化的宏观扩散型方程，其与声子BTE完全导出并对所有knudsen数字有效。在扩散制度中渐近渐近傅里叶的热传导方程的合成方程包含与傅里叶的定律相关的术语，并且由反映非傅里叶传热的分布函数的二阶时间确定的术语。脑镜动力学方程和宏观扩散型方程紧密耦合，因为宏观方程为BTE提供了温度，而BTE为扩散型方程提供了高阶矩。该合成迭代方案加强了相位空间中具有不同波矢量的声子的耦合，以便于从扩散到弹道制度的快速收敛。一个，两个和三维问题中的典型数值测试表明，我们的方案可以准确和有效地描述多尺度传热问题。对于所有测试用例，本趋势比近扩散制度的传统隐式DOM快一到三个数量级。

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  • 来源
    《International Journal of Heat and Mass Transfer》 |2021年第8期|121308.1-121308.13|共13页
  • 作者

    Chuang Zhang; Songze Chen; Zhaoli Guo; Lei Wu;

  • 作者单位

    State Key Laboratory of Coal Combustion School of Energy and Power Engineering Huazhong University of Science and Technology Wuhan 430074 China;

    State Key Laboratory of Coal Combustion School of Energy and Power Engineering Huazhong University of Science and Technology Wuhan 430074 China;

    State Key Laboratory of Coal Combustion School of Energy and Power Engineering Huazhong University of Science and Technology Wuhan 430074 China;

    Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Shenzhen 518055 Guangdong China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Multiscale heat transfer; Phonon Boltzmann transport equation; Discrete ordinate method; Synthetic acceleration scheme;

    机译：多尺度传热;Phonon Boltzmann运输方程式;离散纵坐标法;合成加速度方案;

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