• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>International Journal of Heat and Mass Transfer >Hybrid ballistic-diffusive solution to the frequency-dependent phonon Boltzmann Transport Equation
【24h】

Hybrid ballistic-diffusive solution to the frequency-dependent phonon Boltzmann Transport Equation

机译：频率依赖的声子玻耳兹曼输运方程的混合弹道扩散解

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

The phonon Boltzmann Transport Equation (BTE) is appropriate for modeling heat conduction in semiconductor materials at the nanoscale. However, the BTE is difficult to solve on account of the directional and spectral nature of the phonon intensity, which necessitates angular and spectral discretization, and ultimately results in a large number (typically few hundreds) of four-dimensional partial differential equations. In the ballistic (large Knudsen number) regime, the phonon intensity is highly anisotropic, and therefore, angular resolution is desirable. However, in the diffusive (small Knudsen number) regime, the intensity is fairly isotropic, and hence, angular discretization is wasteful. In such scenarios, the method of spherical harmonics (P_N approximation) may be effectively used to reduce the large number of directional BTEs to a few partial differential equations. Since the Knudsen number is frequency dependent, the decision to preserve or eliminate angular discretization may be made frequency by frequency based on whether the spectral Knudsen number is large or small. In this article, a hybrid method is proposed in which for some frequency intervals (bands), full angular discretization is used, while for others, the P_1 approximation is invoked to reduce the number of directional BTEs. The accuracy and efficiency of the hybrid method is tested by solving several steady state and transient nanoscale heat conduction problems in two and three-dimensional geometries. Silicon is used as the candidate material. It is found that hybridization is effective in significantly improving the efficiency of solution of the BTE-sometimes by a factor of three-without significant penalty on the accuracy.
机译：声子玻耳兹曼输运方程（BTE）适用于在纳米尺度上模拟半导体材料中的热传导。但是，由于声子强度的方向和频谱性质，BTE难以解决，这需要角度和频谱离散化，并最终导致大量（通常为数百个）四维偏微分方程。在弹道（大克努森数）状态下，声子强度是高度各向异性的，因此，需要角分辨率。但是，在扩散（克努森数小）的情况下，强度是各向同性的，因此角度离散化是浪费的。在这种情况下，可以有效地使用球谐函数（P_N近似）方法将大量的定向BTE减少为几个偏微分方程。由于克努森数与频率有关，因此可以基于频谱克努森数是大还是小，逐个频率地决定是否保留或消除角度离散。在本文中，提出了一种混合方法，其中对于某些频率间隔（频带），使用全角度离散化，而对于其他频率，调用P_1近似以减少定向BTE的数量。通过解决二维和三维几何中的几个稳态和瞬态纳米级导热问题，测试了混合方法的准确性和效率。硅用作候选材料。发现杂交有效地将BTE的溶液效率有时提高了三倍，而准确性没有明显的损失。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号