State Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China.
Phys Rev E. 2017 Dec;96(6-1):063311. doi: 10.1103/PhysRevE.96.063311. Epub 2017 Dec 21.
An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a macroscopic equation to accelerate the convergence in the diffusive regime. The macroscopic equation can be taken as a moment equation for phonon BTE. The heat flux in the macroscopic equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the macroscopic equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the macroscopic equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.
提出了一种隐式动力学方案来求解多尺度传热问题的静态声子玻尔兹曼输运方程（BTE）。与传统的离散坐标方法相比，本方法采用宏观方程在扩散区域加速收敛。宏观方程可以作为声子 BTE 的矩方程。宏观方程中的热流是根据 BTE 中的非平衡分布函数来评估的，而 BTE 中的平衡状态则由宏观方程确定。这两个过程从不同的尺度交换信息，使得该方法适用于具有广泛 Knudsen 数的问题。隐式离散化用于求解宏观方程和 BTE。此外，原本为静态动力学方程开发的内存减少技术也被扩展到声子 BTE。数值比较表明，本方案在弹道和扩散区域都能以高效率预测合理的结果，而内存需求与求解热传导的傅立叶定律相同。与基准的极好一致性和快速收敛历史证明，所提出的宏-微耦合是多尺度传热问题的一种可行解决方案。
