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Discrete unified gas kinetic scheme for multiscale heat transfer with arbitrary temperature difference

机译：任意温差的多尺度传热的离散统一气体动力学方案

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摘要

In this paper, a finite-volume discrete unified gas kinetic scheme (DUGKS) based on the non-gray phonon transport model is developed for multiscale heat transfer problem with arbitrary temperature difference. Under large temperature difference, the phonon Boltzmann transport equation (BTE) is essentially multiscale, not only in the frequency space, but also in the spatial space. In order to realize the efficient coupling of the multiscale phonon transport, the phonon scattering and advection are coupled together in the present scheme on the reconstruction of the distribution function at the cell interface. The Newtonian method is adopted to solve the nonlinear scattering term for the update of the temperature at both the cell center and interface. In addition, the energy at the cell center is updated by a macroscopic equation instead of taking the moment of the distribution function, which enhances the numerical conservation. Numerical results prove that the present scheme can describe the multiscale heat transfer phenomena accurately with arbitrary temperature difference in a wide range. In the diffusive regime, even if the time step is larger than the relaxation time, the present scheme can capture the transient thermal transport process accurately. Compared to that under small temperature differences, as the temperature difference increases, the variation of the temperature distribution behaves quite differently and the average temperature in the domain increases in the ballistic regime but decreases in the diffusive regime. (C) 2019 Elsevier Ltd. All rights reserved.
机译：针对任意温差的多尺度传热问题，提出了一种基于非灰色声子输运模型的有限体积离散统一气体动力学方案（DUGKS）。在较大的温差下，声子玻耳兹曼输运方程（BTE）本质上是多尺度的，不仅在频率空间，而且在空间空间。为了实现多尺度声子传输的有效耦合，在本方案中，在重建细胞界面处的分布函数时，声子散射和对流耦合在一起。采用牛顿法求解非线性散射项，以更新单元中心和界面温度。另外，通过宏观方程更新单元中心处的能量，而不用采用分布函数的矩，这增强了数值守恒。数值结果证明，该方案能够在较宽的温度范围内，准确地描述多尺度传热现象。在扩散状态下，即使时间步长大于弛豫时间，本方案也可以准确地捕获瞬态热传输过程。与小温差条件下的温度相比，随着温差的增加，温度分布的变化表现得截然不同，并且在弹道区域内平均温度升高，而在扩散区域内平均温度降低。 （C）2019 Elsevier Ltd.保留所有权利。

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