标题： 半隐式Lax-Wendroff粒子输运方案 显示英文标题

标题： Semi-implicit Lax-Wendroff kinetic scheme for multi-scale phonon transport

摘要： 快速且准确地预测温度的时空分布对于微电子器件的多尺度热管理和安全运行至关重要。为了实现这一点，开发了一种高效的半隐式Lax-Wendroff动能方案，用于数值求解从弹道到扩散区间的瞬态声子玻尔兹曼输运方程（BTE）。在有限体积法的框架下，对单元中心的声子BTE进行离散化，其中梯形法则和中点法则分别用于处理声子散射和对流项的时间积分。对于界面分布函数的重构，将单元界面处的声子BTE以有限差分法的形式进行离散化并数值求解，其中二阶迎风格式和中心格式分别用于处理界面分布函数的空间插值和梯度。宏观控制方程用于单元中心和界面处宏观场的演化，其中宏观通量通过取界面分布函数的矩得到。数值结果表明，该方案可以准确预测从弹道到扩散区间内固体材料中的稳态/非稳态热传导，其时间和单元大小不受弛豫时间和声子平均自由程的限制。本研究可为多尺度热工程中宏观时空分布的高效预测提供有用的工具。 显示英文摘要

摘要： Fast and accurate predictions of the spatiotemporal distributions of temperature are crucial to the multi-scale thermal management and safe operation of microelectronic devices. To realize it, an efficient semi-implicit Lax-Wendroff kinetic scheme is developed for numerically solving the transient phonon Boltzmann transport equation (BTE) from the ballistic to diffusive regime. The phonon BTE at the cell center is discretized under the framework of finite volume method, where the trapezoidal and midpoint rules are used to deal with the temporal integration of phonon scattering and convection terms, respectively. For the reconstruction of the interfacial distribution function, the phonon BTE at the cell interface is discretized in the form of finite difference method and solved numerically, where second-order upwind and central scheme are used to deal with the spatial interpolation and gradient of interfacial distribution function, respectively. The macroscopic governing equations are invoked for the evolution of macroscopic fields at both the cell center and interface, where the macroscopic flux is obtained by taking the moment of the interfacial distribution function. Numerical results show that the present scheme could accurately predict the steady/unsteady heat conduction in solid materials from the ballistic to diffusive regime, and its time and cell size are not limited by the relaxation time and phonon mean free path. The present work could provide a useful tool for the efficient predictions of the macroscopic spatiotemporal distributions in the multi-scale thermal engineering.