双弛豫时间非灰声子玻尔兹曼输运方程的合成迭代格式
A Synthetic Iterative Scheme for Non-Gray Phonon Boltzmann Transport Equation with Dual Relaxation Times
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中文总结 AI 辅助
本文针对模式分辨双弛豫非灰声子玻尔兹曼输运问题，提出通用合成迭代格式GSIS，可在石墨烯算例中避免传统迭代格式的慢收敛问题，且在极限下与对应热传导方程一致。
中文摘要 AI 辅助
求解非灰Callaway声子玻尔兹曼输运方程可实现正常散射与电阻散射的双弛豫时间近似，并解析模式相关的声子谱。确定性求解的传统迭代格式（CIS）可避免整体相空间求逆，但在材料特征长度较大时，其碰撞源迭代会变得极慢。现有合成加速格式仅针对非灰单弛豫模型或灰双弛豫模型，缺少针对模式分辨的双弛豫输运的专用加速框架。本文针对定态、线性化的非灰Callaway方程，提出通用合成迭代格式（GSIS）：通过一阶Chapman-Enskog本构关系闭合的精确能量与准动量平衡定律，提供正常过程伪温度与声子漂移速度的合成近似，非平衡项由动力学解计算，电阻过程伪温度由上述两量得到；每次迭代耦合迎风节点间断伽辽金动力学扫描与合成方程的可杂交间断伽辽金求解，以实现高阶空间离散。分支与频率分辨的傅里叶分析证实CIS会出现性能恶化，且针对研究的石墨烯材料，GSIS的收缩因子始终远离1；渐近分析表明，在流体动力学与扩散极限下，GSIS分别退化为类Guyer-Krumhansl方程与傅里叶热传导定律的一致离散格式。
英文摘要
Solving the non-gray Callaway phonon Boltzmann transport equation allows a dual-relaxation-time approximation of separate normal and resistive scatterings and resolving the mode-dependent spectrum. The conventional iterative scheme (CIS) for deterministic solutions avoids a monolithic phase-space inversion, but its collision-source iteration can become prohibitively slow at a large characteristic length of a material. Existing synthetic acceleration schemes address either non-gray single-relaxation models or gray dual-relaxation models, leaving mode-resolved dual-relaxation transport without a dedicated acceleration framework. We develop a general synthetic iterative scheme (GSIS) for the stationary, linearized, non-gray Callaway equation, where synthetic approximations for the normal-process pseudo-temperature and phonon drift velocity are provided by exact energy and quasi-momentum balance laws closed with first-order Chapman-Enskog constitutive relations and non-equilibrium terms evaluated from the kinetic solution. The resistive-process pseudo-temperature is retrieved from the two quantities. Each iteration couples an upwind nodal discontinuous Galerkin kinetic sweep and a hybridizable discontinuous Galerkin solution of the synthetic equations to achieve high-order spatial discretization. A branch- and frequency-resolved Fourier analysis identifies the deterioration of CIS and shows that the GSIS contraction factor remains bounded away from unity for the considered graphene material. Asymptotic analysis indicates that GSIS reduces to a consistent discretization of a Guyer-Krumhansl-like equation and Fourier's law of heat conduction in the hydrodynamic and diffusive limits, respectively.
