AI 中文总结
本文针对MCV热传导模型的初始化难题，评估三种策略后提出将精确空间依赖导数映射到交错网格的热力学一致初始化技术，可获稳健瞬态响应且适用于非局部模型。
AI 中文摘要
本文研究一维麦克斯韦-卡塔内奥-韦尔诺特（MCV）热传导模型的数值初始化，解决非平衡态初始时间导数定义这一关键数学挑战。在现代高频热工程应用中，传统时间积分方案和商用有限元求解器处理非傅里叶模型时，常引入严重数值伪影。本研究系统评估三种初始化策略：零导数、空间均匀非零导数、精确空间依赖导数。采用显式交错有限差分方案，对比绝热边界条件下指数分布初始温度场的瞬态响应与伽辽金法得到的解析解。结果表明，假设零导数或空间均匀初始导数会引入显著非物理振荡偏差，随弛豫时间增加导致热流预测误差；反之，将精确空间依赖导数映射到交错网格可保留初始态的局域热力学结构，得到匹配解析基准的稳健瞬态响应，且无明显计算开销。这些发现建立了一种可扩展至非局部模型的热力学一致初始化技术。
英文摘要
This paper investigates the numerical initialization of the one-dimensional Maxwell--Cattaneo--Vernotte (MCV) heat conduction model, addressing the critical mathematical challenge of defining the initial time derivative for non-equilibrium states. In modern high-frequency thermal engineering applications, traditional time-integration schemes and commercial finite-element solvers frequently introduce severe numerical artifacts when handling non-Fourier models. This study systematically evaluates three initialization strategies: a zero derivative, a spatially uniform non-zero derivative, and an exact space-dependent derivative. Using an explicit staggered finite-difference scheme, the transient responses to an exponentially distributed initial temperature field under adiabatic boundary conditions are compared against an analytical solution using the Galerkin method. The results demonstrate that assuming a zero or spatially uniform initial derivative introduces significant unphysical oscillatory deviations, leading to heat-flux prediction errors as the relaxation time increases. Conversely, mapping the exact space-dependent derivative onto the staggered grid preserves the local thermodynamic structure of the initial state, yielding robust transient responses that match the analytical benchmark without meaningful computational overhead. These findings establish a thermodynamically consistent initialization technique that can be extended to non-local models as well.
