Abstract This work proposes a mechanical analog of the unsteady energy conservation equation for analysis of the stability of its numerical solution. The space discretized energy conservation equation is the analog of the linear momentum equation, from which no relevant information can be extracted concerning the stability of its numerical solution. The corresponding angular momentum equation can be obtained from the space discretized energy conservation equation, from which relevant information can be extracted concerning stability of the numerical solution. In that equation, the angular perturbation is the analog of the temperature perturbation. This approach/analogy and results help for a better understanding of the stability/instability of the numerical solution of unsteady diffusion problems.

中文翻译：

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非定常热传导数值解的稳定性：一种力学方法

摘要 本文提出了非定常能量守恒方程的力学模拟，用于分析其数值解的稳定性。空间离散能量守恒方程是线性动量方程的类比，从中不能提取出有关其数值解稳定性的相关信息。从空间离散能量守恒方程可以得到相应的角动量方程，从中可以提取有关数值解稳定性的相关信息。在该方程中，角度扰动是温度扰动的模拟。这种方法/类比和结果有助于更好地理解不稳定扩散问题数值解的稳定性/不稳定性。