This work aims at presenting a new numerical solution to a nonlinear, one-dimensional problem of heat wave propagation in a thick slab of a rigid thermal conductor. The model predicts dependence of second sound velocity on temperature and heat flux. For this, an unconditionally stable numerical scheme is constructed using a kind of weighted average nonstandard finite difference discretization. Stability analysis of this scheme is studied by von Neumann technique, and its accuracy is proved. Numerical simulations are given for all quantities of physical interest to confirm the reliability of the proposed method. The model and the numerical results shed light on characteristics of heat wave propagation within the theory of extended thermodynamics.

这项工作旨在为刚性热导体的厚板中热波传播的非线性，一维问题提供新的数值解决方案。该模型预测第二声速对温度和热通量的依赖性。为此，使用一种加权平均非标准有限差分离散化构造了无条件稳定的数值格式。用冯·诺依曼技术研究了该方案的稳定性，并证明了其准确性。给出了对所有物理量感兴趣的数值模拟，以确认所提出方法的可靠性。该模型和数值结果阐明了扩展热力学理论中的热波传播特性。