Fülöp Tamás, Kovács Róbert, Szücs Mátyás, Fawaier Mohammad
Department of Energy Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, Hungary.
Montavid Thermodynamic Research Group, 1112 Budapest, Hungary.
Entropy (Basel). 2020 Jan 28;22(2):155. doi: 10.3390/e22020155.
On the example of the Poynting-Thomson-Zener rheological model for solids, which exhibits both dissipation and wave propagation, with nonlinear dispersion relation, we introduce and investigate a finite difference numerical scheme. Our goal is to demonstrate its properties and to ease the computations in later applications for continuum thermodynamical problems. The key element is the positioning of the discretized quantities with shifts by half space and time steps with respect to each other. The arrangement is chosen according to the spacetime properties of the quantities and of the equations governing them. Numerical stability, dissipative error, and dispersive error are analyzed in detail. With the best settings found, the scheme is capable of making precise and fast predictions. Finally, the proposed scheme is compared to a commercial finite element software, COMSOL, which demonstrates essential differences even on the simplest-elastic-level of modeling.
以固体的坡印廷 - 汤姆森 - 齐纳流变模型为例，该模型既表现出耗散又表现出波传播，具有非线性色散关系，我们引入并研究了一种有限差分数值格式。我们的目标是展示其特性，并简化后续连续介质热力学问题应用中的计算。关键要素是离散量的定位，它们在空间和时间上相对于彼此偏移半个步长。这种排列是根据量及其控制方程的时空特性来选择的。详细分析了数值稳定性、耗散误差和色散误差。通过找到的最佳设置，该格式能够进行精确且快速的预测。最后，将所提出的格式与商业有限元软件COMSOL进行比较，结果表明即使在最简单的弹性建模水平上两者也存在本质差异。
