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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >A comparison of the finite-difference and finite-volume methods for a numerical solution of a hyperbolic thermoelasticity problem utilizing the implicit and explicit schemes
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A comparison of the finite-difference and finite-volume methods for a numerical solution of a hyperbolic thermoelasticity problem utilizing the implicit and explicit schemes

机译：利用隐含和显式方案的双曲热弹性问题数值解的有限差分和有限体积方法的比较

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摘要

A numerical solution for a coupled hyperbolic thermoelasticity problem of the Lord- Shulman type is presented. An infinite layer with free boundaries that are kept at a constant temperature is irradiated by a short laser impulse. In this case the problem can be studied in the one-dimensional formulation. An impact of the laser impulse on a medium is modeled by an internal heat source. The laser impulse intensity decays with a distance from an irradiated surface according to the Bouguer law. The layer is in an unperturbed state at the initial moment of time. The material properties of copper are taken to be the thermo-mechanical properties of the layer. Two approaches for the boundary value problem are considered: the finite-difference method (FDM) and the finite-volume method (FVM). In the first case the system of two second-order PDE is investigated, in the second case a system of integral balance equations and an integral thermal conductivity equation are composed. To integrate these equations both the explicit and implicit schemes are used. The obtained results are compared with each other and with an analytical solution. A numerical error is estimated for different time and space step sizes. The features inherent in various ways of integration of the coupled hyperbolic thermoelastic problem with the thermal excitation are found.
机译：介绍了主 - 舒尔曼型耦合双曲热弹性问题的数值解决方案。通过短的激光脉冲照射具有保持在恒定温度下的自由边界的无限层。在这种情况下，问题可以在一维配方中研究。激光脉冲对介质的影响是由内部热源建模的。激光脉冲强度根据Bouguer Laver的距离辐射表面衰减。该层在最初的时间时刻处于不受干扰状态。铜的材料特性被认为是层的热机械性能。考虑了边值问题的两种方法：有限差分法（FDM）和有限体积法（FVM）。在第一种情况下，研究了两个二阶PDE的系统，在第二种情况下，组成了整体平衡方程的系统和积分导热率方程。要将这些等式集成，可以使用显式和隐式方案。得到的结果彼此比较并用分析溶液进行比较。针对不同的时间和空间步骤尺寸估计数值误差。找到了各种耦合双曲热弹性问题与热激励的各种方式固有的特征。

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