首先根据多孔介质理论，利用饱和多孔介质的能量方程和本构关系，推导出饱和多孔弹性杆局部热平衡的热传导方程；继而引入正交变量，将热传导方程导入Hamilton系统，得到饱和多孔弹性杆热传导方程的广义多辛形式和多种局部守恒律形式；接着采用中点离散方法对热传导方程的广义多辛形式进行数值离散；最后利用计算机数值实现了饱和多孔弹性杆的热传导过程，并且讨论了参数取值的不同对热传导过程的影响，同时在数值模拟过程中记录了广义多辛格式的局部动量误差。研究结果表明，构造的广义多辛方法能够很好地模拟系统的热传导过程和耗散效应，同时也可长时间保持系统的固有几何性质。%Based on the theory of porous media, the thermal conduction equation of fluid saturated poroelastic rod is established by using the energy equation and constitutive relations of the two constitutes firstly in this paper. Then introducing orthogonal variables, we use the generalized multi⁃symplectic method to derive a first⁃order generalized multi⁃symplectic form for thermal conduction equation and several errors of conservation laws illustrating the local properties of the system. Thirdly, a midpoint box generalized multi⁃symplectic scheme is constructed;furthermore, discrete errors of generalized multi⁃symplectic conservation law and generalized local momentum conservation law are also obtained. Finally, the dissipation effect in thermal conduction process of saturated poroelastic rod and gen⁃eralized local momentum conversation law are investigated numerically;moreover, the influence of parameter values for thermal conduction process is established later. From results of the numerical experiments, it can be preliminari⁃ly concluded that the generalized multi⁃symplectic scheme constructed in this paper has excellent accuracy, long⁃time numerical behavior and good conservation properties.
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