Generalized multi-symplectic method and numerical experiment for thermal conduction of saturated poroelastic rod

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 generalized 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 preliminarily concluded that the generalized multi-symplectic scheme constructed in this paper has excellent accuracy, long-time numerical behavior and good conservation properties.