Simulation and characteristics analysis of a wavefield in a thermoelastic medium adopting the rotated staggered-grid pseudo-spectral method and L-S theory

The simulation of wave propagation in high-temperature media requires thermoelastic theory. In this paper, we apply the rotated-staggered-grid pseudo-spectral method (RSG-PSM) to solving thermoelastic governing equations based on L-S theory. A time splitting method is used to solve the stiffness problem of the equations, and we introduce the rotated staggered pseudo-spectral operator and centered pseudo-spectral operator to compute the first-order spatial derivatives and second-order spatial derivatives, respectively. In the case of the heterogeneous-medium model, the Crank-Nicolson explicit method is used instead of the pseudo-spectral method to compute the wavefield. The properties and propagation of the thermal coupled wavefield are discussed, and we compare the simulation results obtained using the pseudo-spectral method, staggered-grid pseudo-spectral method, and RSG-PSM. In the case of an isotropic homogeneous medium, we obtain stable and highly accurate results using the time splitting method combined with the RSG-PSM. However, the algorithm cannot be applied with a large time step when the thermal conductivity changes dramatically, and the algorithm is unstable when the reference temperature has a gradient distribution. The optimal combined application of the mesh generation mode and numerical algorithm is explored, laying a foundation for the extension of these methods to thermoporoelasticity, thermoviscoelasticity, and anisotropy.