热/声耦合, 解耦分析, 有限差分法, 数值粘性修正, 五点 CDD8 格式

In this paper we consider the equation coupled by a thermoelastic wave equation and a heat conduction equation in a homogeneous isotropic medium, and give the decoupling analysis and numerical implementation with the finite difference method. Inside solids, the governing equation of acoustic wave propagation consists of coupled heat conduction equation and thermoelastic dynamic equation due to the temperature effect and elastic deformation of medium acoustic parameters, which makes it very difficult to solve numerically. The bidirectional coupling is decoupled into sequential coupling according to the different characteristic time advances of the two equations. Omitting the influence of strain displacement on the heat conduction equation, we first solve the heat conduction equation, and then the thermoelastic wave equation is solved by taking the temperature field as an additional thermal load to obtain the strain displacement field of the structure. The heat conduction equation is solved by the classical finite difference method. We investigate the application of finite difference method to thermoelastic wave equation. Because the hyperbolic equation has high demand for stability of the algorithm, the ordinary explicit and implicit difference methods cannot achieve ideal effect. We apply the principle of numerical viscosity correction and the five points CDD8 format to finite difference method in the elastic wave equation. The program is coded in FORTRAN. The numerical results show that the accuracy and efficiency are satisfactory.

Thermal/acoustic coupling, Decoupling analysis, Finite difference method, Numerical viscosity

correction, Five points CDD8 format