Application of Legendre wavelet collocation method to the analysis of poro-thermoelastic coupling with variable thermal conductivity

The current investigation has attempted to propose a numerical method based on Legendre Wavelet for the thermo-mechanical coupling analysis of poroelastic material. The porothermoelasticity theory within the context of Lord-Shulman (LS) model is adopted to formulate the theoretical model taking into account the temperature-dependent thermal conductivity. Nonlinear terms in the governing equations due to variable thermal conductivity are linearized by the Kirchhoff mapping. In the proposed method, after linearization, the time domain is discretized by using a finite-difference approach and subsequently space domain is approximated with the use of Legendre wavelets. By utilizing the collocation points, a system of algebraic equations is constructed and solved. The method is finally implemented to obtain the numerical solution of an initial boundary value problem of porothermoelasticity for a suitable material. The field variables of solid and fluid phases for the present problem are obtained by MATLAB programming and displayed graphically. Various graphs demonstrate the behavior of displacement, temperature and stress of solid and fluid phases. The impacts of porosity, relaxation parameters and variable thermal conductivity are examined in detail from numerical findings. The outcomes demonstrate that the aforementioned parameters significantly influence the field variables. Computer simulations reveal that the proposed method is computationally efficient, quick, dependable and relatively good even with the small number of collocation points.

Automated summary

This study presents a numerical method based on Legendre Wavelet for the thermo-mechanical coupling analysis of poroelastic material. The proposed method linearizes the nonlinear terms in the governing equations due to variable thermal conductivity using the Kirchhoff mapping. It discretizes the time domain using a finite-difference approach and approximates the space domain with Legendre wavelets.