Gradient preserved method for solving heat conduction equation with variable coefficients in double layers

Recently, we have developed an accurate compact finite difference scheme called the Gradient Preserved Method (GPM) for solving heat conduction equation with constant coefficients in double layers. Since functionally graded materials are becoming paramount than materials having uniform structures with the development of new materials, this article extends the GPM to the case where coefficients are variable (and even temperature-dependent). The higher-order compact finite scheme is obtained based on three grid points and is proved to be unconditionally stable and convergent with O(tau(2) +h(4)), where tau and h are the time step and grid size, respectively. Numerical errors and convergence orders are tested in an example. Finally, we apply the scheme for predicting electron and lattice temperatures of a gold thin film padding on a chromium film exposed to the ultrashort-pulsed laser. (C) 2020 Elsevier Inc. All rights reserved.