A meshless singular boundary method for transient heat conduction problems in layered materials

The transient heat conduction problems in layered materials are common encountered in practical application, but bring great challenge to most numerical algorithms. In this study, the singular boundary method (SBM), a meshless boundary collocation technique, is first employed to numerically simulate such problems based on the time-dependent fundamental solution of diffusion equation. Taking the boundary conditions and interface conditions into account, the computing system of the SBM for layered materials is established, and then is solved. The proposed method fully inherits the merits of conventional boundary-type methods while possessing its distinctive advantages. Furthermore, it is simple, straightforward, computationally efficient, and stable since it does not need to discretize temporal derivative term. Three numerical experiments are performed to verify the efficiency and accuracy of the proposed scheme. Numerical results clearly indicate the efficiency, accuracy and stability of the presented SBM for solving transient heat conduction problems in layered materials.