Analysis of 3D transient heat conduction in functionally graded materials using a local semi-analytical space-time collocation scheme

Abstract

A local semi-analytical space-time collocation scheme, combined the localized space-time method of fundamental solutions (LSTMFS) and transformed function, is proposed for simulating 3D transient heat transfer in functionally graded materials. In this computation, the governing equation of the transient heat transfer in functionally graded materials is reduced to a standard diffusion equation by using transformed function. The transformed equation has a fundamental solution satisfying the governing equation, and thus the LSTMFS is used in estimating the solution of the degraded diffusion equation. As a local semi-analytical meshless method, the proposed LSTMFS has the advantages of a simple mathematical expression, high precision, and easy implementation. In comparison with the conventional space-time method of fundamental solutions, the developed approach forms a sparse linear system and is more suitable for high-dimensional problems and large-scale complex structures. Three benchmark numerical examples are provided to confirm the accuracy and feasibility of the proposed scheme.