Analysis of three-dimensional heat conduction in functionally graded materials by using a hybrid numerical method

•Developing a combined scheme for 3D transient heat conduction in FGMs.•The method is accurate and stable in long-time simulations.•Large time step-sizes can be used in temporal discretization.•A large-scale simulation with almost 100,000 degree of freedoms is performed. A hybrid numerical method is developed for three-dimensional (3D) heat conduction in functionally graded materials (FGMs) by integrating the advantages of the generalized finite difference method (GFDM) and Krylov deferred correction (KDC) technique. The temporal direction of the problems is first discretized by applying the KDC approach for high-accuracy results, which yields a partial differential equation (PDE) boundary value problem at each time step. The corresponding PDE boundary value problem is then solved by introducing the meshless GFDM that has no requirement of time-consuming meshing generation and numerical integration for 3D problems with complex geometries. Numerical experiments with four types of material gradations are provided to verify the developed combination scheme, and numerical results demonstrate that the method has a great potential for 3D transient heat conduction in FGMs especially for those in a long-time simulation.