A novel space-time generalized FDM for transient heat conduction problems

Abstract

In this paper, a novel space-time generalized finite difference method (GFDM) is proposed for solving transient heat conduction problems by integrating a direct space-time discretization technique into the meshless GFDM. The spatial and temporal dimensions are simultaneously discretized by randomly distributed nodes in the coupled space-time continuum. Transient heat conduction in homogenous and heterogeneous materials are analyzed by this novel meshless space-time GFDM. Examples involving multidimensional spatiotemporal domains and various complex boundary conditions are studied and discussed. The high accuracy and efficiency of this new algorithm are verified by comparing with analytical and other numerical results.