An alternative space–time meshless method for solving transient heat transfer problems with high discontinuous moving sources

Abstract

The aim of this work is the development of a space-time diffuse approximation meshless method (DAM) to solve heat equations containing discontinuous sources. This work is devoted to transient heat transfer problems with static and moving heat sources applied on a metallic plate and whose power presents temporal discontinuities. The space-time DAM using classical weight function is convenient for continuous transient heat transfer. Nevertheless, for problems including discontinuities, some spurious oscillations for the temperature field occur. A new weight function, respecting the principle of causality, is used to eradicate the physically unexpected oscillations.

A Novel Spatio-Temporal Fully Meshless Method for Parabolic PDEs

“…The previous discretization of the computational domain for parabolic PDEs is not new. Several meshless numerical methods have recently been applied, such as a kernel-based method [11], the space-time diffuse approximation meshless method [12], the Trefftz method [13], the localized radial basis function collocation method [14] and the multiquadratic method with the radial basis collocation method [15]. In addition, the GFDM has been applied to solve space-time problems in [16][17][18].…”