Modification of the least square MPS method for the heat conduction problems

Abstract

In this work, new Least Square Moving Particle Semi-implicit (LSMPS) formulations for the modelling of the heat conduction in laser irradiation processes are developed. These new LSMPS formulations guarantee the conservation of the total thermal energy during the heat exchange between particles. By conducting the heat conduction simulations, in which the standard LSMPS method can provide accurate temperature distribution, and by comparing the results with an analytical solution, it was confirmed that the proposed method is as accurate as the standard LSMPS method. Moreover, the heat conduction with an external heat source, in which the total thermal energy is not conserved by using the standard LSMPS method, was successfully simulated by using the proposed method. The simulation of laser irradiation was also conducted and the validity of the proposed method has been confirmed by comparing numerical results with experimental data.