SPH-FDM Boundary Method for the Heat Conduction of Geotechnical Materials Considering Phase Transition

Abstract

A coupled SPH-FDM boundary is proposed for the analysis of thermal process in geotechnical materials, in which the smoothed particle hydrodynamics (SPH) method is used in the inner computational domain; and the finite difference method (FDM) is used as the function approximation near the boundary. The proposed coupled SPH-FDM boundary is applicable to the analysis of heat conduction in geotechnical materials, including the problems with discontinuous interface in the computational domain and the solidification of porous materials with a moving phase transition boundary. The effect of latent heat released in the phase transition is considered in the SPH method, and a weighted mean is used to determine the thermal parameters at the phase transition interface, which can be easily used to analyze the evolution of the moving phase transition interface over time. In general, there is a good agreement between the SPH results obtained using the three boundary treatments (coupled SPH-FDM boundary, no virtual particles, and virtual particles) and the analytical solution. The maximum error decreases gradually over time. Besides, it shows that as the thermal diffusion coefficient increases after the phase transition, the velocity of the moving phase transition interface increases, and the reduction rate in temperature in the non-solidified region decreases.