SPH numerical modeling for ballistic-diffusive heat conduction

The classic Fourier heat diffusion theory, in general, does not apply to micro/nanoscale or ultrafast thermal processes, where the mean free path of the heat carriers is comparable to the system size and/or typical times are comparable to the carrier relaxation time. For these processes, the ballistic-diffusive equation is a good alternative. In this context, the smoothed particle hydrodynamics (SPH) method is further developed to solve the one-dimensional ballistic-diffusive equation, by using a boundary treatment technique based on the normalization property of the SPH smoothing kernel. The results indicate that the SPH is a reliable and accurate method capable of yielding correct temperature and heat flux representations in the ballistic-diffusive heat conduction regime.