Heat Transfer with Explicit SPH Method in LS-DYNA

In this paper, we introduce an explicit formalism to model heat conduction with Smoothed Particle Hydrodynamics method. With Taylor series approximation and SPH kernel interpolation, a simpler SPH discretization of the Laplace operator can be obtained for the thermal conduction equation. The formulation manifestly conserves thermal energy and is stable in the presence of small-scale temperature noise. This formalism allows us to evolve the thermal diffusion equation with an explicit time integration scheme along with the ordinary hydrodynamics. A series of simple test problems were used to demonstrate the robustness and accuracy of the method. Heat transfer with explicit SPH method can be coupled with structure for thermal stress and thermal structure coupling analysis.