Enthalpic lattice Boltzmann formulation for unsteady heat conduction in heterogeneous media

In this paper, we propose an enthalpic lattice Boltzmann formulation for heat transfer in heterogeneous media. This formulation leads to the appearance of a source term, which introduces the jump conditions at the interface between two phases or components, with different thermal properties. It conserves conductive heat flux, which makes it suitable for modeling heat conduction in multiphase and multi-component systems. This approach is simple to implement and can be easily applied to simulate heat transfer with complex and time dependent interfaces, efficiently. It does not require any specific treatment dependent on interface topology. It is also independent on the choice of lattice. This approach is validated by comparisons with analytical and numerical results of several test problems with flat and curved interfaces. Both 2- and 3-dimensional conduction transfer problems were simulated. The obtained results show excellent agreements with reference solutions.