A simple enthalpy-based lattice Boltzmann scheme for complicated thermal systems

To extend the lattice Boltzmann (LB) method to describe the applicable energy systems, the first key step is to build a suitable thermal LB model and corresponding boundary treatments. There are two main shortcomings in the existing related works: either some additional energy source terms are inconvenient to be naturally incorporated or the implementation of non-Dirichlet-type thermal boundary conditions is extremely difficult and sometimes impossible in them for complicated thermal systems, which restrict their applicability to only a few special classes of problems. In order to overcome these drawbacks by a simple way, in this paper a thermal LB model and corresponding boundary treatments are constructed based on the total enthalpy. The specific benefits due to the introduction of the total enthalpy are analyzed and it is found that the numerical results obtained by the present scheme agree well with the analytical solutions and/or the data reported in previous studies.