Simulating two-dimensional thermal channel flows by means of a lattice Boltzmann method with new boundary conditions

Thermal boundary conditions for a doubled-populations BGK model are introduced and numerically demonstrated. The unknown thermal distribution functions at the boundary are assumed to be equilibrium distribution functions, with a counter-slip internal energy density which is determined consistently with Dirichlet and/or Neumann boundary constraints. The hydrodynamic boundary conditions are adapted to situations of engineering interest, and viscous heating effects are taken in account. The method is used to simulate channel flows; numerical results and theoretical solutions are found in satisfactory agreement for both hydrodynamic and thermal fields.