Mixed Boundary Conditions for Two-Dimensional Transient Heat Transfer Conduction under Lattice Boltzmann Simulations

In this paper, lattice Boltzmann implementations of several types of boundary conditions are introduced and numerically demonstrated. A thermal lattice BGK model is used to simulate thermal fields for flows. The unknown thermal distribution functions at the boundary are subjected to the bounce back concept which is determined consistently with Dirichlet and/or Neumann and/or convective boundary conditions. A consistency analysis using heat transfer conduction is given and the algorithms are numerically tested in two space dimensions with respect to accuracy, numbers of iterations and CPU time. The method is used to simulate conduction transfer problems; numerical results and reference’s solutions are found in satisfactory agreement for thermal fields.

Keywords:

Dirichlet boundary , Lattice Boltzmann method , Boundary conditions , Newmann boundary , ۲D heat transfer , convective boundary