Numerical implementation of thermal boundary conditions in the lattice Boltzmann method

Solution of inverse heat conduction problem using the lattice Boltzmann method

“…Therefore, Peng et al developed a simplified method regardless of the compression work exerted by the pressure and viscous heat dissipation terms [16]. Other studies also have been dedicated to the thermal boundary condition such as constant temperature and constant heat flux [17][18][19][20].…”

Effects of slip boundaries on thermal convection in 2D box using lattice Boltzmann method

“…The detailed implementations of partial slip boundaries for LBM are described in [19]. The non-equilibrium mirror-reflection schemes are used for isothermal and adiabatic boundary conditions [20]. The scheme for prescribed Bi in [21] is applied in this study.…”

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

“…Moreover, the influences of viscous dissipation and compression work in the energy equation can not be described by them. The works to deal with the Neumann thermal boundary have also been conducted by different groups [22,16,18]. Although they work well for straight walls, these schemes for heat flux boundary condition are extremely difficultly used on complicated curved walls because in them the heat flux can not be treated explicitly or ''directly'' (one has to convert the given heat flux on the wall into the temperature there and the conversion process is very complicated and nonlocal).…”

“…In spite of the significant differences in their appearances and technical details, almost all existing LB models share two common shortcomings in simulating thermal systems: in them, some additional energy source terms are inconvenient to be naturally incorporated [14,15] and the implementation of non-Dirichlet-type thermal boundary conditions (e.g., the Neumann and Cauchy types) is extremely difficult and sometimes impossible in the systems confined by complicated curved solid boundaries [15][16][17][18], which restrict their applicability to only a few special classes of problems [8,14].…”

“…(17) in [16]). Recently, Kuo and Chen [18] designed a non-equilibrium mirror-reflection scheme to implement the adiabatic boundary condition condition for a DDF-type thermal LB model. However, their scheme is hardly extended to complicated curved walls and arbitrary heat flux conditions yet.…”