Enthalpy-based cascaded lattice Boltzmann method for conjugate heat transfer

Lattice Boltzmann (LB) methods for conjugate heat transfer are widely studied because of the simplicity and efficiency in dealing with complex boundary conditions. Recently, cascaded (or central-moments-based) LB (CLB) method has shown the potential to improve the stability of LB method. For conventional CLB method which is constructed through the continuous equilibrium distribution function, the temperature-based energy equation is recovered and solved. The continuity of temperature and heat flux at conjugate interface is unable to be accurately enforced without special treatment. To circumvent this deficiency, an enthalpy-based CLB method for conjugate heat transfer is developed in this work. In the proposed method, the enthalpy-based formulation of equilibrium moments is directly designed in the central-moment space, and the macroscopic quantity solved is converted from temperature to enthalpy. As demonstrated by the Chapman-Enskog multiscale analysis, the enthalpy-based energy equation can be recovered by the CLB equation. Compared with the conventional CLB method, the continuity condition for temperature and heat flux on the conjugate interface can be enforced automatically without special treatment. In addition, the proposed CLB method provides a new way to develop a CLB equation that can recover to a general convection-diffusion equation. Finally, the accuracy and stability of the temperature field are validated by benchmarks for the proposed enthalpy-based CLB method.