Due to the different thermal physical properties of solids and fluids in porous media, there exists a serious local thermal nonequilibrium phenomenon in the flow and heat transfer process in porous media, especially under conditions of higher thermal conductivity ratios and heat capacity ratios. Therefore, accurately and delicately capturing the flow and temperature changes in porous media has become a hot and difficult issue. The traditional BGK model relies on a single relaxation parameter, which results in poor computational stability of the model, while the MRT model, due to the introduction of multiple relaxation factors, causes large computational workload and implementation complexity. To address the issues of accuracy, stability, and complexity in numerical simulation of flow and heat transfer processes in porous media, a TRT-LB model is innovatively developed based on the REV scale under local thermal nonequilibrium conditions. In this model, two TRT-LB equations are introduced to calculate, respectively, the temperature distribution in the fluid and solid regions. The external term and source term are introduced into the model to predict the internal heat source and convective heat transfer process in the porous media more accurately. Then, the correctness of the model is verified by deducing the macroscopic control equation from the proposed model using the Chapman-Enskog method. Subsequently, the model is verified by using three classic benchmark cases: mixed convection in a porous channel, steady-state natural convection in a porous medium containing a heat-generating solid matrix, and transient natural convection in foam metals. The results show that the TRT-LB model can accurately and stably capture the flow and heat exchange processes in porous media, more accurately display the subtle differences in temperature in porous media under local thermal nonequilibrium conditions, and significantly reduce the implementation complexity and computational cost.
Cao et al. (Mon,) studied this question.