A consistent thermal lattice Boltzmann model for solids, fluids and porous media and its applications

Heat transfer in composite solid–fluid–porous systems is complicated by discontinuous heat capacity and thermal diffusivity, often requiring explicit correction terms in unified thermal lattice Boltzmann models. Building on Wang's unified local thermal equilibrium (LTE) formulation, the published D2Q5 model is extended to D2Q9 as a matched reference, and a source-term-free moment-feedback reconstructed-equilibrium BGK model (MFRE-BGK) is developed. The heat-capacity-ratio correction is generated from current local non-equilibrium moments and embedded in the collision target, avoiding explicit evaluation of the macroscopic temperature time derivative and storage of the preceding temperature field. Chapman–Enskog analysis recovers the target energy equation within smooth material subdomains, and a resolved half-link benchmark confirms temperature and heat-flux consistency under ideal contact. Numerical tests show near-second-order accuracy for smooth convection–diffusion, errors below 0.5% in moderate-contrast cases, and bounded solutions in the tested high-contrast cases. The reservoir application captures advection-controlled thermal-front migration and heat-load redistribution. Under the retained 16-thread reservoir protocol, MFRE-BGK reduces total runtime by 29.1% and increases thermal throughput by 48.1% relative to the explicit-correction formulation. These results demonstrate the applicability of MFRE-BGK to two-dimensional heterogeneous conjugate heat-transfer problems.