A lattice Boltzmann flux solver with the 1D-link interpolation scheme for simulating fluid flow and heat transfer in fractured porous media

In this study, we propose an improved lattice Boltzmann flux solver (LBFS) to simulate the thermal-hydraulic (TH) processes within fractured porous media. In LBFS, the flux at cell interfaces is calculated using a locally reconstructed lattice Boltzmann model (LBM). Unlike conventional methods that use direct mathematical approximations, LBFS can suppress the oscillation of solutions and has better accuracy. However, when simulating two-dimensional fractured porous media problems, the rock matrix is divided into surface cells, while fractures are usually divided into line cells. This increases the complexity of implementing the LBFS, as the reconstruction of interface flux in different dimensions requires the use of discrete velocity models (DmQn) in different dimensions. To address this challenge, we introduce an innovative interpolation scheme based on the improved D1Q3 model, thereby establishing a dimensionally independent approach for the reconstruction of the interface flux. This approach greatly reduces the complexity of applying the LBFS to hybrid dimensional problems and simplifies the computational process. The present method is validated by simulating three typical cases and the results show good agreement with the reference solutions. Finally, the improved LBFS is applied to analyze the TH coupling behavior in fractured porous media with a single fracture and a more complex scenario involving two intersected fractures.