Application of multifidelity proper orthogonal decomposition-based surrogate models to rarefied gas dynamics

Numerical simulation of fluid dynamics is essential for modeling gas transport; however, high-fidelity solvers require extensive computational resources to resolve fine-scale physics. Low-fidelity simulations provide a cost-effective alternative but omit the sub-grid details present in high-fidelity solutions. This study applies the Proper Orthogonal Decomposition Mapping Method (PODMM) to predict gas transport in slip and transitional flow regimes within complex nanoporous media. The numerical framework employs the lattice Boltzmann method with specular reflection boundary conditions to capture rarefaction effects and is validated against direct simulation Monte Carlo benchmarks. The methodology utilizes a multiscale approach with coarse and fine resolutions, where the fine-resolution grid is four times denser than the coarse grid. Training PODMM involves stacking coarse- and fine-resolution simulation snapshots into a single matrix, which allows the model to learn the spatial mapping required to predict fine-resolution flow fields from coarse-resolution inputs. For five synthetically generated porous media cases, PODMM achieved an average relative error of 6.3% while providing an eightfold increase in computational speed. The method was also tested on a real-world shale sample based on a scanning electron microscopy image of Mowry shale. Using a training set comprising 30% of the available snapshots, PODMM produced a 15% relative error and a 3.2-fold speedup. Performance comparisons with early-stopped numerical simulations show that PODMM predictions yield higher accuracy when targeting steady-state fine-resolution solutions. This approach facilitates the transition from molecular-scale flow modeling to system-scale behavior in disordered porous media. By utilizing reduced-order modeling techniques, this work enables rapid estimation of transport properties in unconventional reservoirs, where full-scale numerical simulation is constrained by the complexity of the pore network and the associated computational costs of resolving rarefied gas transport.