Mechanical Engineering Research Projects

​This project develops numerical simulations through parallel development of a Boltzmann model to capture and elucidate multiscale thermos-fluids behaviors in porous media, as well as the fluid-solid interactions.

​To accurately simulate porous media flow problem, a kinetic model based on the Boltzmann equation (BE) was developed. Two primary reasons justified the choice of a BE-based approach over conventional Navier-Stokes (N-S) computational fluid dynamics (CFD) methods. First, the fluid flow within porous media often occurs in extremely narrow channels, representing high-Knudsen-number flow regimes. The Knudsen number (Kn), defined as the ratio of molecular mean free path to the smallest channel dimension, indicates that traditional N-S equations are physically inadequate for accurately describing these flow conditions. Conversely, BE-based models are well-established to yield physically accurate results for high-Kn flows. Second, from a computational standpoint, the BE inherently involves a simpler mathematical structure due to its linear advection term, substantially reducing computational overhead compared to the nonlinear N-S equations. This simplification significantly improves computational efficiency, especially critical for simulating flow within complex porous structures. To better capture the complex boundaries in porous media, a meshless discretization method of the BE has been developed in this project. This meshless approach entirely eliminates dependency on mesh generation, offering significant advantages in accurately simulating flow through porous media.