A comparative study on the accuracy and conservation properties of the SPH method for fluid flow interaction with porous media. (July 2022) - Kazemi, Ehsan; Luo, Min
Highlights: The physics of flow in porous media is re-visited and two types of governing equations are rigorously derived in the framework of particle-based spatial averaging. Two types of modelling processes are clarified based on phase averaging of density (leading to apparent density) and intrinsic phase averaging of density (representing fluid's density). Two types of problems are simulated, i.e., closed porous media flow under fully saturated condition and free-surface flow under varying saturation condition. Results suggest that the apparent-density-based governing equations lead to the conservation of fluid volume for the first type of problem only, while the intrinsic-density-based model leads to fluid's volume conservation for both types of problems. Abstract: Smoothed Particle Hydrodynamics (SPH) has successfully been employed in the last decade for macroscopic simulation of fluid flow in porous media. However, there are still certain inconsistencies in the existing models with regard to both the definition of the governing equations and the adopted numerical treatments. In this study, thus, in order for a comparative investigation of the existing practices, the method of spatial averaging is employed to derive two types of macroscopic conservation equations of mass and momentum through phase averaging and intrinsic phase averaging of fluid density. Consistent discretisation methods are adopted for the determination of particle's volume, in the Weakly Compressible SPH form, and velocity by which particles move; and they are used to construct three numerical models. The models are then employed to solve two different types of problems: i) a fully saturated soil medium under the closed channel flow condition, and ii) a porous medium under a free surface flow condition with varying saturation. The results of the models are compared with analytical and experimental data; and particle distribution, water surface elevation, conservation of fluid volume, and pressure distribution are investigated. It is shown that only the latter type of modelling (i.e., intrinsic phase averaging of fluid density) leads to the conservation of fluid volume for both types of the problems, while the former type of formulation (i.e., based on phased averaged density, also known as apparent density) is suitable for closed porous media flow conditions only. Comparisons with other numerical models and the author's previous study indicate that the adopted numerical treatments, especially the δ-SPH formulation, have led to an improvement in the smoothness of particles distribution and pressure field. A few recommendations are finally made about potential further improvements of the developed models and extensions of their applicability.