Review of smoothed particle hydrodynamics modeling of fluid flows in porous media with a focus on hydraulic, coastal, and ocean engineering applications

A comprehensive review is conducted on the application of Lagrangian mesh-free methods for simulating flows in various types of porous media, ranging from fixed structures like coastal breakwaters to deformable and transportable media. Deformable porous media refer to soil structures that may deform under the influence of currents and waves, while transportable media involve processes such as sediment transport and scour around hydraulic, coastal, and ocean structures. This review addresses problem dimensionality, governing equations, domain discretization schemes, interaction mechanisms, and applications. The literature analysis reveals that while various numerical techniques have been employed to model the complex interaction between fluid and solid phases, not all methods are physically or mathematically justifiable. However, some approaches have significantly advanced the modeling process over the past two decades. Based on these findings, a modeling framework is proposed to guide the construction of mesh-free models for simulating flow interactions with natural or engineered porous structures. It highlights two effective approaches: (i) Three-dimensional (3D) pore-scale microscopic modeling of flow through large-sized solid particles using coupled smoothed particle hydrodynamics (SPH) and discrete element method (DEM), and (ii) two-dimensional (2D) macroscopic modeling of flow in small-sized porous media using the mixture theory and SPH. The framework highlights the mixture-theory-based methods as particularly effective for large-scale simulations and the advanced SPH-DEM coupling techniques that enable precise simulations of complex fluid-solid interactions. The framework serves as a guide for researchers developing mesh-free numerical models to simulate fluid flows in porous media for hydraulic, coastal, and ocean engineering applications.