A modified weakly compressible smoothed particle hydrodynamics mixture model for accurate simulation of wave and porous structure interaction

In this study, a modified weakly compressible smoothed particle hydrodynamics (WCSPH) mixture model was developed to more accurately simulate the interaction between waves and porous structures. In this model, we enhanced the governing equations of the traditional WCSPH mixture model by introducing Darcy velocity, apparent density, and an adjustable smoothing length. This refinement ensures that the modified model effectively maintains the conservation of fluid volume in seepage simulations. Additionally, this paper proposes a permeable interface treatment technique that replaces traditional smoothed particle hydrodynamics interpolation with finite element shape function interpolation, significantly enhancing computational efficiency. At the same time, we also introduced and revised a particle shifting technique, which further increases the computational precision of the model. The modified WCSPH mixture model was then applied to simulate several physical experiments, including the dam-break wave propagation in a permeable dam, the attenuation of solitary waves on a permeable riverbed, the propagation of the solitary wave on a submerged porous structure, and the breaking process of waves passing through permeable breakwaters. Through comparison with the experimental data and other numerical results, the current model was comprehensively verified from various aspects, such as fluid volume conservation, wave evolution in and around the porous structure, and pressure distribution characteristics. The results confirm the excellent performance of the current model in simulating the interaction between waves and porous structures.