Hydrodynamic Analysis for Mangrove Forests under Wave and Current Effects Using High-Order Phase-Resolving CutFEM

Abstract

This paper presents the implementation of a high-order phase-resolving cut finite-element method (CutFEM) to simulate the hydrodynamic features within an artificial mangrove forest caused by wave and current based on the incompressible two-phase Navier–Stokes model. The key advantage of CutFEM is that the fluid phase is fully resolved around the solid phase. This enables precise replication of the free-surface deformation and hydrodynamic drag, particularly for waves strongly interacting with the intricate prop roots of mangrove trees. Additionally, the present method employs the equivalent polynomial to compute the integration on the embedded surface with Heaviside and Dirac distributions. No explicit generation of cut cell meshes, adaptive quadrature, or local refinement is required. Hence, it uses the same number of degrees of freedom as the underlying conforming Galerkin method on the fixed background mesh. The classical FEM can be upgraded since the same element assembly structures are used. This paper characterizes different components of the hydrodynamic drag induced by the mangrove forest. The reduced-order model accounts for the equivalent wave damping and is further established to replicate the wave attenuation. The numerical results and experimental measurements are compared. The results show that CutFEM is robust, accurate, and efficient for solving complex fluid–structure interactions. This research not only offers a convenient method for upgrading existing finite-element codes but also benefits practical design applications. Coastal areas are increasingly vulnerable to extreme weather events and rising sea levels, making environmental sustainability and resilience crucial concerns. Nature-based features like mangroves and dunes are proving to be effective solutions for mitigating coastal hazards and stabilizing shorelines. This research provides precise numerical models and stable computational toolkits to conduct multiscale analyses on the hydrodynamic effect induced by the mangrove forest. Validation of the numerical method is achieved through wave experiments, specifically evaluating the mangrove trunk-root system’s effectiveness in wave attenuation. Hence, excessive fielding tests and laboratory work can be avoided as digital models are established. This research contributes to the advancement of engineering design for natural-based coastal protection and ecosystem restoration. Furthermore, it can upgrade conventional FEM codes to expand their applicability to a wider range of engineering simulations. Therefore, the proposed methods can address intricate fluid–structure interaction challenges, encompassing diverse physical phenomena ranging from particulate to environmental scales in real-world coastal and ocean engineering scenarios.