An efficient numerical solver for highly compliant slender structures in waves: Application to marine vegetation

This paper presents a fully explicit coupled wave–vegetation interaction model capable of efficiently solving the coupled wave dynamics and flexible vegetation motion with large deflections. The flow model is formulated using the continuity equation and linearized momentum equations of an incompressible fluid, with additional terms within the canopy region accounting for the presence of vegetation. This linearized flow solver is unconditionally stable and second-order accurate. The flow model is validated and verified against experimental measurements and analytical solutions for waves over a rigid canopy, demonstrating its capability to accurately capture the wave dissipation and flow velocity profiles, even with a relatively coarse grid. A truss-spring model is proposed to capture vegetation motion with substantial deflections, and is proven to be mathematically consistent with the governing equation for the flexible vegetation motion. It allows for explicit time integration with large time steps when dealing with highly compliant vegetation. The truss-spring model is validated and verified by experimental and numerical results for large-amplitude motions of a single elastic blade subjected to waves and sinusoidal oscillatory flows. The coupled model, combining the linearized flow solver and the truss-spring model, is applied to investigate wave propagating over a heterogeneous, suspended, and flexible canopy, showing high efficiency and good agreement with the experiments concerning wave attenuation and the hydrodynamic loads on the vegetation.