Eulerian–Lagrangian flow-vegetation interaction model using immersed boundary method and OpenFOAM

Abstract

This paper presents a novel coupled flow-vegetation interaction model capable to resolve the flow and motion of flexible vegetation with large deflections simultaneously on a hybrid Eulerian–Lagrangian grid. The hydrodynamics model is based on a Navier–Stokes flow solver with the Volume of Fluid surface capturing method in OpenFOAM. The deforming and moving vegetation are tracked through a series of Lagrangian grids attached to the vegetation and embedded in the computational domain of OpenFOAM. The governing equations for the flexible vegetation motion are based on a slender rod theory and are solved by a Finite Element Method on a vegetation-following Lagrangian grid. The hydrodynamics and vegetation models are coupled through the vegetation-induced hydrodynamic forces using a novel diffused immersed boundary method to avoid excessive fluid grid refinements around the vegetation. The standard two-equation k − ε turbulence model is extended for vegetated flow by incorporating additional closure terms of vegetation effects. The newly developed coupled flow-vegetation model is validated against experiments for both individual single-stem vegetation and a vegetation patch in a large-scale wave flume. Model results of asymmetric displacement of the vegetation motion, wave height decay, and wave kinematics within and outside the vegetation patch are in good agreement with measurements. The drastical change in wave radiation stress by the presence of vegetation patch leads to a strong current jet near the top of vegetation patch, which in turn drives a local circulation pattern around the vegetation patch. The effect of vegetation bending stiffness on the model results and empirical drag and inertia coefficients for calculating the hydrodynamic forces are examined in detail. Maximum turbulence energy is observed close to the bed and the top of vegetation patch just before and after the wave crest/trough, where the relative flow velocity to vegetation is large.