An immersed structure approach for fluid-vegetation interaction

Abstract

We present an immersed structure approach for modeling the interaction between surface flows and vegetation. Fluid flow and rigid and flexible vegetative obstacles are coupled through a local drag relation that conserves momentum. In the presented method, separate meshes are used for the fluid domain and vegetative obstacles. Taking techniques from immersed boundary finite element methods, the effects of the fluid on the vegetative structures and vice versa are calculated using integral transforms. Using a simple elastic structure model we incorporate bending and moving vegetative obstacles. We model flexible vegetation as thin, elastic, inextensible cantilever beams. Using the immersed structure approach, a fully coupled fluid-vegetation interaction model is developed assuming dynamic fluid flow and quasi-static bending. This relatively computationally inexpensive model allows for thousands of vegetative obstacles to be included in a simulation without requiring an extremely refined fluid mesh. The method is validated with comparisons to mean velocity profiles and bent vegetation heights from experiments that are reproduced computationally. We test the method on several channel flow setups. We calculate the bulk drag coefficient in these flow scenarios and analyze their trends with changing model parameters including stem population density and flow Reynolds number. Bulk drag models are the primary method of incorporating small-scale drag from individual plants into a value that can be used in larger-scale models. Upscaled bulk drag quantities from this method may be utilized in larger-scale simulations of flow through vegetation regions.