A depth-averaged two dimensional shallow water model to simulate flow-rigid vegetation interactions

摘要

This paper presents a well-balanced depth-averaged 2D shallow water model for simulating flow-rigid vegetation interactions. The rigid vegetation is modeled as vertical cylinders. A formula of drag force induced by the rigid vegetation is included in the momentum equations as a sink term. Since the bed friction and drag force terms have similar expressions, they are incorporated to be discretized using a splitting implicit scheme which can avoid an exaggerated force when the water depth becomes weak. Limiting value of the incorporated resistance term is derived to ensure stability. The proposed scheme is solved in a finite volume Godunov-type framework based on rectangular mesh with the HLLC approximate Riemann solver to discretize the convection part of equations, while a finite difference method is used to discretize the remaining terms. The MUSCL method is employed to achieve second-order accuracy in space and the second-order accuracy in time is obtained by applying the Runge-Kutta method. The model is tested against measured laboratory experimental data of the interaction of solitary waves with emergent, rigid vegetation. The computed results show good agreement with the experimental data.