2025 Volume 13 Issue 2 Article ID: 24-16142
In this study, a semi-implicit model is proposed for the bed friction and drag force terms of the shallow water equations (SWEs) by calculating bottom pressures to simulate dam-break flows with vegetation. The Manning formula is used for the bed friction term, while the drag force term is evaluated for non-equilibrium conditions considering the base component of drag force expression, water surface variations, and pressure gradient. Our model employs a cell-centered finite volume method with second-order spatial accuracy, while the Runge-Kutta second-order (RKSO) explicit time-stepping scheme is used for temporal discretization. Both the bed friction and drag force terms are treated in a semi-implicit manner, namely, such terms are included in each computing stage of the RKSO scheme with an implicitness factor to calculate depth-averaged (horizontal) velocities. Meanwhile, vertical velocities at water surface and bottom are calculated along with bottom pressures iteratively using the conjugate gradient method but only once for each time step. Henceforth, the bottom pressure values are used to update the horizontal velocities at the same time step. Our numerical model is validated against the experimental data and shows very good agreements in predicting the flow characteristics both inside and outside the vegetation zone.
