Abstract

A hump in the channel bed can have an effect on the free surface profile. This submerged obstruction can be used to regulate the flow of water upstream and downstream. In this study, we present a mathematical model to investigate fluid behavior in the existence of a hump. The governing equation used here is the linearized Boussinesq-type equation. The model is solved analytically to obtain the transient and steady solution. Numerically, we apply finite-difference-based methods, namely FTCS and two-step Lax-Wendroff to solve the model. Validations are performed by comparing the numerical results with the analytical solution. We conclude that the two-step Lax-Wendroff produces a more accurate result. Further, we examine several factors that affect the transient state's duration and the maximum wave elevation, such as the type of incoming flow (subcritical or supercritical) and the hump dimension. The widest hump from subcritical flow generates the longest time for waves to propagate in a transient state, while the narrowest hump from supercritical flow generates the highest wave elevation.

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