Abstract
In this paper, we formulate a numerical model to study unsteady waves generated by fluid flow over a permeable wavy bed. The model is derived from boundary value problems using potential theory. We solve the model numerically using a finite difference method. As a result, we found that the flow over a porous layer generates wave disturbed by bumps on the porous layer. The simulation also showed that the wave profile shifts from the permeable bed. The results of this study can be incorporated into the design of submerged artificial and natural breakwaters.
Highlights
The effect of the porous layer can be seen on the right hand side of Equation (34), with the absorption ability of the porous medium defined by R and d
We derived a linear unsteady model for surface waves generated by a flow passing over a permeable wavy bed
The forward-time centered-space finite difference method has been applied to solve the model numerically. This solution is used to observe the propagation of the fluid surface waves, allowing the effects of the Froude number and the characteristics of the porous medium on wave generation to be observed
Summary
The numerical scheme of Liu et al [4] was validated using data from simple experiments on liquid flows through different porous mediums types. Models for flow over permeable beds have been formulated with the shallow water equations (SWEs) as their base. We derive a model for unsteady waves generated by a flow over a permeable wavy bed based on potential theory and Darcy’s law. A numerical scheme is constructed to solve the governing equations using a second-order forward-time center-space finite difference method This method is chosen because can be solved explicitly and is relatively simple, meanings that it has a low computational cost [18].
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