Abstract
In this paper, we consider water waves excited by moving topography. This problem usually occurs in the tsunami generation and propagation. We use the shallow water wave model governing this wave generation and propagation problem. Two finite difference methods are tested to solve the problem. The first is the forward in time centred in space finite difference method. The second is the Adams-Bashforth--Adams-Moulton method. We obtain that the second gives more flexibility in terms of the choice of time step value.
Highlights
Water waves in the ocean can be generated by a number of sources, such as wind, lunar influence, ship movement, bottom motion, etc
The first is the forward in time centred in space finite difference method
We take the forward in time centred in space (FTCS) and the Adams-Bashforth--Adams-Moulton (ABAM) methods
Summary
Water waves in the ocean can be generated by a number of sources, such as wind, lunar influence, ship movement, bottom motion (moving topography), etc. Water surface waves generated by moving topography have been an interest of a number of authors, as these can be used to simulate tsunami generation and propagation. Jamin et al [3] conducted experiments on the generation of surface waves by a moving topography Case studies on this topic have been conducted, such as by Grilli, et al [4] regarding the coastal tsunami hazard model from submarine mass failures. These previous studies indicate that a reliable numerical method is needed in the simulation of surface wave generation and propagation.
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