A Central-Upwind Scheme for Nonlinear Water Waves Generated by Submarine Landslides
نویسندگان
چکیده
We study a simple one-dimensional (1-D) toy model for landslides-generated nonlinear water waves. The landslide is modeled as a rigid bump translating down the side of the bottom while the water motion is modeled by the Saint-Venant system of shallow water equations. The resulting system is numerically solved using a well-balanced positivity preserving central-upwind scheme. The obtained numerical results are in good agreement with both the two-dimensional (2-D) incompressible flow numerical simulations and the experimental data.
منابع مشابه
Central-Upwind Scheme for Savage-Hutter Type Model of Submarine Landslides and Generated Tsunami Waves
We develop a new central-upwind scheme for a one-dimensional Savage-Hutter type model of submarine landslides and generated tsunami waves. Our scheme exactly preserves physically relevant steady-states, preserves positivity of water depth, is insensitive to choice of discretization of nonconservative products, and properly incorporates friction inherent in the model. We apply our scheme to a va...
متن کاملA numerical study of submarine-landslide-generated waves and run-up
A mathematical model is derived to describe the generation and propagation of water waves by a submarine landslide. The model consists of a depth-integrated continuity equation and momentum equations, in which the ground movement is the forcing function. These equations include full nonlinear, but weak frequencydispersion, e¬ects. The model is capable of describing wave propagation from relativ...
متن کاملSome Aspects of Energy Balance and Tsunami Generation by Earthquakes and Landslides
Tsunamis are generated by displacement or motion of large volumes of water. While there are several documented cases of tsunami generation by volcanic eruptions and landslides, most observed tsunamis are attributed to earthquakes. Kinematic models of tsunami generation by earthquakes — where specified fault size and slip determine seafloor and sea-surface vertical motion — quantitatively explai...
متن کاملTsunami waves generated by submarine landslides of variable volume: analytical solutions for a basin of variable depth
Tsunami wave generation by submarine landslides of a variable volume in a basin of variable depth is studied within the shallow-water theory. The problem of landslide induced tsunami wave generation and propagation is studied analytically for two specific convex bottom profiles (h∼ x4/3 and h∼ x4). In these cases the basic equations can be reduced to the constant-coefficient wave equation with ...
متن کاملSemi-Discrete Central-Upwind Schemes for Elasticity in Heterogeneous Media
We develop new central-upwind schemes for nonlinear elasticity equations in a heterogeneous medium. Finite volume central-upwind schemes consist of three steps: reconstruction, evolution, and projection onto the original grid. In our new method, the evolution is performed in the standard way by integrating the system over the space-time control volumes. However, the reconstruction and projectio...
متن کامل