Port based network modeling of complex lumped parameter physical systems naturally leads to a generalized Hamiltonian formulation of its dynamics. The resulting class of open dynamical systems are called “Port-Hamiltonian systems” [12] which are defined using a Dirac structure, the Hamiltonian and dissipative elements. This formulation has been successfully extended to classes of distributed pa...

In the present work, we analyze the rotating shallow water equations including bottom topography using a space-time discontinuous Galerkin finite element method. The method results in non-linear equations per element, which are solved locally by establishing the element communication with a numerical HLLC flux. To deal with spurious oscillations around discontinuities, we employ a stabilization...

This is a study of the Euler equations for free surface water waves in the case of varying bathymetry, considering the problem in the shallow water scaling regime. In the case of rapidly varying periodic bottom boundaries this is a problem of homogenization theory. In this setting we derive a new model system of equations, consisting of the classical shallow water equations coupled with nonloca...

Consideration is given to the influence of an underwater landslide on waves at the surface of a shallow body of fluid. The equations of motion which govern the evolution of the barycenter of the landslide mass include various dissipative effects due to bottom friction, internal energy dissipation, and viscous drag. The surface waves are studied in the Boussinesq scaling, with time-dependent bat...

In this paper, an analytical solution for the coupled one-dimensional time fractional nonlinear shallow water system is obtained by using the homotopy perturbation method (HPM). The shallow water equations are a system of partial differential equations governing fluid flow in the oceans (sometimes), coastal regions (usually), estuaries (almost always), rivers and channels (almost always). The g...

This paper discusses the applications of linear and nonlinear shallow water wave equations in practical tsunami simulations. We verify which hydrodynamic theory would be most appropriate for different ocean depths. The linear and nonlinear shallow water wave equations in describing tsunami wave propagation are compared for the China Sea. There is a critical zone between 400 and 500 m depth for ...

A well balanced numerical scheme based on stationary waves for shallow water flows with arbitrary topography has been introduced by Thanh et al. [18]. The scheme was constructed so that it maintains equilibrium states and tests indicate that it is stable and fast. Applying the well-balanced scheme for the one-dimensional shallow water equations, we study the early shock waves propagation toward...

We study the modulational instability of a shallow water model, with and without surface tension, which generalizes the Whitham equation to include bi-directional propagation. Without surface tension, the small amplitude periodic traveling waves are modulationally unstable if their wave number is greater than a critical wave number predicting a Benjamin-Feir type instability and the result qual...