A fast finite volume solver for hydrostatic multi-layered shallow water flows with mass exchange is investigated. In contrast to many models for multi-layered hydrostatic shallow water flows where the immiscible suppression is assumed, the present model allows for mass exchange between the layers. The multi-layered shallow water equations form a system of conservation laws with source terms for...

A one-dimensional hybrid numerical model is presented of a shallow-water flume with an incorporated piston paddle. The hybrid model is based on the improved Boussinesq equations by Madsen and Sørensen (1992) and the nonlinear shallow water equations. It is suitable for breaking and non-breaking waves and requires only two adjustable parameters: a friction coefficient and a wave breaking paramet...

The numerical simulation of shallow water acoustic propagation has given rise to a wide variety of modeling techniques with various degrees of accuracy. One technique, involving finite difference methods, is more commonly used in the description of seismic propagation but also occurs in the shallow water propagation literature. This word reported here involves the application of finite differen...

We apply a multiple–time version of the reductive perturbation method to study long waves as governed by the shallow water wave model equation. As a consequence of the requirement of a secularity–free perturbation theory, we show that the well known N–soliton dynamics of the shallow water wave equation, in the particular case of α = 2β, can be reduced to the N–soliton solution that satisfies si...

In the following case study, we consider the so-called shallow water equations. They describe the behaviour of a fluid, in particular water, of a certain (possibly varying) depth h in a twodimensional domain – imagine, for example, a puddle of water or a shallow pond (and compare the 1D sketch given in Figure 1). The main modelling assumption is that we can neglect effects of flow in vertical d...

Our long term goal is to develop accurate models for high-frequency acoustic penetration into, propagation within, and scattering from shallow water ocean sediments. This work should specifically improve the Navy’s ability to detect buried mines and, in general, improve sonar performance in shallow water. Additional objectives of the NRL program are to understand and model the complex interacti...

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...

Title of dissertation: MESHLESS COLLOCATION METHODS FOR THE NUMERICAL SOLUTION OF ELLIPTIC BOUNDARY VALUED PROBLEMS AND THE ROTATIONAL SHALLOW WATER EQUATIONS ON THE SPHERE Christopher D. Blakely, Doctor of Philosophy, 2009 Dissertation directed by: Professor John Osborn Department of Mathematics Professor Ferdinand Baer Department of Atmospheric and Oceanic Science This dissertation thesis has...

The purpose of this study is to model the flow movement in an idealized dam-break configuration. One-dimensional and two-dimensional motion of a shallow flow over a rigid inclined bed is considered. The resulting shallow water equations are solved by finite volumes using the Roe and HLL schemes. At first, the one-dimensional model is considered in the development process. With conservative fini...

The hydrodynamics in Lake Naivasha, a shallow endorheic lake, are simulated using the Delft3D Flow Module to investigate the major driving forces of hydrodynamics in the lake. The results showed wind as the major forcing. The shallow zones of the lake showed currents movement in the same direction as the wind while the deep zones showed currents movements against the wind direction. These findi...