1,721,274 research outputs found
A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics
No full textThis paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equations and the numerics in use. The perspective of the analysis is that of a physicist/engineer rather than of an applied
mathematician. The chronological progress of the currently available BTMs from the pioneering models of the late 1960s is given. The main applications of BTMs are illustrated, with reference to specific models and methods. The evolution in time of the numerical methods used to solve BTMs (e.g. finite differences, finite elements, finite volumes) is described, with specific focus on finite volumes. Finally, an overview of the most important BTMs currently available is presented, as well as some
indications on improvements required and fields of applications that call for attention
Bore-generated macrovortices on erodible beds
No full textThe interaction of free-surface bores and an erodible porous channel bed in a shallow-water flow is analysed based on the assumption of weak coupling between free-surface discontinuities and bed discontinuities and on the simplest closure for the sediment transport rate (cubic with the mean flow velocity). It is shown that free-surface bores with finite cross-stream extent can evolve over the erodible bed by generating vertically oriented macrovortices in a manner similar to, but more complex than, that of free-surface bores of finite cross-stream extent over a rigid channel bottom. An equation for the potential vorticity is derived, which shows that on an erodible bed the vortices are generated by a combination of various mechanisms related to energy dissipation of both surface bores and bed discontinuities. The model is verified and the physics explored by comparison with a number of numerical simulations, typical of both riverine (dam-break test and pit test) and nearshore (bore on a beach test) flows, and with previously published experimental results. For all cases a fairly good agreement is found between the analytically estimated potential vorticity and that computed numerically
Analytical solutions of the nonlinear shallow water equations and their averaging on a plane beach.
No full text
- …
