Time-averaged shallow water model: Asymptotic derivation and numerical validation

Asymptotic derivation of the section-averaged shallow water equations for natural river hydraulics

A Multilayer Saint-venant System with Mass Exchanges for Shallow Water Flows. Derivation and Numerical Validation

The standard multilayer Saint-Venant system consists in introducing fluid layers that are advected by the interfacial velocities. As a consequence there is no mass exchanges between these layers and each layer is described by its height and its average velocity. Here we introduce another multilayer system with mass exchanges between the neighborhing layers where the unknowns are a total height ...

A coupled numerical solution to the shallow water-Hirano model

Numerical Techniques for the Shallow Water Equations

In this report we will discuss some numerical techniques for approximating the Shallow Water equations. In particular we will discuss finite difference schemes, adaptations of Roe’s approximate Riemann solver and the Q-Schemes of Bermudez & Vazquez with the objective of accurately approximating the solution of the Shallow Water equations. We consider four different test problems for the Shallow...

A depth-averaged electrokinetic flow model for shallow microchannels

Electrokinetic flows with heterogeneous conductivity configuration occur widely in microfluidic applications such as sample stacking and multidimensional assays. Electromechanical coupling in these flows may lead to complex flow phenomena, such as sample dispersion due to electro-osmotic velocity mismatch, and electrokinetic instability (EKI). In this work we develop a generalized electrokineti...