This paper proposes a thin layer depth-averaged two-phase model provided by a dissipative energy balance to describe avalanches of solid-fluid mixtures. This model is derived from a 3D two-phase model based on the equations proposed by Jackson [R. Jackson, The Dynamics of Fluidized Particles, 2000] which takes into account the force of buoyancy and the forces of interaction between the solid an...

A computationally efficient, high-resolution numerical model of shallow flow hydrodynamics is described, based on boundary-fitted adaptive quadtree grids. The numerical model solves the two-dimensional non-linear shallow water equations by means of an explicit second-order MUSCL-Hancock Godunov-type finite volume scheme. Interface fluxes are evaluated using an HLLC approximate Riemann solver. T...

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...

In this paper we have developed a robust numerical algorithm for the visco-plastic SaintVenant model with topography. For the time discretization an implicit (backward) Euler scheme was used. To solve the resulting nonlinear equations, a four steps iterative algorithm was proposed. To handle the non-differentiability of the plastic terms an iterative decomposition-coordination formulation coupl...

Recent experiments on a freely evolving dipolar vortex in a homogeneous shallow fluid layer have clearly shown the existence and evolution of complex three-dimensional (3D) flow structures. The present contribution focuses on the 3D structures of a dipolar vortex evolving in a stable shallow two-layer fluid. Experimentally, Stereoscopic Particle Image Velocimetry is used to measure instantaneou...