Fluid mixing plays a fundamental role in many natural and engineered processes, including groundwater flows in porous media, enhanced oil recovery, and microfluidic lab-on-a-chip systems. Recent developments have explored the effect of viscosity contrast on mixing, suggesting that the unstable displacement of fluids with different viscosities, or viscous fingering, provides a powerful mechanism...

In this paper we consider a stochastic model describing the varying number of flows in a network. This model features flows of two types, namely file transfers (with fixed volume) and streaming traffic (with fixed duration), and extends the model of Key, Massoulié, Bain and Kelly [23] by allowing more general bandwidth allocation criteria. We analyse the dynamics of the system under a fluid sca...

The central objective of my research in this project is to understand the mathematical and physical connections between the bred-growing-mode and singular vector techniques recently developed for numerical weather prediction, the Lyapunov vectors and exponents of dynamical systems theory, and instability theories of geophysical fluid dynamics. My intent is to gain insight into fundamental mathe...

This paper is concerned with models describing disperse particles interacting with a fluid. This work is motivated by the transport of pollutants [14, 39], the dispersion of smokes and dusts [18], the modeling of biomedical flows [7, 5] as well as combustion theory, with applications to Diesel engines or propulsors [1, 2, 20, 34, 40]. The basis of the models we are interested in assumes that th...

The Navier-Stokes equations describe a large class of fluid flows but are difficult to solve analytically because of their nonlinearity. We present in this paper a parallel solver for the 3-D Navier-Stokes equations of incompressible unsteady flows with constant coefficients, discretized by the finite difference method. We apply the prediction-projection method which transforms the Navier-Stoke...

This paper presents a new and efficient method for computing the flow of a non-Newtonian fluid. The approach is based on two independent concepts: Time-dependent simulation of viscoelastic flow: A new decoupled algorithm, presented in P. Saramito, Simulation numerique d'ecoulements de fluides viscoelastiques par eRments finis incompressibles et une methode de directions alternees; applications,...

Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the density. An approximate solution of an initial–boundary value problem is calculated using the finite element approximation in space. The fully implicit two–level ...

We examine the optimal control of stationary thermally convected uid ows from the theoretical and numerical point of view. We use thermal convection as control mechanism, that is, control is eeected through the temperature on part of the boundary. Control problems are formulated as constrained minimization problem. Existence of optimal control is given and a rst order necessary conditions of op...