From the Navier-Stokes/Brinkman model, a penalization method has been derived by several authors to compute incompressible Navier-Stokes equations around obstacles. In this paper, convergence theorems and error estimates are derived for two kinds of penalization. The first one corresponds to a L 2 penalization inducing a Darcy equation in the solid body, the second one corresponds to a H 1 penalization and induces a Brinkman equation in the body. Numerical tests are performed to confirm the efficiency and accuracy of the method.

No abstract

This paper focuses on improving the stability as well as the approximation properties of Reduced Order Models (ROM) based on Proper Orthogonal Decomposition (POD). The ROM is obtained by seeking a solution belonging to the POD subspace and that at the same time minimizes the Navier-Stokes residuals. We propose a modified ROM that directly incorporates the pressure term in the model. The ROM is then stabilized making use of a method based on the fine scale equations. An improvement of the POD solution subspace is performed thanks to an hybrid method that couples direct numerical simulations and reduced order model simulations. The methods proposed are tested on the two-dimensional confined square cylinder wake flow in laminar regime.

No abstract

No abstract

No abstract

In this work, a viscosimeter implemented on a microfluidic chip is presented. The physical principle of this system is to use laminar parallel flows in a microfluidic channel. The fluid to be studied flows side by side with a reference fluid of known viscosity. By using optical microscopy, the shape of the interface between both fluids can be determined. Knowing the flow rates of the two liquids and the geometrical features of the channel, the mean shear rate sustained by the fluid and its viscosity can thus be computed. Accurate and precise measurements of the viscosity as a function of the shear rate can be made using less than 300 microL of fluid. Several complex fluids are tested with viscosities ranging from 10(-)(3) to 70 Pa.s.

The aim of this paper is to give open boundary conditions for the incompressible Navier-Stokes equations. From a weak formulation in velocity-pressure variables, some natural boundary conditions involving the traction or pseudotraction and inertial terms are established. Numerical experiments on the flow behind a cylinder show the efficiency of these conditions, which convey properly the vortices downstream. Comparisons with other boundary conditions for the velocity and pressure are also performed.