Édouard Canot

Jet drops ejection in bursting gas bubble processes

The numerical simulation using a boundary element method is presented for a gas bubble bursting at a free surface in a potential flow with a viscous fluid assumption. Systematic comparisons are given with experimental data on the first “jet drop” size in relation with the parent bubble size, and on the critical bubble radius above which no jet drop forms. The computations were made for different liquids. It is pointed out that an exact description of the jet formation and break up requires the complete Navier–Stokes equations only in the final phase of the evolution.

Determination of the Mechanical Properties of a Solid Elastic Medium from a Seismic Wave Propagation Using Two Statistical Estimators

In this paper, we study an inverse problem consisting in the determination of the mechanical properties of a layered solid elastic medium in contact with a fluid medium by measuring the variation of the pressure in the fluid while propagating a seismic/acoustic wave. The estimation of mechanical parameters of the solid is obtained from the simulation of a seismic wave propagation model governed by a system of partial differential equations. Two stochastic methods, Markov chain Monte Carlo with an accelerated version and simultaneous perturbation stochastic approximation, are implemented and compared with respect to cost and accuracy.

Identification of the Thermophysical Properties of the Soil by Inverse Problem

This paper introduces a numerical strategy to estimate the thermophysical properties of a saturated porous medium (volumetric heat capacity (ρC)s , thermal conductivity λs and porosity φ) where a phase change problem (liquid/vapor) appears due strong heating. The estimation of these properties is done by inverse problem knowing the heating curves at selected points of the medium. To solve the inverse problem, we use both the Damped Gauss Newton and the Levenberg Marquardt methods to deal with high nonlinearity of the system and to tackle the problem with large residuals. We use the method of lines, where time and space discretizations are considered separately. Special attention has been paid to the choice of the regularization parameter of the Apparent Heat Capacity method which may prevent the convergence of the inverse problem.

A comparative study of some distributed linear solvers on systems arising from fluid dynamics simulations

This paper presents a comparative study of some distributed solvers on a set of linear systems arising from Navier-Stokes equations and provided by an industrial software. Solvers under consideration implement direct, iterative or domain decomposition methods and most of them are freely available packages. Numerical tests with various parameters are made easier by developing a unified toolbox that links with interface functions provided by these libraries. The intensive numerical tests performed on various sets of processors reveal the good performance results achieved by the recently proposed parallel preconditioner for Krylov methods based on an explicit formulation of multiplicative Schwarz [1].

A new velocity–vorticity boundary integral formulation for Navier–Stokes equations.

An indirect boundary integral method for the numerical solution of Navier-Stokes equations formulated in velocity-vorticity dependent variables is proposed. This wholly integral approach, based on Helmholtzs decomposition, deals directly with the vorticity field and gives emphasis to the establishment of appropriate boundary conditions for the vorticity transport equation. The coupling between the vorticity and the vortical velocity fields is expressed by an iterative procedure

Determination and sensitivity analysis of the seismic velocity of a shallow layer from refraction traveltimes measures

In this paper, we are interested in determining the seismic velocity of a shallow under-ground layer from refraction traveltimes measures. We present a study case taken from an experimental seismic survey. The study case is a wide-angle seismic inversion using experimental traveltimes measures and based on ray tracing technique and genetic algorithms. The hypothesis on the velocity distribution, coming from the seismic experiment, makes the computation of some seismic rays expensive in time. We propose to reduce the computations time by introducing a formulation of the inverse problem that avoids such costly rays, hence the inversion becomes feasible. Also we present a sensitivity analysis based on a singular value decomposition of the jacobian of the traveltimes with respect to velocity. We give the relationship between the traveltimes measure errors and the velocity estimation error. We discuss the advantages of this method over the classical one based on the resolution matrix.

BUBBLE EVOLUTION IN LIQUID. GAS SOLUTIONS, VIEWED AS AN ELEMENTARY CATASTROPHE

The stability of gas micro-bubbles in liquid-gas solutions is of importance in a broad range of applications which include propagation and damping of sound, bubble removal during glassmaking, fermentation, initiation of boiling or cavitation. The latter application has prompted most studies on this subject: the point was to explain why real liquids cannot withstand high tensile stresses as predicted by the various homogeneous nucleation theories. It is then necessary in many cases to postulate that heterogeneous nucleation occurs via the existence of persistent nuclei. The most likely candidates for the role of nuclei are either vapour-gas bubbles trapped in crevices on the wall of a container or on the surface of suspended solid particles, or free vapour-gas micro-bubbles transported in the bulk of the fluid.