Publications by Alexandre Caboussat

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A numerical model for the three-dimensional simulation of liquid-gas flows with free surfaces is presented. The incompressible Navier-Stokes equations are assumed to hold in the liquid domain. In the gas domain, the velocity is disregarded, the pressure is ...

Mathematical and numerical aspects of free surface flows are investigated. On one hand, the mathematical analysis of some free surface flows is considered. A model problem in one space dimension is first investigated. The Burgers equation with diffusion has to be solved on a space interval with one free extremity. This extremity is unknown and moves in time. An ordinary differential equation for the position of the free extremity of the interval is added in order to close the mathematical problem. Local exi

A numerical model for the simulation of three-dimensional liquid-gas flow with free surfaces is presented. The incompressible Navier-Stokes equations are assumed to hold in the liquid domain, while the surrounding gas is assumed to be compressible, with co ...

We present a numerical model for the simulation of 3D poly-dispersed sediment transport in a Newtonian flow with free surfaces. The physical model is based on a mixture model for multiphase flows. The Navier-Stokes equations are coupled with the transport ...

The numerical analysis of a dynamic constrained optimization problem is presented. It consists of a global minimization problem that is coupled with a system of ordinary differential equations. The activation and the deactivation of inequality constraints ...

In this article, we address the numerical solution of the Dirichlet problem for the three-dimensional elliptic Monge-Ampere equation using a least-squares/relaxation approach. The relaxation algorithm allows the decoupling of the differential operators fro ...

A numerical method for the solution to the density-dependent incompressible Navier-Stokes equations modeling the flow of N immiscible incompressible liquid phases with a free surface is proposed. It allows to model the flow of an arbitrary number of liquid ...

We consider a least-squares/relaxation finite element method for the numerical solution of the prescribed Jacobian equation. We look for its solution via a least-squares approach. We introduce a relaxation algorithm that decouples this least-squares proble ...

The gas bubble laden layer under the anodes during the electrolysis of alumina plays an important role in the hydrodynamics and the voltage balance of the reduction cells. Under certain geometrical and operational conditions, very large gas pockets, in the order of hundred cubic centimeters can be formed. The particular shape of these large gas bubbles was first described by Fortin et al in 1984 [1]. In the present paper the results of a combined experimental and numerical approach are described. In the exp

Orthogonal maps are two-dimensional mappings that are solutions of the so-called origami problem obtained when folding a paper. These mappings are piecewise linear, and the discontinuities of their gradient form a singular set composed of straight lines re ...

A one-dimensional free surface problem is considered. It consists in Burgers' equation with an additional diffusion term on a moving interval. The well-posedness of the problem is investigated and existence and uniqueness results are obtained locally in ti ...

Alexandre Caboussat

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Numerical simulation of free surface incompressible liquid flows surrounded by compressible gas

Analysis and numerical simulation of free surface flows

Numerical simulation of two-phase flow with interface tracking by adaptive Eulerian grid subdivision

A semi-Lagrangian splitting method for the numerical simulation of sediment transport with free surface flows

Optimization Problem Coupled with Differential Equations: A Numerical Algorithm Mixing an Interior-Point Method and Event Detection

A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge-Ampere Equation

Numerical simulation of 3D free surface flows, with multiple incompressible immiscible phases. Applications to impulse waves

A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation

Large Gas Bubbles under the Anodes of Aluminum Electrolysis Cells

An anisotropic adaptive method for the numerical approximation of orthogonal maps

Analysis of a one-dimensional free boundary flow problem