Publications de Alexandre Caboussat

A cut-cell method for the numerical simulation of 3D multiphase flows with strong interfacial effects

Alexandre Caboussat, Alexandre Masserey, Marco Picasso, Julien Hess

We present a numerical model for the approximation of multiphase flows with free surfaces and strong interfacial effects. The model relies on the multiphase incompressible Navier-Stokes equations, and includes surface tension effects on the interfaces betw ...

Academic Press Inc Elsevier Science2024

Error assessment of an adaptive finite elements-neural networks method for an elliptic parametric PDE

Alexandre Caboussat, Marco Picasso, Maude Girardin

We present a finite elements-neural network approach for the numerical approximation of parametric partial differential equations. The algorithm generates training data from finite element simulations, and uses a data -driven (supervised) feedforward neura ...

Elsevier Science Sa2024

An anisotropic adaptive method for the numerical approximation of orthogonal maps

Alexandre Caboussat, Marco Picasso, Dimitrios Gourzoulidis

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 ...

ELSEVIER2022

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

Alexandre Caboussat, Dimitrios Gourzoulidis

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 ...

SPRINGER/PLENUM PUBLISHERS2022

Numerical Approximation Of Orthogonal Maps

Alexandre Caboussat, Marco Picasso, Dimitrios Gourzoulidis

Orthogonal maps are the solutions of the mathematical model of paper-folding, also called the origami problem. They consist of a system of first-order fully nonlinear equations involving the gradient of the solution. The Dirichlet problem for orthogonal ma ...

2019

A Numerical Model For The Simulation Of Shallow Laser Surface Melting

Alexandre Caboussat, Alexandre Masserey, Marco Picasso, Julien Hess

We present a multi-physics model for the approximation of the coupled system formed by the temperature-dependent Navier-Stokes equations with free surfaces. The main application is the industrial process of shallow laser surface melting (SLSM), for laser p ...

INT CENTER NUMERICAL METHODS ENGINEERING2019

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

Alexandre Caboussat, Marco Picasso, Gilles Steiner, Arwa Mrad

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 ...

PERGAMON-ELSEVIER SCIENCE LTD2018

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

Alexandre Caboussat, Dimitrios Gourzoulidis

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 ...

SPRINGER/PLENUM PUBLISHERS2018

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

Alexandre Caboussat, Marco Picasso

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 ...

Wiley-Blackwell2014

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

Alexandre Caboussat, Jacques Rappaz, Pascal Clausen

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 ...

2012

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

Alexandre Caboussat, Jacques Rappaz, Christian Landry

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 ...

2010

Solving Optimization-Constrained Differential Equations With Discontinuity Points, With Application To Atmospheric Chemistry

Alexandre Caboussat, Chantal Landry

Ordinary differential equations are coupled with mixed constrained optimization problems when modeling the thermodynamic equilibrium of a system evolving with time. A particular application arises in the modeling of atmospheric particles. Discontinuity poi ...

2009

Analysis of a one-dimensional free boundary flow problem

Alexandre Caboussat, Jacques Rappaz

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 ...

Springer2005

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

Alexandre Caboussat, Marco Picasso, Jacques Rappaz

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 ...

2005