Publications de Jacques Rappaz

A mixture model for a dilute dispersion of gas in a liquid flow: Mathematical analysis and application to aluminium electrolysis

Marco Picasso, Jacques Rappaz, Emile Tryphon Pierre Soutter

A mixture model to take into account the flow of small carbon dioxide bubbles dissolved in a liquid is presented. The model describes the evolution of the velocity fields (mixture and gas), the pressure and the volume fraction of gas. The system of equatio ...

2021

On Von Karman Modeling For Turbulent Flow Near A Wall

Jacques Rappaz, Jonathan Rochat

Mixing-length models are often used by engineers in order to take into account turbulence phenomena in a flow. This kind of model is obtained by adding a turbulent viscosity to the laminar one in Navier-Stokes equations. When the flow is confined between t ...

2019

Conservation Schemes For Convection-Diffusion Equations With Robin Boundary Conditions

Jacques Rappaz, Stéphane Flotron

In this article, we present a numerical scheme based on a finite element method in order to solve a time-dependent convection-diffusion equation problem and satisfy some conservation properties. In particular, our scheme is able to conserve the total energ ...

EDP Sciences2013

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

Modelling and mathematical results arising from ferromagnetic problems

Jean Descloux, Michel Flück, Jacques Rappaz

In this article, we investigate the equations of magnetostatics for a configuration where a ferromagnetic material occupies a bounded domain and is surrounded by vacuum. Furthermore, the ferromagnetic law takes the form ...

SP Science China Press, Springer2012

Modelling and Numerical Simulation of the Dynamics of Glaciers Including Local Damage Effects

Marco Picasso, Jacques Rappaz, Martin Funk

A numerical model to compute the dynamics of glaciers is presented. Ice damage due to cracks or crevasses can be taken into account whenever needed. This model allows simulations of the past and future retreat of glaciers, the calving process or the break- ...

2011

Existence and stability of steady-state solutions of the shallow-ice-sheet equation by an energy-minimization approach

Jacques Rappaz, Heinz Blatter, Guillaume Jouvet

The existence of solutions of the non-sliding shallow-ice-sheet equation on a flat horizontal bed with a mass balance linearly depending on altitude is proven for fixed margins. Free-margin solutions for the same mass balance do not exist. Fixed-margin sol ...

International Glaciological Society2011

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

Scientific Computing For Aluminum Production

Michel Flück, Marco Picasso, Jacques Rappaz, Gilles Steiner, Thomas Hofer

Numerical simulation in aluminum production envolves many different topics, this paper is dedicated to some aspects of two of them. In the first part, a numerical approach for the computation of the motion of the fluids in an electrolitic cell is presented ...

2009

Numerical simulation of thermal problems coupled with magnetohydrodynamic effects in aluminium cell

Michel Flück, Jacques Rappaz

A system of partial differential equations describing the thermal behavior of aluminium cell coupled with magnetohydrodynamic effects is numerically solved. The thermal model is considered its a two-phases Stefan problem which consists of a non-linear conv ...

Elsevier2009

Numerical simulation of Rhonegletscher from 1874 to 2100

Marco Picasso, Jacques Rappaz, Heinz Blatter, Guillaume Jouvet

Due to climatic change, many Alpine glaciers have significantly retreated during the last century. In this study we perform the numerical simulation of the temporal and spatial change of Rhonegletscher, Swiss Alps, from 1874 to 2007, and from 2007 to 2100. ...

Elsevier2009

A new algorithm to simulate the dynamics of a glacier: theory and applications

Marco Picasso, Jacques Rappaz, Heinz Blatter, Guillaume Jouvet

We propose a novel Eulerian algorithm to compute the changes of a glacier geometry for given mass balances. The surface of a glacier is obtained by solving a transport equation for the volume of fluid (VOF). The surface mass balance is taken into account b ...

International Glaciological Society2008

Multiscale algorithm with patches of finite elements

Marco Picasso, Jacques Rappaz, Vittoria Augusta Rezzonico Janka

We develop a discretization and solution technique for elliptic problems whose solutions may present strong variations, singularities, boundary layers and oscillations in localized regions. We start with a coarse finite element discretization with a mesh s ...

2008

Numerical integration of the three-dimensional Green kernel for an electromagnetic problem

Alexandre Masserey, Jacques Rappaz, Roland Rozsnyo

In this paper, we present a method for the numerical integration of the three-dimensional Green kernel over two triangles. This method is compared with the results obtained by other algorithms. The comparison proves the efficiency of the technique in remov ...

2005

Finite element approximation of multi-scale elliptic problems using patches of elements

Jacques Rappaz

In this paper we present a method for the numerical solution of elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. The method consists in calculating successive corrections to the solution in patches whose discre ...

Springer2005

Mathematical and numerical analysis of a three-dimensional fluid flow model in glaciology

Adrian Reist, Jacques Rappaz

The main goal of this article is to analyze a three-dimensional model for stress and velocity fields in grounded glaciers and ice sheets including the role of normal deviatoric stress gradients. This model leads to a nonlinear system of stationary partial ...

2005

Weak solution of a stationary convection-diffusion model describing binary alloy solidification processes

Jacques Rappaz

Our goal is to study the existence of weak solution for the stationary system of equations describing the solidification process of a binary alloy confined in a bounded regular domain in R-3 and having mixed boundary conditions. (c) 2005 Elsevier Ltd. All ...

2005

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