Numerical simulation in reservoir engineering

Development of numerical software for simulation of oil and gas recovery:
Implementation of a finite element method for the numerical simulation of fluid flow in porous media.
Development of a finite element code for the numerical simulation of CBM (Coal Bed Methane) recovery: two-phase (gas and water) flow in porous media taking into account desorption process.

Level set formulations and numerical solution of interface propagation problems

Obtained results

• We have derived an iterative process for the solution of the Bernoulli problem
• Derivation and implementation of a second order fast marching method for the level set equation to solve the Bernoulli problem via an integral representation
• Derivation and implementation of accurate finite element methods for elliptic problems with mild singularities

This work was realized in a large scale collaboration with F. Bouchon (Clermont-Ferrand), S. Clain (University of Minho, Portugal), P. Gremaud (Raleigh, USA), C. Kuster (PhD, Raleigh, USA), and G. Peichl (Graz, Austria).

Eddy Currents

Magnetohydrodynamics

Flow of metal liquids under the action of a magnetic field, Computation of a free boundary: interface metal - air.

Mathematical analysis

Results concerning existence of a solution of a problem that couples eddy current and Navier-Stokes equations. Convergence of the used numerical methods.

Numerical solution

Use of a coupled Finite Element / Boundary Element method. Construction of an iteration process to solve the free boundary problem

This work was realized at the Swiss Federal Institute of Technology with J. Rappaz and under a contract with ALCAN.

Applications

Electromagnetic casting, stirring and forming.

Induction heating

Numerical modelling of an induction heating process for two-dimensional geometries. Treatment of magnetic materials with accounting for Curie point. Optimal control of the process.

Mathematical analysis

Results concerning existence of a solution of a quasi-stationary model problem.

Numerical solution

Use of a time two-scale method to simulate the process. Techniques of optimal control to optimize the process in function of parameters as: Inductor shape, frequency, voltage sampling, ...
This work was realized in part at the gateio with S. Clain, J. Rappaz, M. Swierkosz, under a contract with the AMYSA Yverdon Company at the Blaise Pascal University with the Renault company.

Eddy currents in thin conductors

Use of asymptotic techniques to obtain models for thin conductors. The aim is to couple field equations (in thick conductors) with circuit equations in inductors.

Obtained results

• We have obtained a coupling between Kirchhoff circuit equation with a Maxwell equation in a 2-D case.
• Asymptotic expansion of the inductance of a thin toroidal conductor in function of its thickness and an estimation of the deviation.

This work is realized in collaboration with Y. Amirat.
Publication of a monograph on eddy currents and magnetostatics (Springer)

Numerical Methods in Computational Fluid Dynamics

Development of efficient numerical techniques in computational fluid dynamics. Namely: Projection Finite Element Methods:
Development of a projection method using the mini-finite element for space discretization of time dependent incompressible Navier-Stokes equations.
Numerical Simulation of Instabilities in a Heat Island: Development of a mathematical model and numerical code, in collaboration with T. Dubois for the simulation of transition to turbulence in a heat island.