Scientific project: Mathematical modeling and numerical simulations of processes in thin or porous domains
Link to the poject web page.
Financed by Croatian Science Foundation
Involved institutions
Duration: 2014,2018
Bilateral research project France-Croatia ("COGITO", Hubert Curien) :
Modélisation, analyse et simulation numérique d'écoulements
multiphasiques en milieux poreux hétérogènes
Involved institutions
- University of Zagreb, Faculty of Science, Department of Mathematics.
- Laboratoire de Mathématiques et de leurs Applications de Pau, Université de Pau (UPPA).
Coordinator: Prof. Brahim Amaziane.
Duration: 2011,2012
Scientific project : Modélisation d'Ecoulements d'Eau dans les Sols non Saturés :
Aspects Mathématiques et Logiciels de Simulation Numérique
Financed by L'agence universitaire de la francophonie : Projet de la coopération scientifique
inter-universitaire
Duration: 2011,2012
Universités associées au projet
- Université de Zagreb (Croatie), Faculté de Sciences, Département de Mathématiques (coordinateur du projet).
- Université de Pau et des Pays de l'Adour (France), Laboratoire de Mathématiques et de leurs Applications.
- Université Moulay Ismail (Maroc), ENSAM de Meknès, Département de Mathématiques.
- Université Sidi Mohamed Ben Abdellah de Fès (Maroc), Département de Géologie.
- Université Cadi Ayyad (Maroc), Faculté des Sciences, Département de Mathématiques.
Objectifs
Ce projet a pour objectif l’étude de la modélisation et la simulation numérique de l’intrusion d’eau
marine dans les nappes aquifères côtières. Cette thématique environnementale est fort préoccupante
dans une conjoncture marquée par la diminution sans cesse croissante de la ressource et le recours
de plus en plus fréquent aux eaux souterraines notamment côtières. Il s’agira d’examiner ce problème
sous plusieurs volets :
- Examen critique de modèles physico-mathématiques existants,
- Choix de modèles (interface net, modèle de type miscible, écoulements multiphasiques,…),
- Analyse et simulation numérique de ces modèles,
- Développements de logiciels de simulation numérique,
- Validation et homologation de ces logiciels,
- Problèmes d'homogénéisation associés pour le traitement des hétérogénéités,
- Implémentation dans une plate-forme dédiée à la simulation des écoulements multiphasiques en milieux poreux.
Thèses doctorale en co-tutelle entre l’Université de Zagreb et l’Université de Pau:
- Ana Žgaljić Keko,
Faculty of Electrical Engineering and Computing, University of Zagreb (soutenue, 10/02/2011).
- Anja Vrbaški, Faculty of Science -- Department of Mathematics, University of Zagreb.
Scientific project : Numerical modelling of fluid flow through porous media
Project no: 037-0372787-2798
Financed by Ministry of Science, Education and Sports of the Republic of Croatia
(public.mzos.hr)
Duration: 2007-2012
Objective of this project is mathematical and numerical modeling of fluid flow through porous medium.
Mathematical models of interest come from hydrogeology and oil reservoir engineering,
but applications to biology and some technical systems are also possible.
We consider, in particular, compressible two-phase immiscible flow model (e.g. water and oil, oil and gas)
and compressible two-phase partially miscible flow model
(e.g. water/oil and gas, with dissolution of gas and volatility of water/oil).
These models are described by a system of partial differential equations
that present several difficulties:
strong nonlinearity, degeneracy and change of type in some flow regimes,
convection dominated convection-diffusion process, strong heterogeneity and anisotropy of the medium.
The project has several goals.
1. By using mathematical modelling we search for a mathematical formulation of fluid flow
problem that is well suited for numerical discretization. This includes an introduction of new
variables such as, for example, global pressure, which has higher smoothness than the phase pressures,
or variables that describe the flow system in all possible regimes, including disappearance/reappearance
of some phase. A mathematical analysis of new models will be undertaken.
2. Numerical discretization of the flow models by appropriate techniques will be studied.
We are interested in applications to flow of water, gas and contaminant in the vicinity of
underground radioactive waste repository on a large time scale. The scheme should be able to handle strong
heterogeneity and initial disequilibrium. The first approach will be with robust finite volume
schemes. A theoretical analysis of discrete system will be undertaken.
3. Numerical methods will be implemented in a computer code using object oriented techniques.
Development tool will be C++ programming language and finite element libraries/frameworks such as
Libmesh (http://libmesh.sourceforge.net/).
4. Upscaling of two-phase flow models from the Darcy scale to a regional scale is of
great interest in porous domains with multiscale heterogeneities, as in underground nuclear waste
repositories. We will analyze heterogeneous two-phase flow models using stochastic and
periodic homogenization and develop software tools for implementation of homogenized models.
Proposed project is a continuation of the project 0037111, Effective parameters in mathematical reservoir models
financed by Ministry of Science, Education and Sports of the Republic of Croatia.
Ph.D. students on the project:
- Ana Žgaljić Keko, Faculty of Electrical Engineering and Computing, University of Zagreb.
- Anja Vrbaški, Faculty of Science -- Department of Mathematics, University of Zagreb.
Created by Mladen Jurak