RESEARCH CENTRE

Inria Centre
at Université Côte d’Azur

IN PARTNERSHIP WITH:

CNRS, Université Côte d’Azur

2023
ACTIVITY REPORT

Project-Team

COFFEE

COmplex Flows For Energy and
Environment

IN COLLABORATION WITH: Laboratoire Jean-Alexandre Dieudonné (JAD)

DOMAIN

Digital Health, Biology and Earth

THEME

Earth, Environmental and Energy
Sciences

Contents

Project-Team COFFEE

1 Team members, visitors, external collaborators

2 Overall objectives

3 Research program

4 Application domains

4.1 Multiphase porous media flows and multi-physics coupling . . . . . . . . . . . . . . . . . . .
4.2 Particulate and mixture flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Fluid-structure interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Neurosciences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Fungal network growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Tumor growth and immune response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7 Self organization in population dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 Social and environmental responsibility

5.1 Impact of research results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 Highlights of the year

7 New software, platforms, open data

7.1 New software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.1 AP_PartFlow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.2 Mka3d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.3 Compass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.4 NS2DDV-M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.5 SimBiof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.6 CELIA3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 New platforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 Open data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8 New results

9 Bilateral contracts and grants with industry

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10 Partnerships and cooperations

10.1 International research visitors

10.1.1 Visits to international teams

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10.2 National initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
10.2.1 ANR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
10.2.2 National and European networks

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11 Dissemination
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
11.1 Journal
11.2 Scientific expertise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
11.3 Research administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
11.4 Teaching - Supervision - Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
11.4.1 Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
11.4.2 Supervision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
11.4.3 Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
11.5 Popularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
11.5.1 Interventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

12 Scientific production

12.1 Publications of the year

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Project COFFEE

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Project-Team COFFEE

Creation of the Project-Team: 2013 January 01

Keywords

Computer sciences and digital sciences

A6.1.1. – Continuous Modeling (PDE, ODE)

A6.1.4. – Multiscale modeling

A6.1.5. – Multiphysics modeling

A6.2.1. – Numerical analysis of PDE and ODE

A6.2.7. – High performance computing

A6.5. – Mathematical modeling for physical sciences

A6.5.2. – Fluid mechanics

A6.5.3. – Transport

A6.5.4. – Waves

Other research topics and application domains

B1.1.5. – Immunology

B1.1.8. – Mathematical biology

B3.3.1. – Earth and subsoil

B4.1. – Fossile energy production (oil, gas)

B4.2. – Nuclear Energy Production

B7.1. – Traffic management

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Inria Annual Report 2023

1 Team members, visitors, external collaborators

Research Scientists

• Thierry Goudon [Team leader, INRIA, Senior Researcher, HDR]

• Laurent Monasse [INRIA, HDR]

Faculty Members

• Florent Berthelin [Universite Cote d’Azur, Professor, until Aug 2023, HDR]

• Konstantin Brenner [Universite Cote d’Azur, Associate Professor]

• Remi Catellier [Universite Cote d’Azur, Associate Professor]

• Stéphane Junca [Universite Cote d’Azur, Associate Professor, HDR]

• Stella Krell [Universite Cote d’Azur, Associate Professor]

• Roland Masson [Universite Cote d’Azur, Professor, HDR]

Post-Doctoral Fellow

• Ali Haidar [INRIA, Post-Doctoral Fellow]

PhD Students

• Sebastian Baudelet [Universite Cote d’Azur]

• Charbel Ghasb Dite Ghosn [Universite Cote d’Azur]

• Paul Paragot [Universite Cote d’Azur, until Sep 2023]

• Christian Tayou Fotso [CNRS]

Interns and Apprentices

• Awadi Bedja Mroinkodo Said [INRIA, Intern, from Jun 2023 until Jul 2023]

• Nathan Imbert [Universite Cote d’Azur, from May 2023 until Jul 2023]

Administrative Assistant

• Marie-Cecile Lafont [INRIA]

External Collaborators

• Daniel Castanon-Quiroz [IIMAS-UNAM, Mexico]

• Jerome Droniou [Monash University]

Project COFFEE

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2 Overall objectives

The project aims at studying mathematical models issued from environmental and energy management
questions. We consider systems of PDEs of hydrodynamic type or hybrid fluid/kinetic systems. The
problems we have in mind involve unusual coupling, which in turn lead to challenging difficulties for
mathematical analysis and the need of original numerical solutions. By nature many different scales arise
in the problems, which allows to seek hierarchies of reduced models based on asymptotic arguments.
The topics require a deep understanding of the modeling issues and, as far as possible boosted by the
mathematical analysis of the equations and the identification of key structure properties, we wish to
propose innovative and efficient numerical schemes. To this end, the development of innovative Finite
Volumes schemes with unstructured meshes on complex geometries will be a leading topic of the team
activity.

3 Research program

Mathematical modeling and computer simulation are among the main research tools for environmental
management, risks evaluation and sustainable development policy. Many aspects of the computer codes
as well as the PDEs systems on which these codes are based can be considered as questionable regarding
the established standards of applied mathematical modeling and numerical analysis. This is due to
the intricate multiscale nature and tremendous complexity of those phenomena that require to set up
new and appropriate tools. Our research group aims at contributing to bridging the gap by developing
advanced abstract mathematical models as well as related computational techniques.

The scientific basis of the proposal is two–fold. On the one hand, the project is “technically–driven”:
it has a strong content of mathematical analysis and design of general methodology tools. On the other
hand, the project is also “application–driven”: we have identified a set of relevant problems motivated by
environmental issues, which share, sometimes in a unexpected fashion, many common features. The
proposal is precisely based on the conviction that these subjects can mutually cross-fertilize and that
they will both be a source of general technical developments, and a relevant way to demonstrate the skills
of the methods we wish to design.

To be more specific:

• We consider evolution problems describing highly heterogeneous flows (with different phases or
with high density ratio). In turn, we are led to deal with non linear systems of PDEs of convection
and/or convection-diffusion type.

• The nature of the coupling between the equations can be two-fold, which leads to different diffi-
culties, both in terms of analysis and conception of numerical methods. For instance, the system
can couple several equations of different types (elliptic/parabolic, parabolic/hyperbolic, parabolic
or elliptic with algebraic constraints, parabolic with degenerate coefficients....). Furthermore, the
unknowns can depend on different sets of variables, a typical example being the fluid/kinetic
models for particulate flows. In turn, the simulation cannot use a single numerical approach to
treat all the equations. Instead, hybrid methods have to be designed which raise the question of
fitting them in an appropriate way, both in terms of consistency of the discretization and in terms
of stability of the whole computation. For the problems under consideration, the coupling can
also arise through interface conditions. It naturally occurs when the physical conditions are highly
different in subdomains of the physical domain in which the flows takes place. Hence interface
conditions are intended to describe the exchange (of mass, energy...) between the domains. Again
it gives rise to rather unexplored mathematical questions, and for numerics it yields the question of
defining a suitable matching at the discrete level, that is requested to preserve the properties of the
continuous model.

• By nature the problems we wish to consider involve many different scales (of time or length
basically). It raises two families of mathematical questions. In terms of numerical schemes, the
multiscale feature induces the presence of stiff terms within the equations, which naturally leads
to stability issues. A clear understanding of scale separation helps in designing efficient methods,
based on suitable splitting techniques for instance. On the other hand asymptotic arguments can

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be used to derive a hierarchy of models and to identify physical regimes in which a reduced set of
equations can be used.

We can distinguish the following fields of expertise

• Numerical Analysis: Finite Volume Schemes, Well-Balanced and Asymptotic-Preserving Methods

– Finite Volume Schemes for Diffusion Equations and Viscous Flows

– Finite Volume Schemes for Conservation Laws

– Well-Balanced and Asymptotic-Preserving Methods

– Domain Decomposition Methods

• Modeling and Analysis of PDEs

– Kinetic equations and hyperbolic systems

– PDEs in random media

– Interface problems

4 Application domains

4.1 Multiphase porous media flows and multi-physics coupling

Our research focuses on the numerical modeling of multiphase porous media flows accounting for
complex geology and for nonlinear and multi-physics couplings. It is applied to various problems in
the field of energy such as the simulation of geothermal systems in collaboration with BRGM, of nuclear
waste repositories in collaboration with Andra, and of oil and gas recovery in collaboration with Total.
We are starting a new program through the Inria-IFPEN initiative. Our research directions include the
development of advanced numerical schemes adapted to polyhedral meshes and highly heterogeneous
media in order to represent more accurately complex geologies. A special focus is made on the modeling
of multiphase flows in network of faults or fractures represented as interfaces of co-dimension one
coupled to the surrounding matrix. We also investigate nonlinear solvers adapted to the nonlinear
couplings between gravity, capillary and viscous forces in highly heterogeneous porous media. In the
same line, we study new domain decomposition algorithms to couple non-isothermal compositional
liquid gas flows in a porous medium with free gas flows occurring at the interface between the ventilation
gallery and the nuclear waste repository or between a geothermal reservoir and the atmosphere. We
are exploring the coupling between the multiphase flow in the porous matrix and the solid mechanics
involved in opening fractures.

4.2 Particulate and mixture flows

We investigate fluid mechanics models referred to as “multi-fluids” flows. A large part of our activity is
more specifically concerned with the case where a disperse phase interacts with a dense phase. Such
flows arise in numerous applications, like for pollutant transport and dispersion, the combustion of
fuel particles in air, the modeling of fluidized beds, the dynamic of sprays and in particular biosprays
with medical applications, engine fine particles emission... There are many possible modelings of such
flows: microscopic models where the two phases occupy distinct domains and where the coupling arises
through intricate interface conditions; macroscopic models which are of hydrodynamic (multiphase) type,
involving non standard state laws, possibly with non conservative terms, and the so–called mesoscopic
models. The latter are based on Eulerian–Lagrangian description where the disperse phase is described
by a particle distribution function in phase space. Following this path we are led to a Vlasov-like equation
coupled to a system describing the evolution of the dense phase that is either the Euler or the Navier-
Stokes equations. It turns out that the leading effect in such models is the drag force. However, the role of
other terms, of more or less phenomenological nature, deserves to be discussed (close packing terms, lift
term, Basset force...). Of course the fluid/kinetic model is interesting in itself and needs further analysis
and dedicated numerical schemes. In particular, in collaboration with the Atomic Energy Commission

Project COFFEE

5

(CEA), we have proposed a semi-Lagrangian scheme for the simulation of particulate flows, extending
the framework established in plasma physics to such flows.

We also think it is worthwhile to identify hydrodynamic regimes: it leads to discuss hierarchies of
coupled hydrodynamic systems, the nature of which could be quite intriguing and original, while they
share some common features of the porous media problems. We are particularly interested in revisiting
the modeling of mixture flows through the viewpoint of kinetic models and hydrodynamic regimes. We
propose to revisit the derivation of new mixture models, generalizing Kazhikov-Smagulov equations,
through hydrodynamic asymptotics. The model is of “hybrid” type in the sense that the constraint
reduces to the standard incompressibility condition when the disperse phase is absent, while it involves
derivatives of the particle volume fraction when the disperse phase is present.

4.3 Fluid-structure interactions

The simulation of motions of solid bodies in a fluid, as well as fracturation, fissuration phenomena leads
to numerical difficulties: they can undergo deformations, fragmentation and contact which deform
dramatically the fluid domain, rendering remeshing techniques less effective. The numerical suite
Mka2d/Mka3d/Celia2d/Celia3d/Precis addresses this issue. On the solid side, the adopted discrete
element discretization works on general polyhedral meshes, and again uses different types of degree of
freedom, stored at the cell and face centers, with suitable reconstruction procedures in order to guaranty
the conservation properties. On the fluid side, we use a cut-cell approach designed in order to preserve
exactly the discrete mass and energy conservations for general Finite Volume methods. This approach
is an alternative to ALE methods which would require costly remeshing and can induce severe stability
conditions due to mesh deformations. It is particularly adapted to manage fragmentation events, which
lead to changes in the topology of the fluid domain. The delicate geometrical issues are handled by
using robust, efficient and fast geometric intersection procedures. Such issues are also investigated for
the modeling of urban floods; our methodologies on finite volume schemes on complex geometries
and domain decomposition methods are reinvested on such problems through the ANR project Top-up
(exploiting formal analogies between Shallow-Water equations and Richard’s equation in the regimes of
interest).

4.4 Neurosciences

The NeuroMod Institute for Modeling in Neuroscience and Cognition aims at promoting modeling as an
approach for integrating brain mechanisms and cognitive functions. It has selected the project proposed
by C. Guerrier and S. Krell about the modeling and simulation of the variations of the electric field in the
dendritic tree of neurons as well as the electrodiffusion of ions in the neuronal cytoplasm, considered as
an electrolyte (P. Paragot’s PhD thesis). Thus, the model is based on the Nernst-Planck equation coupled
to the Poisson equation; it has many similarities with convection-diffusion models arising for flows
in porous media. Difficulties arise from the multi-scale configuration, and the presence of boundary
layers between the cytoplasm, the membrane, and the external neuron’s environment. This leads to new
developments for the Discrete Duality Finite Volume (DDFV) framework and its application with domain
decomposition approaches.

4.5 Fungal network growth

Members of the team have started an original research program devoted to fungal network growth. We
started working on this subject through a collaboration with biologists and physicists at LIED (Université
Paris Diderot) and probabilists in CMAP (Ecole Polytechnique) and Université Paris Sud, involving Rémi
Catellier and Yves D’Angelo (team Atlantis). The motivation is to understand branching networks as
an efficient space exploration strategy, with fungus Podospora Anserina being the biological model
considered. This research is supported by ANR-project NEMATIC and by various local fundings.

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4.6 Tumor growth and immune response

We have developed a size and space structured model describing interaction of tumor cells with immune
cells based on a system of partial differential equations. This model is intended to describe the earliest
stages of this interaction and takes into account the migration of the tumor antigen-specific cytotoxic
effectors cells towards the tumor microenvironment by a chemotactic mechanism. This study reveals
cancer persistent equilibrium states as expected by biologists, as well as escape phases when protumoral
immune responses are activated. This effect which leads to persistent tumors at a controlled level was
inferred from clinical observations and demonstrations using mouse model. Therefore, the maintenance
of cancer in a viable equilibrium state represents a relevant goal of cancer immunotherapy. The mathem-
atical interpretation of the equilibrium state by means of eigenvalue problems and constrained equations,
has permitted us to develop new numerical algorithms in order to predict at low numerical cost the main
features of the equilibrium and to discriminate, in biologically relevant cases, the parameters that are the
most influential on the equilibrium.

4.7 Self organization in population dynamics

This topic is addressed mainly with Paulo Amorim (Univ. Federal Rio de Janeiro) and Fernando Peruani
(Lab. de Physique Théorique et Modélisation, Cergy Paris Université).

We are interested in the mathematical modeling of physico-biological phenomena that drive towards
a self-organization of a population of individuals reacting to external signals. It might lead to the forma-
tion of remarkable patterns or the following of traveling external signal. We develop microscopic and
hydrodynamic models for such phenomena, with a specific interest in the modeling of ant foraging.

5 Social and environmental responsibility

5.1 Impact of research results

The team results span various applications with impacts on energy (oil and gas recovery, nuclear waste
disposal, geothermal energy), carbon sequestration, health (tumor growth, biosprays, neurosciences)
and security (effects of explosions).

Accordingly, the team has tight connections with public or privates companies involved in such
research activities. In particular, our main software achievement, the code Compass, is co-developped
with BRGM. It is intended to be a reference code, addressing relevant benchmarks, for the simulation of
multiphase flows in complex environments.

6 Highlights of the year

L. Monasse defended his "Habilitation à diriger des recherches" (HDR) in October 2023.

The COFFEE project arrives to its term after 12 years of activities.

7 New software, platforms, open data

7.1 New software

7.1.1 AP_PartFlow

Functional Description: We are developing experimental codes, mainly based on Finite Differences,
for the simulation of particulate flows. A particular attention is paid to guaranty the asymptotic
properties of the scheme, with respect to relaxation parameters.

Contact: Thierry Goudon

Project COFFEE

7.1.2 Mka3d

Name: Mka3d

7

Keywords: Scientific computing, Elasticity, Elastodynamic equations

Functional Description: The Mka3d method simulates an elastic solid by discretizing the solid into
rigid particles. An adequate choice of forces and torques between particles allows to recover the
equations of elastodynamics.

URL: http://cermics.enpc.fr/~monassel/Mka3D/

Contact: Laurent Monasse

Partners: Ecole des Ponts ParisTech, CEA

7.1.3 Compass

Name: Computing Architecture to Speed up Simulation

Keywords: Finite volume methods, Porous media, High performance computing

Functional Description: Compass is a parallel code initiated in 2012 and co-developed by LJAD-Inria
Coffee and BRGM since 2015. It is devoted to the simulation of multiphase flows in porous media,
it accounts for non isothermal and compositional flows and includes complex network of fractures
or faults represented as interfaces of co-dimension one coupled to the surrounding matrix. The
discretization is based on vertex and cell unknowns and is adapted to polyhedral meshes and
heterogeneous media. The ComPASS code is co-developed since december 2016 by the partners of
the ANR CHARMS project including BGRM, LJAD-Inria Coffee, Storengy, MdS and LJLL with the
objective to develop a new generation simulator for geothermal systems focusing on fluids and
accounting for complex fault networks and wells.

URL: http://www.anr-charms.org/page/compass-code

Contact: Roland Masson

Participants: Simon Lopez, Farid Smai, Michel Kern, Yacine Ould Rouis, Nabil Birgle, Laurence Beaude,

Konstantin Brenner, Roland Masson

Partners: BRGM, Université Côte d’Azur (UCA)

7.1.4 NS2DDV-M

Name: 2D Navier-Stokes equations with variable density

Functional Description: The NS2DDV Matlab toolbox is an open-source program written in Matlab for
simulating 2D viscous, incompressible and inhomogeneous flows. The computation kernel of
the code is based on Finite Elements - Finite Volumes hybrid methods applied on the 2D Navier-
Stokes equations. It works on unstructured meshes and can include mesh refinements strategies.
We develop and freely distribute a new version of the Matlab code NS2DDV-M (equipped with a
graphic interface and an accurate documentation) to promote new collaborations in the domain,
allow some easy comparisons with concurrent codes on the same benchmark cases, and compare
alternative numerical solution methods.

URL: https://wikis.univ-lille.fr/painleve/ns2ddv/download

Contact: Caterina Calgaro

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7.1.5 SimBiof

Keywords: Bioinformatics, Chemistry

Functional Description: We are developing numerical methods, currently by using Finite Differences
approaches, for the simulation of biofilms growth. The underlying system of PDEs takes the
form of multiphase flows equations with conservation constraints and vanishing phases. The
numerical experiments have permitted to bring out the influence of physical parameters on the
multidimensional growth dynamics.

Contact: Thierry Goudon

7.1.6 CELIA3D

Name: CELIA3D

Keywords: Fluid mechanics, Multi-physics simulation

Functional Description: The CELIA3D code simulates the coupling between a compressible fluid flow
and a deformable structure. The fluid is handled by a Finite Volume method on a structured
Cartesian grid. The solid is handled by a Discrete Element method (Mka3d scheme). The solid
overlaps the fluid grid and the coupling is carried out with immersed boundaries (cut cells) in a
conservative way.

URL: http://cermics.enpc.fr/~monassel/CELIA3D/

Contact: Laurent Monasse

Partners: Ecole des Ponts ParisTech, CEA

7.2 New platforms

Participants: Roland Masson , Konstantin Brenner , Florent Chave , Ali Haidar ,
Mohamed Laazari , Konstantin Brenner , Thierry Goudon , Miranda
Boutilier , Paul Paragot , Charbel Ghosn , Sebastian Baudelet , Laurent
Monasse , Christian Tayou Fotso .

• Our main software achievement is the code ComPASS. It is developped since 2013 through several
collaborations, by means of PhD and postdocs, with BRGM, ANDRA, Maison de la Simulation,
Storengy, LJLL and has benefitted from the support of Carnot Institute and ANR through the project
Charms. (The project has not been fortunate enough to receive an engineer support from Inria,
though.) The objective is to propose an alternative to commercial codes, like Tough2, which faces
limitations, at least for some specific situations. The code is an open source parallel code, it works
on complex geometry, with complex unstructured meshes, it accounts for faults, fractures and
deals with polyphasic and compositional flows. It applies in particular to geothermal flows.

Since 2021, both ANDRA and BRGM are committed to the partnership and the development of
ComPASS. The management of the code is shared with S. Lopez and L. Beaude from BRGM. The
common ANDRA/BRGM roadmap explicitly refers to ComPASS in the simulation strategy of these
organisms. The code is distributed from the Inria Gitlab platform under the opensource license
CeCILL2.1/GPLv3. It has been effectively used for several user-cases:

– for ANDRA to study the evolution of the repository site and the desaturation of the walls of

the aeration galleries, in the framework of the Donut-Eurad project;

– for BRGM for geothermal applications like Géodenergies Reflet, Heatstore, the modeling of

Paris bassin de Paris, Lamentine Bay, Bouillante, simulation of Le Teil seismic event. . .

Further information available on the Compass website.

Project COFFEE

9

• The numerical suite Mka2d/Mka3d/Celia2d/Celia3d/Precis simulates an elastic solid by discret-
izing the solid into rigid particles in 2d or 3d configurations. An adequate choice of forces and
torques between particles allows to recover the equations of elastodynamics. The code Celia2d-3d is
devoted to fluid-structure interactions. The code Precis is a more mature version of these softwares,
with further visualization procedures. The codes are on a GitLab plateform, with the objective of a
diffusion beyond our circle of close collaborators. Moreover, a part of our methodologies aim at
being reinvested in industrial collaborations (in discussion).

Further information available on the website: Mka3d and Celia3d

• We are also developing several prototype codes, for internal use. For instance we have a quite
well advanced Scilab code for the simulation of Euler systems, with Cartesian and unstructured
meshes, and a fortran DDFV code for the simulation of Navier-Stokes equations, including domain
decomposition functionalities. In the same category falls the Python code based on nonlinear
diffusive equations for urban floods modeling. They are regularly improved; in particular through
the commitment of PhD students. We develop also specific simulation tools for the applications of
our academic partners.

7.3 Open data

Coffee supports as far as possible Open Data objectives: the main software achievements, the code
COMPASS, co-developped with BRGM is open source. The team is also involved in the journal SMAI
Journal of Computational Mathemarics, a publication which is free of charges for authors and readers,
published through the CNRS-UGA plateform Mersenne.

8 New results

Participants:

Thierry Goudon, Roland Masson, Laurent Monasse, Stella Krell,
Florent Berthelin,
Konstantin Brenner,
Daniel Castanon-Quiroz, Remi Catellier, Ali Haiddar, Sebastian Baude-
let, Paul Paragot, Charbel Ghosn, Christian Tayou Fotso.

Stephane

Junca,

New results are concerned with

• Analysis and development of Finite Volume Methods for polyphasic flows in porous media with

fractures

• Analysis and development of Finite Volume Methods for complex flows

• Domain decomposition methods for Discrete Duality Finite Volume schemes

• Analysis of PDEs describing the behavior of classical and quantum particles interacting with their

environment: Landau damping and dissipation mechanisms

• Analysis of systems of conservation laws: stochastic source terms and regularity analysis by means

of fractional BV (Bounded Variations) spaces.

• Simulation of fluid-structure interactions

• Modeling of tumor-immune system interactions

9 Bilateral contracts and grants with industry

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Inria Annual Report 2023

Participants:

Thierry Goudon, Roland Masson, Laurent Monasse, Konstantin Bren-
ner.

The research of the team is regularly supported by several contracts with industrial partners: BRGM,
Storengy, IFP-EN, on scientific computing issues in geosciences. This has permitted to welcome many
PhD and postdocs. The transfer strategy is built on the development of the opensource code ComPASS,
specifically oriented towards the simulation of mass and heat transfers in fractured media. The code is
identified by the consortium Andra/BRGM as an alternative of the commercial code Tough2 for security
simulations of transient hydraulic-gas flows.

• BRGM-Andra (2022-2025) funding of Mohamed Laaziri’s PhD thesis

• IFPEN/Inria initiative (2022-2023) funding of Ali Haidar’s postdoctoral fellowship

• BRGM (2020-2023) for a participation to the PhD thesis of Sabrine Ben Rhouma, Univ. Orléans

• european project EURAD, WP DONUTS, funding of Florent Chave’s postdoctoral fellowship

• BRGM/Storengy (2019-2022) funding of Daniel Castanon-Quiroz postdoctoral fellowship

We are currently in touch with the company Altair for the development of simulation tools for fluid
structure interactions problems and with the Atomic Energy Commission at Cadarache about simulations
for safety issues in nuclear reactors.

10 Partnerships and cooperations

Participants:

Thierry Goudon, Roland Masson, Laurent Monasse, Stella Krell,
Florent Berthelin,
Konstantin Brenner,
Stephane
Daniel Castanon-Quiroz, Remi Catellier, Jerome Droniou.

Junca,

10.1 International research visitors

10.1.1 Visits to international teams

Research stays abroad In the continuation of the assosiated team HDTM with Monash University in
Australia, Roland Masson visited Jerome Droniou for a couple of month in 2023, working on the analysis
of finite volume schemes for the simulation of flows in porous media.

10.2 National initiatives

10.2.1 ANR

• ANR TOP-UP (2020-2024), Konstantin Brenner, Roland Masson: LJLL CNRS-Sorbonne Univ., Ecole
des Ponts, LNCC Brazil. The project is devoted to the numerical modeling of urban floods, helping
to size and position protective systems including dams, dikes or rainwater drainage network. This
project gives raise to a PhD thesis and it involves a collaboration with F. Valentin, International
Inria Chair.

• ANR JCJC GeoFun (ANR-19-CE46-0010, 2020-2024) The project GEOphysical Flows with UNified
models is coordinated by Martin Parisot, member of the team CARDAMOM, from Inria Bordeaux,
CNRS and University of Bordeaux. This project explores geophysical flows and the modeling of
aquifers, wishing to propose a unified numerical library for the coupling between shallow free
surface flows and the underground flow in porous medium.

Project COFFEE

11

• ANR JCJC COMODO (2019–2023) led by V. Ehrlacher (Ecole des Ponts), fosters the collaboration
with C. Cancès (Inria Lille), M. Burger (FAU Erlangen), J. Frederik Pietschmann (TU Chemnitz). It is
concerned with the simulation of cross-diffusion systems set on moving geometries, with on-going
collaborations.

• ANR JCJC NEMO (2021–2025) led by L. Giraldi (PI, Centre Inria d’Université Côte d’Azur), with
M. Binois (Centre Inria d’Université Côte d’Azur), C. Prud’homme (Univ. Strasbourg), S. Régnier
(Sorbonne Univ.) is concerned with the development of fictious domain methods for models of
micro-swimmers. We are concerned by the development of fluid-structure methodologies for the
simulation of micro-swimmers. The project has supported a master internship and a PhD has
started in 2023.

• ANR PRC NEMATIC (2021–2025): led by researchers of the Laboratoire Interdisciplinaire des
Energies de Demain, this project is concerned with the developpement of models and methods for
studying hyphal networks. We propose a derivation from branching processes of kinetic-like and
hydrodynamic models, and numerical procedures in order to capture accurately the propagating
front. Starting from a microscopic description of the Spitzenkörper (vesicules in hyphal cells which
drive the growth of the cellular membrane), we intend to propose a chemically and physically
informed model for branching rates. One PhD thesis is concerned with this project, and another
one is going to start.

10.2.2 National and European networks

• GdR MathGeoPhy

The research group MathGeoPhy has activities centered around scientific computing, design of new
numerical schemes and mathematical modeling (upscaling, homogenization, sensitivity studies,
inverse problems,...). Its goal is to coordinate research in this area, as well as to promote the
emergence of focused groups around specific projects

• GdR Mamovi

The team is involved in the activities of the research group dedicated to applications to life sciences.

• S. Junca is involved in GdR 3437 DYNOLIN “Dynamique non linéaire” and GdR MecaWave.

• LJAD-Inria and BRGM are the French partners of the Norvergian, German French project InSPiRE
"International Open Source Simulation Software Partnership in Research and Education” which
has just been accepted by the Research Council of Norway with the code ComPASS as one of the
softwares of this project together with Dune, Dumux and OPM.

• Coffee is involved in the national project PEPR Sous-sol, with tight connections with IFP-EN. The

post-doctoral fellowship of Ali Haiddar will be continued on this program.

11 Dissemination

Participants:

Thierry Goudon, Roland Masson, Laurent Monasse, Stella Krell,
Florent Berthelin, Stephane Junca, Konstantin Brenner.

11.1 Journal

Member of the editorial boards T. Goudon is co-editor of chief of SMAI Journal of Computational
Mathematics.

Reviewer - reviewing activities We are regularly committed for evaluation reports in journals of the
mathematical analysis or scientific comouting communities (SIAM J. Math. Anal., Achiv. Rat. Mech. Aanl.,
Ann. PDEs, SIAM J. Scient. Comput., SIAM J. Numer. Anal., J. Comput. Phys., etc)

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Inria Annual Report 2023

11.2 Scientific expertise

T. Goudon is Scientific Officer at the Ministre for Research and Higher Education. As such he participated
to the Boards of CIRM, CIMPA, IHES, IHP. He is involved in the follow-upo and evaluation of various
national programs (PEPR, IA plan...).

11.3 Research administration

L. Monasse is an elected member of the Scientific Committee of EUR SPECTRUM at Université Côte
d’Azur.

L. Monasse is member of the Steering Committee of "Maison de la Simulation et Interactions" at

Université Côte d’Azur.

T. Goudon has been chair of the Scientific Board of the Department of Mathematics at Université

Côte d’Azur. He is now Chair of the research unit J. A. Dieudonné.’

T. Goudon is the Chair of the Nice Comitee, for postdoc selection, and attribution of reduction of

teaching duties for faculties collaborating with Inria teams.

11.4 Teaching - Supervision - Juries

11.4.1 Teaching

• Florent Berthelin, Master 2 Mathématiques fondamentales, Univ Côte d’Azur, 120h.

• Florent Berthelin, Chair of the Master 2 Mathématiques fondamentales, Univ Côte d’Azur.

• Florent Berthelin, Analysis, L2, Univ Côte d’Azur, 72h.

• Laurent Monasse, Mathématiques pour l’ingénieur 2, L3, 36h., Polytech’Nice Sophia, Univ. Cote

d’Azur

• Laurent Monasse, Modèles numériques pour les EDPs, M1, 12h., Polytech’Nice Sophia, Univ. Cote

d’Azur

• Thierry Goudon: CliMaths program. Lecture on traffic flows modeling, Ecole Centrale de Marseille

• Thierry Goudon: Master, lectures on signal processing, Univ Côte d’Azur

• Thierry Goudon: Master, lecture on PDEs, Univ. Côte d’Azur

• Stella Krell: Master, Finite Volume methods, Univ. Côte d’Azur

11.4.2 Supervision

• Paul Paragot is supervised by S. Krell and C. Guerrier on Numerical analysis, Modeling and Data ana-
lysis : characterizing and localizing calcium sources in the neuronal denditric tree, to understand
the foundations of cognitive development, with a funding from MeuroMod Institute.

• Christian Tayou Fotso is supervised by Thierry Goudon on Modeling and Simulation of Tumor

Growth and Immune Response Interactions, funded by the Interaction program of CNRS.

• Charbel Ghosn is supervised by T. Goudon and S. Minjeaud on Multidimensional simulations of

fluid equations with schemes on staggered grids.

• Sebastian Baudelet is supervised by R. Catellier on Modeling and simulation of branching in

mycelian networks.

11.4.3 Juries

T. Goudon is member of the Jury of agregation, the national competition to hire teachers in mathematics.

Project COFFEE

13

11.5 Popularization

11.5.1 Interventions

Laurent Monasse participates in program "Cordées de la réussite" with various scientific presentations at
high-school level.

Members of the team participate to the local initiatives, like Fete de la Sciences, through the incitent-

ives of the Mathemarium or Terra Numerica.

12 Scientific production

12.1 Publications of the year

International journals

[1] L. Beaude, F. Chouly, M. Laaziri and R. Masson. ‘Mixed and Nitsche’s discretizations of Coulomb
frictional contact-mechanics for mixed dimensional poromechanical models’. In: Computer Meth-
ods in Applied Mechanics and Engineering 213 (Aug. 2023), p. 116124. DOI: 10.1016/j.cma.2023
.116124. URL: https://hal.science/hal-03949272.

[2] K. Brenner, F. Chave and R. Masson. ‘Gradient discretization of a 3D-2D-1D mixed-dimensional
diffusive model with resolved interface, application to the drying of a fractured porous medium’.
In: IMA Journal of Numerical Analysis 43.6 (4th Nov. 2023), pp. 3522–3563. DOI: 10.1093/imanum
/drac076. URL: https://hal.science/hal-04365765.

[3] C. Cancès, V. Ehrlacher and L. Monasse. ‘Finite Volumes for the Stefan-Maxwell Cross-Diffusion
System’. In: IMA Journal of Numerical Analysis (5th June 2023). DOI: 10.1093/imanum/drad032.
URL: https://hal.science/hal-02902672.

[4] D. Castanon Quiroz and D. Di Pietro. ‘A pressure-robust HHO method for the solution of the
incompressible Navier-Stokes equations on general meshes’. In: IMA Journal of Numerical Analysis
(Apr. 2023). DOI: 10.1093/imanum/drad007. URL: https://hal.science/hal-03608248.

[5] B. Guelmame. ‘Global weak solutions of the Serre–Green–Naghdi equations with surface tension’.
In: Annales de l’Institut Henri Poincaré C, Analyse non linéaire (2023). URL: https://hal.science
/hal-03585433.

[6] B. Guelmame. ‘On a Hamiltonian regularization of scalar conservation laws’. In: Discrete and

Continuous Dynamical Systems - Series A (2023). URL: https://hal.science/hal-02512810.

International peer-reviewed conferences

[7] C. Ghosn, T. Goudon and S. Minjeaud. ‘A MUSCL-scheme on staggered grids for the Euler equations
on unstructured meshes’. In: Springer Proceedings in Mathematics & Statistics. FVCA 2023 - Interna-
tional Conference on Finite Volumes for Complex Applications. Vol. PROMS-433. Finite Volumes for
Complex Applications X—Volume 2, Hyperbolic and Related Problems FVCA10, Strasbourg, France,
October 30, 2023–November 03, 2023. Strasbourg, France: Springer, 20th Nov. 2023, pp. 141–149.
DOI: 10.1007/978-3-031-40860-1_15. URL: https://hal.science/hal-04294739.

[8]

S. Krell and J. Moatti. ‘Structure-preserving schemes for drift-diffusion systems on general meshes:
DDFV vs HFV’. In: Finite Volumes for Complex Applications X. Vol. Springer Proceedings in Math-
ematics and Statistics. Springer Proceedings in Mathematics & Statistics 432. Strasboug, France:
Springer Nature Switzerland, 1st Oct. 2023, pp. 325–334. DOI: 10.1007/978-3-031-40864-9_27.
URL: https://hal.science/hal-04037264.

Conferences without proceedings

[9] L. Beaude, F. Chouly, M. Laaziri and R. Masson. ‘Mixed and Nitsche’s discretizations of frictional
contact-mechanics in fractured porous media’. In: 14th International Conference on Large-Scale
Scientific Computations. Sozopol, Bulgaria, 5th June 2023. URL: https://hal.science/hal-040
13887.

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Inria Annual Report 2023

Edition (books, proceedings, special issue of a journal)

[10]

J. Droniou, M. Laaziri and R. Masson, eds. Thermodynamically Consistent discretisation of a Thermo-
Hydro-Mechanical model. Vol. 432. Springer Proceedings in Mathematics & Statistics. Springer
Nature Switzerland, 1st Oct. 2023, pp. 265–273. DOI: 10.1007/978-3-031-40864-9_21. URL:
https://hal.science/hal-04105527.

Reports & preprints

[11] A. Armandine Les Landes, L. Beaude, D. Castanon Quiroz, L. Jeannin, S. Lopez, F. Smaï, T. Guillon
and R. Masson. Geothermal Modeling in Complex Geological Systems with ComPASS. 2023. URL:
https://brgm.hal.science/hal-04246471.

[12] V. Ayot, M. Badsi, Y. Barsamian, A. Crestetto, N. Crouseilles, M. Mehrenberger, A. Prost and C.
Tayou-Fotso. High order numerical methods for Vlasov-Poisson models of plasma sheaths. 6th Jan.
2023. URL: https://inria.hal.science/hal-03926305.

[13] M. Boutilier, K. Brenner and V. Dolean. Trefftz approximation space for Poisson equation in perfor-

ated domains. 2023. URL: https://hal.science/hal-04072474.

[14] K. Brenner. On global and monotone convergence of the preconditioned Newton’s method for some

mildly nonlinear systems. 2023. URL: https://hal.science/hal-03876457.

[15] T. Goudon, P. Lafitte and C. Mascia. Shock profiles for hydrodynamic models for fluid-particles flows

in the flowing regime. 2023. URL: https://hal.science/hal-04113011.

[16] T. Goudon and S. Minjeaud. An explicit well-balanced scheme on staggered grids for barotropic Euler

equations. 20th Nov. 2023. URL: https://hal.science/hal-04294768.

[17] C. Guerrier, S. Krell and P. Paragot. Nonlinear coupling of the Poisson-Nernst Planck system of
equations using the Discrete Duality Finite Volumes method, application to ionic and voltage
dynamics in neuronal compartments. 16th Jan. 2024. URL: https://cnrs.hal.science/hal-04
385924.

[18] A. Haidar, R. Masson, J. Droniou, I. Faille and G. Enchéry. A bubble VEM-fully discrete polytopal
scheme for mixed-dimensional poromechanics with frictional contact at matrix fracture interfaces.
2024. URL: https://hal.science/hal-04343287.
<scratchpad>
- Main topic: Research Centre COFFEE (Complex Flows For Energy and Environment) at Inria Centre at Université Côte d’Azur
- Key points:
  - Focus on numerical modeling of multiphase porous media flows and multi-physics coupling
  - Applications in energy, biology, and earth sciences
  - Research program includes analysis and development of Finite Volume Methods for polyphasic flows in porous media
  - Project COFFEE aims to study mathematical models for environmental and energy management questions
  - Team members include researchers from Inria, Université Côte d’Azur, and external collaborators
- Structure: The document is organized into sections for Project-Team COFFEE, Activity Report, and Research Program
- Potential artifacts to ignore: Links, HTML tags, and web-related elements
</scratchpad>

<final_summary>
The COFFEE project, located at the Inria Centre at Université Côte d’Azur, focuses on numerical modeling of multiphase porous media flows and multi-physics coupling. The research program aims to study mathematical models for environmental and energy management questions, with a particular emphasis on polyphasic flows in porous media. The team, comprising researchers from Inria and Université Côte d’Azur, has developed various numerical schemes, including Finite Volume Methods, to tackle complex problems in energy, biology, and earth sciences. The project's goal is to contribute to bridging the gap between mathematical modeling and numerical analysis for environmental and energy management applications.
The COFFEE project, located at the Inria Centre at Université Côte d’Azur, focuses on numerical modeling of multiphase porous media flows and multi-physics coupling. The research program aims to study mathematical models for environmental and energy management questions, with a particular emphasis on polyphasic flows in porous media. The team, comprising researchers from Inria and Université Côte d’Azur, has developed various numerical schemes, including Finite Volume Methods, to tackle complex problems in energy, biology, and earth sciences. The project's goal is to contribute to bridging the gap between mathematical modeling and numerical analysis for environmental and energy management applications.