RESEARCH CENTRE

Inria Saclay Centre

2023
ACTIVITY REPORT

IN PARTNERSHIP WITH:

Office national d’études et de recherches
aérospatiales

Project-Team

GAMMAO

Adaptive Mesh Generation and Advanced
Numerical Methods

DOMAIN

Applied Mathematics, Computation and
Simulation

THEME

Numerical schemes and simulations

Contents

Project-Team GAMMAO

1 Team members, visitors, external collaborators

2 Overall objectives

3 Research program

4 Application domains

5 New software, platforms, open data

5.1 New software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 GHS3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 HEXOTIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.3 FEFLOA-REMESH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.4 Metrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.5 Wolf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.6 ViZiR4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 New results

6.1 Evaluation of heat transfert performance of a film-cooled turbine vane using metric-based
anisotropic mesh adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Mixed-element mesh and Anisotropic adapted mesh comparison . . . . . . . . . . . . . . .
6.3 Pixel-exact rendering for high-order meshes and solutions
. . . . . . . . . . . . . . . . . . .
6.4 High-Order Mesh Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Study of mesh and shape optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6 Improving Adjoint Problem Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7 Accuracy analysis for a Mixed Element Volume scheme . . . . . . . . . . . . . . . . . . . . .
6.8 Addition of Mixing Plane in Wolf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 Bilateral contracts and grants with industry

7.1 Bilateral contracts with industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

2

2

3

4

4
4
4
4
5
5
5
5

6

6
6
6
7
7
7
8
8

8
8

8 Partnerships and cooperations

9
9
8.1 European initiatives: NumPEx - Should start in 2023-2025 . . . . . . . . . . . . . . . . . . . .
8.2 European initiatives: NextAIR - 2023-2026 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

9 Scientific production

9.1 Publications of the year
9.2 Cited publications

11
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Project GAMMAO

1

Project-Team GAMMAO

Creation of the Project-Team: 2023 January 01

Keywords

Computer sciences and digital sciences

A6.2. – Scientific computing, Numerical Analysis & Optimization

A6.2.7. – High performance computing

A6.2.8. – Computational geometry and meshes

A6.5.1. – Solid mechanics

A6.5.2. – Fluid mechanics

Other research topics and application domains

B5.2.3. – Aviation

B5.2.4. – Aerospace

B9.5.1. – Computer science

B9.5.2. – Mathematics

B9.5.3. – Physics

B9.5.5. – Mechanics

2

Inria Annual Report 2023

1 Team members, visitors, external collaborators

Research Scientists

• Frederic Alauzet [Team leader, INRIA, Senior Researcher, from Mar 2023, HDR]

• Guillaume Puigt [Team leader, ONERA, Senior Researcher, from Mar 2023, HDR]

• Julien Vanharen [INRIA, Senior Researcher, from Mar 2023]

PhD Students

• Gabriel Barreau [ONERA, from Mar 2023]

• Thomas Gauchery [INRIA, from Mar 2023]

• Andrea Gobbi [INRIA, from Nov 2023]

• Eloi Guilbert [INRIA, from Mar 2023]

• Lucien Rochery [INRIA, from Mar 2023 until Mar 2023]

Technical Staff

• Loïc Maréchal [INRIA, Engineer, from Aug 2023]

• Matthieu Maunoury [INRIA, Engineer]

• Francois Pechereau [ONERA, Engineer, from Mar 2023]

• Christophe Peyret [ONERA, Engineer, from Mar 2023]

• Cosimo Tarsia Morisco [INRIA, Engineer, from Mar 2023]

Interns and Apprentices

• Riccardo Giordani [INRIA, from Mar 2023 until Aug 2023]

• Andrea Gobbi [INRIA, Intern, from Mar 2023 until Aug 2023]

Administrative Assistant

• Mariana De Almeida [INRIA, from Mar 2023]

2 Overall objectives

Numerical simulation has been booming over the last thirty years, thanks to increasingly powerful
numerical methods, computer-aided design (CAD) and the mesh generation for complex 3D geometries,
and the coming of supercomputers (HPC). The discipline is now mature and has become an integral part
of design in science and engineering applications. This new status has led scientists and engineers to
consider numerical simulation of problems with ever increasing geometrical and physical complexities.
A simple observation of this chart

CAD −→ Mesh −→ Solver −→ Visualization / Analysis .

shows: no mesh = no simulation along with "bad" mesh = wrong simulation. We have concluded
that the mesh is at the core of the classic computational pipeline and a key component to significant
improvements. Therefore, the requirements on meshing methods are an ever increasing need, with
increased difficulty, to produce high quality meshes to enable reliable solution output predictions in an
automated manner. These requirements on meshing or equivalent technologies cannot be removed and
all approaches face similar issues.

Project GAMMAO

3

Gamma’s research program is motivated by four grand challenges in order to achieve certification and
high-fidelity in the numerical simulation pipeline. The goal is to deliver innovative and ground-breaking
solutions to each step of the adaptive numerical simulation pipeline. Not surprisingly, these challenges
(and the themes that result) are clearly indicated in the NASA CFD Vision 2030 Study [41] and have
been mentioned recurrently during the previous evaluations of the Gamma3 team where they have been
judged as very ambitious and long-term. The four grand challenges are:

1. Geometric modeling. The goal is to address geometry modeling issues and their interactions with
the meshing pipeline. To this end, Gamma will develop more versatile and robust geometry and modeling
processes to be embedded within meshing tools.

2. Enhanced generic meshing algorithms. Gamma will pursue its work on state-of-the-art mesh-
ing technologies which should fulfill these three requirements: adaptation, high-order and large size.
Mesh adaptation and high-order meshing will be based on the well-posed metric-based mathematical
framework. The generation of large size mesh will be achieved with hybrid parallelism (multi-thread and
MPI).

3. Toward certified numerical solutions to the Navier-Stokes equations. This research axis will focus
on error estimates and robust numerical schemes (flow solver). Gamma will primarily focus on the design
of uncertainty aware RANS error estimates. We will pursue the work on anisotropic mesh adaptation for
the turbulent Navier-Stokes equations with moving geometries. We envision to develop a new high-order
mesh-adaptive solution platform which requires to design high-order error estimates and a high-order
flow solver.

4. Advanced visualization of mesh and solution. High-order representations (both on the solver and
meshing sides) use higher-degree polynomials to interpolate solution data. The challenge is to develop
algorithms for pixel exact rendering of high-order meshes and solutions which will provide the potential
to reveal features that otherwise might be masked by classic visualization approaches. The visualization
software will be used for pre and post processing by interfacing all the Gamma’s software components.

These four grand challenges cover the whole numerical simulation pipeline depicted below. The
geometric modeling is represented by the green part, the enhanced generic meshing algorithms by the
blue part, the certification of Navier-Stokes simulations by the red part, and the advanced mesh and
solution visualization by the brown part. We can also see the clear interaction between each research axis.

Most of the proposed meshing developments and technologies are generic and can be applied to a
broader field of applications in order to increase the impact of this research program. Flow solver devel-
opments and technologies focus specifically on CFD with applications to aerospace, turbomachinery,
and defense.

3 Research program

The main axes are:

• Geometric Modeling:

– High-fidelity discrete CAD kernel.

– Continuous parametric CAD kernel.

• Enhanced Generic Meshing Algorithm:

– Adaptation (extreme anisotropy, metric-aligned, metric-orthogonal).

CADSurfaceMeshVolumeMeshSolutionResultAnalysisError Analysis4

Inria Annual Report 2023

– High-order (tetrahedra, hexahedra, boundary layer, adapted).

– Large meshes (tetrahedra, hexahedra, adapted).

– Moving mesh methods for moving geometries.

• Toward Certified Solutions to the Navier-Stokes Equations:

– Flow solver and adjoints (Finite Volumes, Finite Elements, Flux Reconstruction).

– Error estimates and correctors.

• Advanced Mesh and Solution Visualisation:

– Pixel exact rendering (High-Order mesh, High-Order solution).

– Pre-processing and post-processing.

4 Application domains

Our research in mesh generation, mesh adaptation and certification of the Numerical Simulation Pipeline
finds applications in several different domains such as aviation and aerospace but also all fields where
computation and simulation are used: fluid mechanics, solid mechanics, solving wave equations (acous-
tic, electromagnetism...), energy or biomedical.

5 New software, platforms, open data

5.1 New software

5.1.1 GHS3D

Keywords: Tetrahedral mesh, Delaunay, Automatic mesher

Functional Description: GHS3D is an automatic volume mesher

URL: http://www.meshgems.com/volume-meshing.html

Contact: Frederic Alauzet

Participants: Paul Louis George, Adrien Loseille, Frederic Alauzet

5.1.2 HEXOTIC

Keywords: 3D, Mesh generation, Meshing, Unstructured meshes, Octree/Quadtree, Multi-threading,

GPGPU, GPU

Functional Description: Input: a triangulated surface mesh and an optional size map to control the size

of inner elements.

Output: a fully hexahedral mesh (no hybrid elements), valid (no negative jacobian) and conformal
(no dangling nodes) whose surface matches the input geometry.

The software is a simple command line that requires no knowledge on meshing. Its arguments are
an input mesh and some optional parameters to control elements sizing, curvature and subdomains
as well as some features like boundary layers generation.

URL: https://team.inria.fr/gamma/gamma-software/hexotic/

Contact: Loic Marechal

Participant: Loic Marechal

Partner: Distene

Project GAMMAO

5

5.1.3 FEFLOA-REMESH

Keywords: Scientific calculation, Anisotropic, Mesh adaptation

Functional Description: FEFLOA-REMESH is intended to generate adapted 2D, surface and volume
meshes by using a unique cavity-based operator. The metric-aligned or metric-orthogonal ap-
proach is used to generate high quality surface and volume meshes independently of the anisotropy
involved.

URL: https://pages.saclay.inria.fr/adrien.loseille/index.php?page=softwares

Contact: Adrien Loseille

Participants: Adrien Loseille, Frederic Alauzet, Rémi Feuillet, Lucien Rochery, Lucille-Marie Tenkes

5.1.4 Metrix

Name: Metrix: Error Estimates and Mesh Control for Anisotropic Mesh Adaptation

Keywords: Meshing, Metric, Metric fields

Functional Description: Metrix is a software that provides by various ways metric to govern the mesh
generation. Generally, these metrics are constructed from error estimates (a priori or a posteriori)
applied to the numerical solution. Metrix computes metric fields from scalar solutions by means of
several error estimates: interpolation error, iso-lines error estimate, interface error estimate and
goal oriented error estimate. It also contains several modules that handle meshes and metrics.
For instance, it extracts the metric associated with a given mesh and it performs some metric
operations such as: metric gradation and metric intersection.

URL: https://pages.saclay.inria.fr/frederic.alauzet/software.html

Contact: Frederic Alauzet

Participants: Adrien Loseille, Frederic Alauzet

5.1.5 Wolf

Keyword: Scientific calculation

Functional Description: Numerical solver for the Euler and compressible Navier-Stokes equations with
turbulence modelling. ALE formulation for moving domains. Modules of interpolation, mesh op-
timisation and moving meshes. Wolf is written in C++, and may be later released as an opensource
library. FELiScE was registered in July 2014 at the Agence pour la Protection des Programmes under
the Inter Deposit Digital Number IDDN.FR.001.340034.000.S.P.2014.000.10000.

URL: https://pages.saclay.inria.fr/frederic.alauzet/software.html

Contact: Frederic Alauzet

Participants: Frederic Alauzet, Adrien Loseille, Rémi Feuillet, Lucille-Marie Tenkes, Francesco Clerici,

Cosimo Tarsia Morisco

5.1.6 ViZiR4

Name: ViZiR4

Keywords: Visualization, Pixel-exact rendering, Instant rendering, High order methods

Functional Description: Its main features are: - Light, simple and interactive visualization software. -
Surface and volume (tetrahedra, pyramids, prisms, hexahedra) meshes. - Pixel exact rendering
of high-order solutions on straight elements. - Almost pixel exact rendering on curved elements
(high-order meshes). - Post-processing tools, such as picking, isolines, clipping, capping.

6

Inria Annual Report 2023

URL: https://pyamg.saclay.inria.fr/vizir4.html

Publications: hal-01686714, hal-02950321, hal-03539257

Contact: Adrien Loseille

Participants: Adrien Loseille, Matthieu Maunoury, Frederic Alauzet

6 New results

6.1 Evaluation of heat transfert performance of a film-cooled turbine vane using

metric-based anisotropic mesh adaptation

Participants:

Frederic Alauzet (correspondant).

We show the ability of metric-based anisotropic mesh adaptation to accurately predict the flow field on
a particularly complex test case: a film-cooled turbine vane. Film-cooled turbine blades are very complex
turbomachinery geometries because they are composed of a cooling network and many different-shaped
film-cooling holes which makes these geometries extremely complex to mesh with structured meshing
approaches (like multi-block hexahedral meshing methods). Consequently, metric-based anisotropic
mesh adaptation seems quite appropriate for such applications as it has demonstrated that it provides
automation of the whole process and it allows significant gains in terms of simulation accuracy by
capturing coherent flow features proper to the turbomachinery physics. The film-cooled turbine vane
simulation was made possible because the mesh-adaptive solution platform was successfully extended
to periodic flows and domains.

6.2 Mixed-element mesh and Anisotropic adapted mesh comparison

Participants:

Frederic Alauzet, Cosimo Tarsia Morisco (correspondant).

In order do to a fair comparison, the same numerical strategy must be used when dealing full-
tetrahedral meshes as well as hybrid/structured meshes. For these reason, an appropriate numerical
strategy was elaborated for extending the Mixed Finite Element-Finite Volume (MEV) scheme to adapted
meshes composed of both triangular and quadrangular elements, called hybrid meshes [23, 22] (also
named mixed-element meshes [37, 39]). Particularly, in the context of mesh adaptation, a specific metric
gradation process is proposed to favor the clustering of structured elements at wall boundaries. The
details are given in [40].

One important challenge is the accurate discretization of turbulence. In the context of RANS simula-
tions, we investigated the numerical behavior of the Spalart-Allmaras SA-neg-QCR2000-R one-equation
turbulence model for the anisotropic mesh adaptation process. The solutions obtained on the adapted
unstructured meshes are compared with those obtained on some "best-practice" structured/hybrid
meshes. Same numerical schemes are adopted to perform a fair comparison. Three test cases of the
High-Fidelity Prediction Workshop [8] are considered: a two-dimensional subsonic flow past a Joukowski
airfoil, a subsonic three-dimensional flow past the wing-body configuration developed for the High-Lift
Prediction Workshop and a subsonic three-dimensional flow past an extruded NACA 0012 wing in a
tunnel.

6.3 Pixel-exact rendering for high-order meshes and solutions

Project GAMMAO

7

Participants:

Adrien Loseille, Matthieu Maunoury (correspondant).

We are developing ViZiR 4, a visualization software with pixel exact rendering to address the high-
order visualization challenges [34, 9]. ViZiR 4 is bundled as a light, simple and interactive high-order
meshes and solutions visualization software. It is based on OpenGL 4 core graphic pipeline. The use of
OpenGL Shading Language (GLSL) allows to perform pixel exact rendering of high order solutions on
straight elements (without extra subdivision or ray casting) and almost pixel exact rendering on curved
elements (high-order meshes). ViZiR 4 enables the representation of high order meshes (up to degree 4)
and high order solutions (up to degree 10) with pixel exact rendering. Unlike other visualization software
(ParaView [20], TecPlot [21], Medit [10], Vizir (OpenGL legacy based version) [29], Gmsh [18]), there is
no subdivision process that is expensive nor visualization error that has to be controlled. Moreover, the
subdivision of the curved entities is done on the fly on GPU which leaves the RAM memory footprint at
the size of the loaded mesh. Furthermore, in comparison with standard visualization techniques based on
legacy OpenGL, the use of OpenGL 4 core version improves the speed of rendering, reduces the memory
footprint and increases the flexibility. Many post-processing tools, such as picking, hidding surfaces,
isolines, clipping, capping, are integrated to enable on the fly the analysis of the numerical results.

6.4 High-Order Mesh Generation

Participants:

Loïc Maréchal (correspondant).

The development of the libHOM library and P1toPk mesh converter continued during my stay at
Dassault-Systemes. The libHOM library handles many basic geometrical and topological operations on
arbitrary order elements and is used by P1toPk which is an end-user software that converts a hybrid
P1 volume mesh into a curved P2 volume mesh. Both programs were started during the collaboration
between Distene and INRIA and development continued at Dassault-Systemes after they acquired Distene.
P1toPk has been integrated as a module in the common numerical simulation toolbox that is shared
across all 3DS’s software products. The work consisted mostly in validation on industrial test cases and
the development of dedicated quality criteria for specific solvers like Abaqus (C3D10 quality model).

6.5 Study of mesh and shape optimization

Participants:

Frédéric Alauzet.

In order to design the new transport devices answering to the climatic challenge, the needs in High-
Fidelity CFD simulation are increasing. High-Fidelity CFD simulation demands: high-fidelity models like
RANS and hybrid RANS/LES,high-fidelity approximations with a strong control of the approximation
error. This work focuses on the combination of design with anisotropic mesh adaptation. The key
components are: unstructured mesh for CFD, use of adjoint state for design, use of mesh adaptation [1,
2].

6.6 Improving Adjoint Problem Convergence

Participants:

Frédéric Alauzet, Thomas Gauchery (correspondant).

We are developing new algorithms to solve the adjoint problem that may struggle to converge. Adjoint
resolution is a key step in the process of goal-oriented mesh adaptation as the error estimate and the

8

Inria Annual Report 2023

metric computed for the remeshing depends of the adjoint solution. Currently, the method used is an
iterative GMRES preconditioned with a symmetric Gauss-Seidel method (SGS). New algorithms have
been implemented such as partitioning method or incomplete LU factorization with k levels of fills in
(ILU(k)) based on the connectivity of the mesh. Some methods have shown some interest but need to
be pushed further especially method that helps recover the parallel implementation of the solver like
restricted Scharz additive method or point implicit method.

6.7 Accuracy analysis for a Mixed Element Volume scheme

Participants:

Andrea Gobbi, Julien Vanharen, Cosimo Tarsia Morisco.

We performed a deep accuracy analysis of a Mixed Element Volume (MEV) numerical scheme [42,
6], namely the V4 scheme [7], by studying it on the 2D linear advection equation and comparing the
results between structured and unstructured triangular meshes of different regularity. The scheme in
fact achieves third order accuracy on this equation with cartesian Friedrichs-Keller triangular meshes,
and second order accuracy on the 3D Euler equations with anisotropic adapted meshes [5]. A solver was
specifically implemented for this analysis, in order to compare the results between structured Friedrichs-
Keller meshes and unstructured Delaunay ones. After that we considered more irregular unstructured
meshes obtained by taking the ones used previously and perturbing them at different levels. These
new meshes were then tested in order to compare the accuracy, in particular with another convergence
study, obtaining a second order accuracy. An analysis of the local truncation error followed, by means of
an algorithm that computes automatically the coefficients of the derivatives in the error terms. These
coefficients were computed for all the families of meshes studied, in an attempt to explain the global
errors computed through the local ones. The results were a third order of local accuracy for the regular
meshes, and a first order for the perturbed ones, in opposition to the second order for the global error.
This difference will be investigated with further studies.

6.8 Addition of Mixing Plane in Wolf

Participants:

Frédéric Alauzet, Eloi Guilbert (correspondant).

The mixing plane method is used typically on turbomachinery in order to model the interaction
between a rotor (rotating part) and a stator (static part). Each row (stator, rotor) has its own computation
which is coupled with his surroundings rows with the mixing plane. The idea is to average quantities
along the pitch direction at the outlet of a row, those averaged values are transferred to the next row.
The same process is done at the inlet of a row and transferred at the previous row. Associating mesh
adaptation with mixing planes requires that the position and the distribution radial discretization must
be automatic and consistent with the current adapted mesh. Therefore, after each mesh adaptation, a
specific radial discretization for the mixing plane is built based on the current adapted mesh size. These
radial discretizations are different on either side of the mixing plane as the adapted meshes do not match
on either side. It allows removing the dependency of the results on the relative position between the rotor
and the stator. Thus, RANS simulation can be used, even if the problem is naturally unsteady.

7 Bilateral contracts and grants with industry

7.1 Bilateral contracts with industry

Participants:

Frédéric Alauzet.

Project GAMMAO

Safran Tech

• Duration: 2017 - 2027

• Inria PI: Frédéric Alauzet

9

• Budget for GammaO: Salary for non-permanent staff, travels

• Objectives: Practical use of metric-based mesh adaptation for turbomachinery industrial applica-

tions

8 Partnerships and cooperations

8.1 European initiatives: NumPEx - Should start in 2023-2025

Participants:

Loïc Maréchal, Julien Vanharen.

Since COVID crisis the air traffic is getting back to normal with a growing trend. Aeronautical engines’
manufacturer did realize this as a critical time for aviation and huge effort should be made to reduce our
environmental impact. For instance, The Advisory Council for Aeronautics Research in Europe aka ACARE
2050 objectives set a reduction of 75% in production of CO2 and of 90% of NOx. This objective brings to
the design of new and groundbreaking parts and requires more efficient and complex numerical tools. To
cope with new challenges an increase in simulation complexity and representativity is needed. It leads
industrials like Safran to wonder if current numerical toolchains can still address those issues or should
we optimize it. Parts, like propellers and turbines are very complex with a large number of technological
effect, taking into account all physical aspect is often not possible since it leads to an exponential growth
of the number of degrees of freedom with no convergence or accuracy guarantee. Thus designers simplify
the geometry to use their traditional old simulation methods. For this reason, SAFRAN is pushing to
develop new numerical toolchains that allows to reach better accuracy and scalability on the key design
parameters. The recent studies in this sense ([3] is an example of application of remeshing technique with
a turbine) highlights how the combination of an anisotropic meshing technique, a robust and accurate
solver and the use of a remeshing technology would bring an improvement on physical quantities
accuracy and reliability. The need of testing integrated parts, like propellers installed on wide body
aircraft or multi-stage turbomachine, shows the interest for industrials of scaling the numerical toolchain
to exascale machines in order to have accurate results to real world design problems.

Nowadays, industrials such as Airbus, Safran or ArianeGroup, are facing major technological chal-
lenges, which include the design of the Airbus A350 high-lift configuration, the cooling system of tur-
bomachinery involving microperforated panels, the Ariane 6 launch vehicle or the consideration of ice
accretion on aircraft wings. All of these challenges imply an intensive use of Computational Fluid Mech-
anics (CFD) in order to alleviate design and manufacturing costs and environmental impacts. However,
three technological roadblocks need to be overwhelmed in the coming decades to treat the previous
quoted industrial applications: the ability to handle very complex geometries, to predict unsteady turbu-
lent flows with a high-fidelity and very quickly, which necessitates the High-Performance Computing
(HPC). The application proposed in this project is out of reach with the present technology. Hence,
disruptive methods need to be proposed to maximize the socio-economic impact. The first challenge
requires to use the automatic generation of tetrahedra meshes, which is developed in our team for
more than thirty years [13, 35, 19, 11, 14, 12, 17, 15, 16, 26, 25, 24, 38, 36, 27, 28]. Indeed, it is for instance
impossible to generate a structured mesh around a real landing gear and even if it would be possible, it
would require an enormous amount of time and resources compared with our automatic unstructured
mesh generator. The last two challenges deal with the importance of having accurate and fast numerical
methods on unstructured tetrahedra meshes to capture unsteady turbulent three-dimensional flows.
Last but not least, these challenges have to be simultaneously addressed and impose strong constraints
on the whole computational workflow. Moreover, anisotropic mesh adaptation, developed in our team
[32, 31, 30, 33] works like a catalyst since it allows to:

10

Inria Annual Report 2023

1. efficiently discretize complex industrial geometries,

2. increase accuracy of numerical schemes,

3. reduce the computational time to achieve the same accuracy thanks to the generation of an optimal

mesh in terms of degrees of freedom for a given configuration.

Our simulation suite is made of two main softwares: Feflo.a and Wolf. Feflo.a is our robust anisotropic
local remeshing software for three-dimensional volume and parametric surface mesh generation con-
forming in sizes and orientations to a prescribed input metric field. It is based on a unique cavity-based
operator [33, 43]. It also includes many components required to generate an initial mesh or generate
highly-adapted meshes. It also handles non-manifold geometries and boundary layer mesh generation.
Wolf is a mixed Finite Volume Finite Element flow solver for the compressible Euler and Navier Stokes
equations with or without moving geometries. It also solves the steady and unsteady adjoint problems. It
achieves second-order accuracy in space and up to fourth-order accuracy in time with explicit or implicit
schemes. These suite has demonstrated its incredible potential and provided substantial breakthroughs
in industrial applications [44, 43, 4].

It is absolutely crucial to keep in mind that the challenge to handle highly anisotropic unstructured
meshes arise from the connectivity table needed to represent an unstructured mesh which induces
loop indirections and load imbalances during computations and from the anisotropy which invalidates
most of the standards geometric algorithms. Very simple standard algorithm such as a cut plane in an
anisotropic tetrahedra mesh should be revised to efficiently run on a distributed memory architecture.
Furthermore, the GPU algorithm has very little to do with the CPU one which notably increases the
development cost to obtain a portable solution.

To continue and improve the capabilities of our suite, we propose a new library GMlib to specifically
address the issue of handling anisotropic unstructured meshes on GPU and an industrial test case in
agreement with the Safran Tech’s roadmap.

8.2 European initiatives: NextAIR - 2023-2026

Participants:

Frederic Alauzet, Eloi Guilbert, Cosimo Tarsia Morisco.

Radical changes in aircraft configurations and operations are required to meet the target of climate-
neutral aviation. To foster this transformation, innovative digital methodologies are of utmost importance
to enable the optimisation of aircraft performances. NEXTAIR will develop and demonstrate innovative
design methodologies, data-fusion techniques and smart health-assessment tools enabling the digital
transformation of aircraft design, manufacturing and maintenance. NEXTAIR proposes digital enablers
covering the whole aircraft life-cycle devoted to ease breakthrough technology maturation, their flawless
entry into service and smart health assessment. They will be demonstrated in 8 industrial test cases,
representative of multi-physics industrial design, maintenance problems and environmental challenges
and interest for aircraft and engines manufacturers.

NEXTAIR will increase high-fidelity modelling and simulation capabilities to accelerate and derisk
new disruptive configurations and breakthrough technologies design. NEXTAIR will also improve the
efficiency of uncertainty quantification and robust optimisation techniques to effectively account for
manufacturing uncertainty and operational variability in the industrial multi-disciplinary design of
aircraft and engine components. Finally, NEXTAIR will extend the usability of machine learning-driven
methodologies to contribute to aircraft and engine components’ digital twinning for smart prototyping
and maintenance.

NEXTAIR brings together 16 partners from 6 countries specialised in various disciplines: digital tools,
advanced modelling and simulation, artificial intelligence, machine learning, aerospace design, and
innovative manufacturing. The consortium includes 9 research organisations, 4 leading aeronautical
industries providing digital-physical scaled demonstrator aircraft and engines and 2 high-Tech SME
providing expertise in industrial scientific computing and data intelligence.

Project GAMMAO

11

9 Scientific production

9.1 Publications of the year

Conferences without proceedings

[1] A. Dervieux, F. Alauzet and D. Chargy. ‘Variational study of mesh and shape optimization’. In:
Computational Methods in Applied Sciences (à paraitre). CM3 Transport 2023 Conference. Jyvaskyla,
Finland: Springer, 15th May 2023. URL: https://hal.science/hal-04372153.

[2] B. Sauvage, F. Miralles, S. Wornom, B. Koobus, F. Alauzet and A. Dervieux. ‘Assessment of mesh
adaptation algorithms for LES and DES simulation of detached flows’. In: CFC 2023 - 22nd Compu-
tational Fluids Conference. Cannes, France, 25th Apr. 2023. URL: https://inria.hal.science
/hal-04372499.

9.2 Cited publications

[3] F. Alauzet, L. Billon, E. Parente, M. Philit, A. Remigi and D. Papadogiannis. ‘Evaluation of heat trans-
fer performance of a film-cooled turbine vane using metric-based anisotropic mesh adaptation’.
In: AIAA SCITECH 2023 Forum. National Harbor, MD, USA, 2023. DOI: 10.2514/6.2023-1399.

[4] F. Alauzet, F. Clerici, A. Loseille, M. Maunoury, L. Rochery, C. Tarsia-Morisco, L.-M. Tenkes and
J. Vanharen. ‘4th AIAA CFD High Lift Prediction Workshop results using metric-based anisotropic
mesh adaptation’. In: AIAA Fluid Dynamics Conference. Chicago, IL, USA, June 2022.

[5] F. Alauzet, A. Loseille and G. Olivier. ‘Time-accurate multi-scale anisotropic mesh adaptation for

unsteady flows in CFD’. In: Journal of Computational Physics 373 (2018), pp. 28–63.

[6] P. Arminjon and A. Dervieux. ‘Construction of TVD-like artificial viscosities on two-dimensional

arbitrary FEM grids’. In: J Comput Phys (1993).

[7] C. Debiez and A. Dervieux. ‘Mixed-element-volume MUSCL methods with weak viscosity for steady

and unsteady flow calculations’. In: Computers & Fluids (2000).

[8] B. Diskin, Y. Liu and M. C. Galbraith. ‘High-Fidelity CFD Verification Workshop 2024: Spalart-

Allmaras QCR2000-R Turbulence Model’. In: AIAA SCITECH 2023 Forum. 2023, p. 1244.

[9] R. Feuillet, M. Maunoury and A. Loseille. ‘On pixel-exact rendering for high-order mesh and

solution’. In: Journal of Computational Physics 424 (2021), p. 109860.

[10] P. J. Frey. Medit: An interactive mesh visualization software, INRIA Technical Report RT0253. 2001.

[11] P. Frey and P. George. Mesh generation. Application to finite elements. 2nd. ISTE Ltd and John Wiley

& Sons, 2008.

[12] P. George and H. Borouchaki. ‘“Ultimate” robustness in meshing an arbitrary polyhedron’. In:

International Journal for Numerical Methods in Engineering 58.7 (2003), pp. 1061–1089.

[13] P. George and H. Borouchaki. Delaunay triangulation and meshing : application to finite elements.

Paris, Oxford: Hermès Science, 1998.

[14] P. George and H. Borouchaki. Delaunay triangulation and meshing. Application to finite elements.

Paris: Hermès, 1998.

[15] P. George, F. Hecht and E. Saltel. ‘Fully automatic mesh generator for 3D domains of any shape’. In:

Impact of Computing in Science and Engineering 2.3 (1990), pp. 187–218.

[16] P. George and F. Hermeline. ‘Delaunay’s mesh of a convex polygon in dimension d. Application
to arbitrary polyedra’. In: International Journal for Numerical Methods in Engineering 33 (1992),
pp. 975–995.

[17] P.-L. George, F. Hecht and É. Saltel. ‘Automatic mesh generator with specified boundary’. In: Com-

puter methods in applied mechanics and engineering 92.3 (1991), pp. 269–288.

[18] C. Geuzaine and J.-F. Remacle. ‘Gmsh: A 3-D finite element mesh generator with built-in pre- and
post-processing facilities’. In: International Journal for Numerical Methods in Engineering 79.11
(2009), pp. 1309–1331.

12

Inria Annual Report 2023

[19] F. Hermeline. ‘Triangulation automatique d’un polyèdre en dimension N ’. In: RAIRO. Analyse

numérique 16.3 (1982), pp. 211–242. DOI: 10.1051/m2an/1982160302111.

[20] K. Inc. ParaView. https://www.paraview.org/.

[21] T. Inc. TecPlot. https://www.tecplot.com/.

[22] Y. Ito, M. Murayama, K. Yamamoto, A. M. Shih and B. K. Soni. ‘Efficient hybrid surface/volume
mesh generation using suppressed marching-direction method’. In: AIAA journal 51.6 (2013),
pp. 1450–1461.

[23] Y. Kallinderis and C. Kavouklis. ‘A dynamic adaptation scheme for general 3-D hybrid meshes’. In:
Computer methods in applied mechanics and engineering 194.48-49 (2005), pp. 5019–5050.

[24] R. Löhner. ‘Automatic unstructured grid generators’. In: Communications in Numerical Methods in

Engineering 12 (1996), pp. 683–702.

[25] R. Löhner. ‘Extensions and improvements of the advancing front grid generation technique’. In:

Communications in Numerical Methods in Engineering 12 (1996), pp. 683–702.

[26] R. Löhner and P. Parikh. ‘Three-dimensional grid generation by the advancing front method’. In:

International Journal for Numerical Methods in Engineering 9 (1988), pp. 1135–1149.

[27] A. Loseille and F. Alauzet. ‘Continuous Mesh Framework Part I: Well-Posed Continuous Interpola-
tion Error’. In: SIAM Journal on Numerical Analysis 49.1 (2011), pp. 38–60. DOI: 10.1137/0907540
78.

[28] A. Loseille, L. Frazza and F. Alauzet. ‘Comparing anisotropic adaptive strategies on the 2nd AIAA
Sonic Boom Workshop geometry’. In: 2nd AIAA sonic boom workshop geometry. AIAA 2017-0281,
Grapevine, TX, USA, 2017.

[29] A. Loseille, H. Guillard and A. Loyer. An introduction to Vizir: an interactive mesh visualization and

modification software. EOCOE, Rome, Italy. 2016.

[30] A. Loseille and R. Löhner. ‘Boundary Layer Mesh Generation and Adaptivity’. In: 49th AIAA Aerospace
Sciences Meeting including the New Horizons Forum and Aerospace Exposition. American Institute
of Aeronautics and Astronautics, Jan. 2011. DOI: 10.2514/6.2011-894.

[31] A. Loseille and R. Löhner. ‘Anisotropic Adaptive Simulations in Aerodynamics’. In: 48th AIAA
Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. American
Institute of Aeronautics and Astronautics, Jan. 2010. DOI: 10.2514/6.2010-169.

[32] A. Loseille and R. Löhner. ‘On 3D anisotropic local remeshing for surface, volume and boundary
layers’. In: 18th International Meshing Roundtable. Salt Lake City, UT, USA: Springer, 2009, pp. 611–
630.

[33] A. Loseille and V. Menier. ‘Serial and Parallel Mesh Modification Through a Unique Cavity-Based
Primitive’. In: 22nd International Meshing Roundtable. Orlando, FL, USA: Springer, 2013, pp. 541–
558.

[34] A. Loseille and R. Feuillet. ‘Vizir: High-order mesh and solution visualization using OpenGL 4.0

graphic pipeline’. In: 2018 AIAA aerospace sciences meeting. 2018, p. 1174.

[35] D. L. Marcum. ‘Efficient Generation of High-Quality Unstructured Surface and Volume Grids’. In:

Eng. Comput. 17.3 (2001), pp. 211–233. DOI: 10.1007/pl00013386.

[36] D. Marcum. ‘Efficient generation of high-quality unstructured surface and volume grids’. In: 9th

International Meshing Roundtable. New Orleans, LA, USA, 2000.

[37] D. Marcum and J. Gaither. ‘Mixed element type unstructured grid generation for viscous flow

applications’. In: 14th Computational Fluid Dynamics Conference. 1999, p. 3252.

[38] D. Mavriplis. ‘An advancing front Delaunay triangulation algorithm designed for robustness’. In:

Journal of Computational Physics 117 (1995), pp. 90–101.

[39] D. Mavriplis. ‘Adaptive meshing techniques for viscous flow calculations on mixed element un-
structured meshes’. In: International journal for numerical methods in fluids 34.2 (2000), pp. 93–
111.

Project GAMMAO

13

[40] C. T. Morisco, L.-M. Tenkès and F. Alauzet. ‘Vertex-Centered Mixed Finite Element–Finite Volume
scheme for 2D anisotropic hybrid mesh adaptation’. In: Computer Methods in Applied Mechanics
and Engineering 419 (2024), p. 116638.

[41]

J. Slotnick, A. Khodadoust, J. Alonso, D. Darmofal, W. Gropp, E. Lurie and D. Mavriplis. CFD Vision
2030 Study: A path to revolutionary computational aerosciences. CR-2014-218178. NASA, Mar. 2014.

[42] B. Stouflet, J. Periaux, F. Fezoui and A. Dervieux. ‘Numerical simulation of 3-D hypersonic Euler
flows around space vehicles using adapted finite element’. In: AIAA Paper 87-0560 (1987).

[43]

[44]

J. Vanharen, A. Loseille and F. Alauzet. ‘Non-manifold anisotropic mesh adaptation: application to
fluid–structure interaction’. In: Eng. Comput. (Aug. 2021). DOI: 10.1007/s00366-021-01435-2.

J. Vanharen, A. Loseille, F. Alauzet and M. A. Park. ‘Nearfield anisotropic mesh adaptation for the
third AIAA Sonic Boom Workshop’. In: J. Aircr. (Mar. 2022). DOI: 10.2514/1.C036502.
<scratchpad>
- Main topic: Research Centre Inria Saclay Centre - GAMMAO project
- Key points:
  - GAMMAO is a research program focused on numerical simulation and mesh generation
  - The project aims to improve the accuracy and efficiency of numerical simulations in various domains
  - Key technologies include metric-based mesh adaptation, high-order mesh generation, and advanced visualization
  - The project has partnerships with industry partners, including Safran Tech and Airbus
  - Research areas include aerodynamics, fluid mechanics, and solid mechanics
- Structure: The document is organized into sections on project team, overall objectives, research program, application domains, new software, and partnerships
- Potential artifacts to ignore: HTML tags, links, and other web-related elements
</scratchpad>

<final_summary>
The GAMMAO project is a research program focused on improving the accuracy and efficiency of numerical simulations in various domains, particularly in aerodynamics, fluid mechanics, and solid mechanics. The project aims to develop innovative mesh generation and adaptation techniques, as well as advanced visualization tools, to enable high-fidelity simulations. With partnerships with industry partners such as Safran Tech and Airbus, the GAMMAO project seeks to address the growing need for complex numerical simulations in various fields. The project's research program is motivated by four grand challenges: geometric modeling, enhanced generic meshing algorithms, certified numerical solutions, and advanced mesh and solution visualization. By addressing these challenges, the GAMMAO project aims to deliver innovative solutions for high-fidelity numerical simulations.
The GAMMAO project is a research program focused on improving the accuracy and efficiency of numerical simulations in various domains, particularly in aerodynamics, fluid mechanics, and solid mechanics. The project aims to develop innovative mesh generation and adaptation techniques, as well as advanced visualization tools, to enable high-fidelity simulations. With partnerships with industry partners such as Safran Tech and Airbus, the GAMMAO project seeks to address the growing need for complex numerical simulations in various fields. The project's research program is motivated by four grand challenges: geometric modeling, enhanced generic meshing algorithms, certified numerical solutions, and advanced mesh and solution visualization. By addressing these challenges, the GAMMAO project aims to deliver innovative solutions for high-fidelity numerical simulations.