FESTIM: empowering tritium transport modelling

Remi Delaporte-Mathurin

Application: ITER PFCs

We need a numerical tool

CuCrZr

Particle and heat fluxes

Convection

14 mm

Problem: predict T retention and permeation

Multi-dimensional
Multi-material
non homogeneous temperature

What is FESTIM

User inputs

Material properties
Trap properties
Geometry
Boundary conditions
Initial conditions
...

Heat transfer model

Hydrogen transport model

McNabb & Foster
Multi-level trapping
Multi-isotopes
...

FESTIM

Outputs

H concentration fields \(c(x,t)\)
Temperature field \(T(x,t)\)

surface fluxes
inventories
average concentration
...

2022

2019

Start of development

1D/2D/3D
Finite elements
Python
multi-material
Heat transfer

History of FESTIM

open-source

development continuing at MIT

Oct 2023

v1.0 release

2024

Meet the development team

Jonathan Dufour

CEA, France

+ other contributors

Remi Delaporte-Mathurin

MIT, US

@RemDelaporteMathurin

Samuele Meschini

MIT, US

@SamueleMeschini

Etienne Hodille

CEA, France

@ehodille

Gabriele Ferrero

PoliTo, Italy

@gabriele-ferrero

James Dark

CEA, France

@jhdark

Vladimir Kulagin

MEPhI, Russia

@KulaginVladimir

FESTIM is open-source

Check it out on Github

github.com/festim-dev/FESTIM

✅ More transparency

✅ More collaborations

✅ More flexibility

The code is missing a feature?

Just add it!

Found a bug?

Report it and we'll fix it!

FESTIM's development workflow

Anyone can create their own copy (fork) of the FESTIM repository and make changes
PRs are a place where FESTIM's maintainers review the proposed changes
~500 tests are automatically run
The PR is only merged when all the tests pass ✅

fork

pull request

FESTIM

Jane Doe

FESTIM

John Doe

FESTIM

festim-dev

pull request

How to use FESTIM

github.com/festim-dev/festim

User-support forum

festim.discourse.group

User-support forum

Join the Slack channel

Documentation

and installation instructions

festim.readthedocs.io

FESTIM is user-friendly

Very easy to learn
Plenty of libraries (numpy, scipy, matplotlib, HTM...)
Inuitive interface

conda install -c conda-forge fenics
pip install festim

Two lines to install!

import festim as F
import numpy as np

my_model = F.Simulation()

my_model.mesh = F.MeshFromVertices(
    vertices=np.linspace(0, 1e-6, num=1001)
)

my_model.materials = F.Material(id=1, D_0=1.9e-7, E_D=0.2)

my_model.T = 500  # K

my_model.boundary_conditions = [
    F.DirichletBC(
        surfaces=[1, 2],
        value=1e15,  # H/m3/s
        field=0
        )
]

my_model.settings = F.Settings(
    absolute_tolerance=1e10,
    relative_tolerance=1e-10,
    final_time=100  # s
    )


my_model.dt = F.Stepsize(0.1)  # s

my_model.initialise()

my_model.run()

FESTIM workshop

The FESTIM workshop is a series of tutorials

from basic problems to more advanced cases

festim.discourse.group

FESTIM is user-friendly

FESTIM is fully documented

Check out the complete documentation at

festim.readthedocs.io

Installation instructions

User guide

Development guide
Tutorials
Theory background
API reference

FESTIM is verified & validated

Validated against TDS, permeation experiments...
Verified against analytical solutions in many different problems
New V&V online book

festim-vv-report.readthedocs.io

14 verification cases (4 in progress)

6 validation cases (5 in progress)

V&V

Effective-diffusion through a slab

2D multi-material

Exact

Computed concentration

Method of Exact Solution

governing equations

exact solutions

parameters (sources, BCs, ICs)

FESTIM

computed solutions

solve

run

compare

⚠️sometimes very complex!

Method of Manufactured Solutions

governing equations

manufactured solutions

source terms, BCs and ICs

FESTIM

computed solutions

compare

FESTIM is used worldwide

8 private companies

13 universities

18 research organisations

IPP soon?

📈5 years of development

📑13+ publications

🗣️110+ citations

🧑‍💻20+ contributors

🏛️26+ institutions using the code

🧑‍💻70+ Slack members

⭐88+ stars on GitHub

FESTIM in numbers

Evolution of GitHub stars

Open source

SOFE

New reference paper

Kyoto Fusioneering

UKAEA

Retention studies

Delaporte-Mathurin et al 2024 International Journal of Hydrogen Energy 63 786–802
Delaporte-Mathurin et al 2024 Nucl. Fusion 64 026003

ITER plasma facing components
Transient estimation of tritium retention

Detritiation studies

Delaporte-Mathurin et al 2024 Nucl. Fusion 64 026003

Influence of ELMs on retention

Kulagin, V., & Gasparyan, Y. Numerical Simulation of deuterium retention in tungsten under ELM-like conditions. J. Nucl. Mater. (under revision)

1D model of a ITER monoblock
Transient heat transfer simulation
Varying surface heat flux

Breeding Blanket modelling

DEMO WCLL
Complex 3D geometry
Coupled to fluid dynamics
Tritium generation in the LiPb volume (computed from OpenMC)

James Dark et al 2021 Nucl. Fusion 61 116076

Tritium extraction system

courtesy of K. Dunnell (MIT)

Permeation Against Vacuum
Complex 3D geometry
Coupled with fluid dynamics
Tritium extraction from permeable membranes

Tritium extraction system

courtesy of K. Dunnell (MIT)

① neutrons are generated

② tritium is created from nuclear reactions

③ tritium is transported in the salt

④ tritium is released into the gas phase

⑤ tritium is collected and counted

BABY breeding experiment

👀 Presentation tomorrow...

BABY breeding experiment

Velocity

Temperature

Tritium concentration

Metal Foil Pumps for DIR

H is implanted in the first \( 10 \ \mathrm{nm} \)
Super-permeation regime is attained at high recombination energy (upstream surface)
Source code

Benedikt & Day, (2017) Fusion Engineering and Design

Neutron-induced trap model

Custom trapping model
Dynamic evolution of trap densities including annealing
Parametrised on IPP TDS data!

James Dark et al 2024 Nucl. Fusion 64 086026

Permeation experiment

No barrier

with barrier

Permeation barrier

Substrate

High H pressure

Low H pressure

Conservation of chemical potential

Permeation flux

\frac{c^-}{K_S^-} = \frac{c^+}{K_S^+}

FESTIM can inform fuel cycle models

Samuele Meschini et al 2023 Nucl. Fusion 63 126005

Text

Kinetic surface model

to be submitted

New in v1.3!

FESTIM development plans

FESTIM limitations

Parallel scaling issues

Technical debt

Legacy FEniCS deprecated

Current interface condition does not scale well

Many hard coded foudations

More complex implementationof new features

Bugs not being fixed

Can't take advantage of new features

FEniCSx

FESTIM 2.0

Next steps...

New computational engine

Community-driven

New Features

New computational engine

FEniCS deprecated in 2019

FEniCSx

Designed from the ground up for parallelisation
Better performance
More cell types and control over the domain

Community-driven

Mailing list

User-support forum

Slack channel

Features wanted by the community?

New Features

Multi-isotope transport

New mesh types

Validation on PFCs

Chemical reactions

External physics integration

Anisotropic diffusion

Multilevel trapping

Massively parallel

Towards the future: FESTIM 2

Chemical reactions

More suitable for molten salts
Even more flexibility

Multi-species transport

Isotopic exchange
Multi-level trapping
Transport of impurities, He, interstitials...
Validation on WEST PFCs

Finite element engine upgrade

Better performances (including in parallel)
Bigger models
Mixed topology meshes

Graphical user interface?

Follow the development roadmap

github.com/orgs/festim-dev/projects/2

New examples

github.com/festim-dev/FESTIM-workshop-fenicsx

Isotope swapping

\mathrm{H} + [\ \ \ ]_\mathrm{trap} \ \substack{p \\[-1em] \longleftarrow\\[-1em] \longrightarrow \\[-1em] k} \ [\mathrm{H}]_\mathrm{trap}

\mathrm{D} + [\ \ \ ]_\mathrm{trap} \ \substack{p \\[-1em] \longleftarrow\\[-1em] \longrightarrow \\[-1em] k} \ [\mathrm{D}]_\mathrm{trap}

\mathrm{D} + [\mathrm{H}]_\mathrm{trap} \ \substack{k_\mathrm{swap} \\[-1em] \longleftarrow\\[-1em] \longrightarrow \\[-1.2em] k_\mathrm{swap}} \ [\mathrm{D}]_\mathrm{trap} + \mathrm{H}

same underlying equations!

Can be represented by festim.Reaction

Isotope swapping

my_model.species = [
    mobile_H,
    mobile_D,
    trapped_H,
    trapped_D,
]

my_model.reactions = [
    F.Reaction(
        k_0=k_0,
        E_k=0.39,
        p_0=1e13,
        E_p=1.2,
        reactant1=mobile_H,
        reactant2=empty_trap,
        product=trapped_H,
        volume=my_subdomain,
    ),
    F.Reaction(
        k_0=k_0,
        E_k=0.39,
        p_0=1e13,
        E_p=1.2,
        reactant1=mobile_D,
        reactant2=empty_trap,
        product=trapped_D,
        volume=my_subdomain,
    ),
    F.Reaction(
        k_0=k_0,
        E_k=0.1,
        p_0=k_0,
        E_p=0.1,
        reactant1=mobile_H,
        reactant2=trapped_D,
        product=[mobile_D, trapped_H],
        volume=my_subdomain,
    ),
]

Usual trapping reactions

Swapping reaction

4 species are defined

Multi-isotope, multi-level trapping

7 different species
6 reactions
\( c_H = 10^{20} \ \mathrm{m^{-3}} \) on the left
\( c_D = 10^{19} \ \mathrm{m^{-3}} \) on the right
Source code available here

1 trap, 2 levels, 2 isotopes

\mathrm{H} + [\ \ \ ] \ \substack{p_1 \\[-1em] \longleftarrow\\[-1em] \longrightarrow \\[-1em] k_1} \ [\mathrm{H}_1\mathrm{D}_0]

\mathrm{H} + [\mathrm{H}_1\mathrm{D}_0] \ \substack{p_2 \\[-1em] \longleftarrow\\[-1em] \longrightarrow \\[-1em] k_2} \ [\mathrm{H}_2\mathrm{D}_0]

\mathrm{D} + [\ \ \ ] \ \substack{p_3 \\[-1em] \longleftarrow\\[-1em] \longrightarrow \\[-1em] k_3} \ [\mathrm{H}_0\mathrm{D}_1]

\mathrm{D} + [\mathrm{H}_0\mathrm{D}_1] \ \substack{p_4 \\[-1em] \longleftarrow\\[-1em] \longrightarrow \\[-1em] k_4} \ [\mathrm{H}_0\mathrm{D}_2]

\mathrm{H} + [\mathrm{H}_0\mathrm{D}_1] \ \substack{p_5 \\[-1em] \longleftarrow\\[-1em] \longrightarrow \\[-1em] k_5} \ [\mathrm{H}_1\mathrm{D}_1]

\mathrm{D} + [\mathrm{H}_1\mathrm{D}_0] \ \substack{p_6 \\[-1em] \longleftarrow\\[-1em] \longrightarrow \\[-1em] k_6} \ [\mathrm{H}_1\mathrm{D}_1]

\( \mathrm{H} \) = mobile H

\( \mathrm{D} \) = mobile D

\( [\mathrm{H}_x\mathrm{D}_y] \) = \(x\) H and \(y\) D in trap

Spherical cavity trapping

see Zibrov and Schmid, NME, 2024

for complete description

Implementation in FESTIM of the spherical cavity trapping model developed by Zibrov and Schmid
Custom trapping equations
Smooth implementation in FESTIM

Anisotropy

Anisotropic materials can be simulated with very few modifications
Composites
Anisotropic microstructures

D = \begin{bmatrix} D_{xx} & 0\\ 0 & D_{yy} \end{bmatrix}

Interface discontinuity

2 materials
1 mobile + 1 trap

Example dolfinx code available in issue #719

But this changes a lot of things!

FESTIM 1

with dolfinx

1 mesh for the whole domain

Submesh 1

Submesh 2

VectorFunctionSpace \(V\) (eg. 3 components)

Function \(u\) (eg. 3 components)

VectorFunctionSpace \(V_1\)

\(V_2\)

Function \(u_1\) (eg. 2 comps.)

\(u_2\) (eg. 3 comps.)

1 function for the whole domain

1 function per subdomain

Workshop time

The workshop

github.com/festim-dev/FESTIM-workshop

📖Tasks

Basic

Simple model
Simulating a TDS
Permeation experiment
Post-processing

Advanced

Fitting a TDS
Kinetic Surface model
HTM integration
Neutron induced traps

Bonus

Permeation barrier
Non cartesian meshes
Multi-dimension

💪Challenges

A: Evaluate a PRF
B: Fit a TDS spectrum
C: Permeation flux through a pipe

🚀Contribution/Hackathon

You'll need a GitHub account for this

What is a contribution?

Bug fixes
New functionality
Enhancements
Documentation updates/fixes
Testing
Architecture (CI, CD...)

We curated a list of easy issues for this workshop:

Documentation
Quality of Life
Bug fixes

github.com/festim-dev/FESTIM/milestone/17

Anyone can make a copy of the repository and make changes there
Changes are reviewed by official maintainers via pull-requests
~500 tests are run automatically
Changes are only merged when all the tests pass ✅

fork

pull request

FESTIM

Jane

FESTIM

John

FESTIM

festim-dev

pull request

The contribution workflow

✅

❌

How to contribute to the documentation (easy)

festim.readthedocs.io

How to contribute to the documentation

Make changes to the docs folder locally
Compile the documentation locally
Inspect the HTML files
Push changes
Documentation is automatically built with PR

cd docs/source
make html

We need to test our code

def add_two(x):
    return x + 2


def test_add_two():
    assert add_two(2) == 4
    assert add_two(3) == 5
    assert add_two(4) == 6
    assert add_two(5) == 7


test_add_two()

test_example.py

$ python test_example.py

We want to test this function

We write a test function

We can test more functions

def add_two(x):
    return x + 2


def add_three(x):
    return x + 3


def test_add_two():
    assert add_two(2) == 4
    assert add_two(3) == 5
    assert add_two(4) == 6
    assert add_two(5) == 7


def test_add_three():
    assert add_three(2) == 5
    assert add_three(3) == 6
    assert add_three(4) == 7
    assert add_three(5) == 8


test_add_two()
test_add_three()

test_example.py

$ python test_example.py

We use `pytest` instead

def add_two(x):
    return x + 2


def add_three(x):
    return x + 3


def test_add_two():
    assert add_two(2) == 4
    assert add_two(3) == 5
    assert add_two(4) == 6
    assert add_two(5) == 7


def test_add_three():
    assert add_three(2) == 5
    assert add_three(3) == 6
    assert add_three(4) == 7
    assert add_three(5) == 8

test_example.py

$ python -m pytest test_example.py

================================================================ test session starts ================================================================
platform linux -- Python 3.11.9, pytest-7.4.4, pluggy-1.0.0
rootdir: /home/remidm/FESTIM-workshop
collected 2 items                                                                                                                                   

example_test.py ..                                                                                                                            [100%]

================================================================= 2 passed in 0.01s =================================================================

Let's split the scripts

from example import *

def test_add_two():
    assert add_two(2) == 4
    assert add_two(3) == 5
    assert add_two(4) == 6
    assert add_two(5) == 7


def test_add_three():
    assert add_three(2) == 5
    assert add_three(3) == 6
    assert add_three(4) == 7
    assert add_three(5) == 8

test_example.py

$ python -m pytest test_example.py

def add_two(x):
    return x + 2


def add_three(x):
    return x + 3

example.py

================================================================ test session starts ================================================================
platform linux -- Python 3.11.9, pytest-7.4.4, pluggy-1.0.0
rootdir: /home/remidm/FESTIM-workshop
collected 2 items                                                                                                                                   

example_test.py ..                                                                                                                            [100%]

================================================================= 2 passed in 0.01s =================================================================

This is basically FESTIM

from example import *

def test_add_two():
    assert add_two(2) == 4
    assert add_two(3) == 5
    assert add_two(4) == 6
    assert add_two(5) == 7


def test_add_three():
    assert add_three(2) == 5
    assert add_three(3) == 6
    assert add_three(4) == 7
    assert add_three(5) == 8

test_example.py

def add_two(x):
    return x + 2


def add_three(x):
    return x + 3

example.py

festim/festim

festim/test

github.com/festim-dev/FESTIM/tree/main/festim

github.com/festim-dev/FESTIM/tree/main/test

Testing is automated with GitHub Actions

name: CI
on: [pull_request, push]

jobs:
  build:
    runs-on: ubuntu-latest

    steps:
    - name: Checkout code
      uses: actions/checkout@v2

    - name: Set up Conda
      uses: conda-incubator/setup-miniconda@v2
      with:
        activate-environment: myenv
        channels: conda-forge, defaults

    - name: Create Conda environment
      shell: bash -l {0}
      run: |
        conda install -c conda-forge fenics numpy=1.24

    - name: Install dependencies
      shell: bash -l {0}
      run: |
        pip install pytest pytest-cov

    - name: Run tests
      shell: bash -l {0}
      run: |
        pytest test/ --cov festim --cov-report xml --cov-report term
    
    - name: Upload coverage to Codecov
      uses: codecov/codecov-action@v4
      with:
        token: ${{ secrets.CODECOV_TOKEN }}

Triggered by pushes and PRs

Runs-on cloud ubuntu machine

Clone FESTIM repository

Install dependencies

Run the tests

Upload code coverage

Workflow file stored in .github/workflows/

It shows up during PRs

Now you know

✅Continuous Integration

We also have automation for

pip distribution
building the documentation
testing the documentation
computing coverage
...

Code coverage tells you how much of the code is tested

app.codecov.io/gh/festim-dev/FESTIM/tree/main/festim

FESTIM: empowering tritium transport modelling

Application: ITER PFCs

What is FESTIM

History of FESTIM

Meet the development team

FESTIM is open-source

FESTIM's development workflow

How to use FESTIM

FESTIM is user-friendly

FESTIM workshop

FESTIM is user-friendly

FESTIM is fully documented

FESTIM is verified & validated

V&V

Method of Exact Solution

Method of Manufactured Solutions

FESTIM is used worldwide

FESTIM in numbers

Retention studies

Detritiation studies

Influence of ELMs on retention

Breeding Blanket modelling

Tritium extraction system

Tritium extraction system

BABY breeding experiment

BABY breeding experiment

Metal Foil Pumps for DIR

Neutron-induced trap model

Permeation experiment

FESTIM can inform fuel cycle models

Kinetic surface model

FESTIM development plans

FESTIM limitations

FESTIM 2.0

Next steps...

New computational engine

Community-driven

New Features

New computational engine

Community-driven

New Features

Towards the future: FESTIM 2

Follow the development roadmap

New examples

Isotope swapping

Isotope swapping

Multi-isotope, multi-level trapping

1 trap, 2 levels, 2 isotopes

Spherical cavity trapping

Anisotropy

Interface discontinuity

But this changes a lot of things!

Workshop time

The workshop

🚀Contribution/Hackathon

What is a contribution?

The contribution workflow

How to contribute to the documentation (easy)

How to contribute to the documentation

We need to test our code

We can test more functions

We use pytest instead

Let's split the scripts

This is basically FESTIM

Testing is automated with GitHub Actions

It shows up during PRs

Now you know

✅Continuous Integration

Code coverage tells you how much of the code is tested

We use `pytest` instead