FESTIM in 2026: what the code can do for tritium modelling

Rémi Delaporte-Mathurin, on behalf of the whole FESTIM community

50th Tritium Focus Group | Aiken, SC | October 2026

Diffuse, trap, react, release

One framework for solids, liquids, gases and the interfaces between them

Zoom in: the wall at atomic scale

\partial_t c_\mathrm{m} = \nabla \cdot \left( D \nabla c_\mathrm{m} - c_\mathrm{m}\, \mathbf{u} \right) + S - \sum_i \partial_t c_{\mathrm{t},i}

\partial_t c_{\mathrm{t},i} = k_i\, c_\mathrm{m} \left( n_i - c_{\mathrm{t},i} \right) - p_i\, c_{\mathrm{t},i}

mobile hydrogen: diffusion, drift, sources

one equation per species

FESTIM on one slide

1D, 2D, 3D, up to CAD-meshed components
Multi-material, multi-isotope, arbitrary species and reactions
Traps, surface kinetics, Sieverts / Henry, coupled heat transfer
Python API: physics vocabulary, no finite elements exposed
Built on FEniCSx, MPI-parallel
Open source (Apache 2.0), on conda-forge

import festim as F

model = F.HydrogenTransportProblem()
model.mesh = F.Mesh1D(np.linspace(0, 1e-3, 1001))

steel = F.Material(D_0=1e-7, E_D=0.2)
bulk = F.VolumeSubdomain1D(1, borders=[0, 1e-3], material=steel)
left = F.SurfaceSubdomain1D(1, x=0)
right = F.SurfaceSubdomain1D(2, x=1e-3)
model.subdomains = [bulk, left, right]

T = F.Species("T")
model.species = [T]
model.temperature = 600
model.boundary_conditions = [
    F.FixedConcentrationBC(left, value=1e20, species=T),
    F.FixedConcentrationBC(right, value=0, species=T),
]
model.exports = [F.SurfaceFlux(field=T, surface=right)]

model.initialise()
model.run()

What people use it for

Retention in a divertor monoblock

ARC breeding blanket

Heat exchanger contamination

Tritium permeator probe

TDS spectrum fitting

Hydrogen in a microstructure

Tritium inventory in ITER

HISP, an open-source workflow built on FESTIM, with the ITER Organization: how much tritium stays in the wall, and how well can we get it out?

■ tungsten ■ boron co-deposit
HISP wall bins, from the open data

Plasma code outputs
fluxes, heat loads

Wall split in bins
first wall + divertor

1D FESTIM model
per bin, W or B

2-week DT scenarios
baking, GDC, DD

→

K. Dunnell, A. Lleal, E. A. Hodille, J. Dufour, R. Delaporte-Mathurin, T. Wauters, Hydrogen Inventory Simulations for PFCs (HISP), Nucl. Mater. Energy (2026)

Can you trust it?

Verification

650+ tests on every push and pull request, on two DOLFINx versions
~60 system tests against manufactured and exact solutions, 1D to 3D
The TMAP benchmark suite
Cross-checked against TMAP8, and independently against MHIMS and mHIT

Validation

8 experimental campaigns: permeation, retention in damaged W, Be co-deposition, H in Ti, EUROFER
BABY-1L breeding campaign (MIT, ClLiF): calibrated on 4 runs, predicts 2 withheld runs without recalibration

H. Yang et al., in preparation

Every case is a runnable script. The report rebuilds from them, in public.

festim-vv-report.readthedocs.io

What's new: FESTIM 2

2019 to 2024 | FESTIM 1

Legacy FEniCS
One mobile species + traps
Change of variable at interfaces
Validated against experiments

2024 to today | FESTIM 2

DOLFINx
Arbitrary species: H, D, T, HT, DT...
One field per material
~11× faster, MPI-native

Dark, Delaporte-Mathurin, Dokken et al., FESTIM v2.0, Int. J. Hydrogen Energy 220 (2026)

And since this summer, v2.2

Gas enclosures and pumps

NEW

Permeation rigs, double-walled pipes, purged gaps, gloveboxes: a wall feeding a gas volume whose pressure feeds back on the wall.

\frac{\mathrm{d}P}{\mathrm{d}t} = \frac{R\,T}{V} \int_{\partial \Omega} \varphi \, \mathrm{d}s \; - \; \text{pumping}

Pressure is one extra unknown, solved together with the wall (implicit)
F.GasSpecies, F.Enclosure; surfaces exchange via Sieverts or surface reactions
A Pump is an opening on the enclosure; a purge stream is the same object

Two membranes with a pumped gap. Pump on: gap pressure 25 Pa → 0, hydrogen reaching the second membrane down ~5 orders of magnitude.

Fast lanes: grain boundaries

NEW

Subdomains can now be one dimension lower than the mesh: grain boundaries, thin films, coolant channels.

Here: hydrogen reaches depth through the boundary network long before the bulk front arrives.

gb = F.VolumeSubdomain(
    id=2,
    material=gb_material,
    dim=1,  # a line in a 2D mesh
    locator=on_boundaries,
)

Much of this built by FESTIM Fellow Ian Wojtowicz (U. Minnesota)

Drift terms

NEW

Hydrogen does not only follow its own gradient: it drifts with temperature, electric potential, stress, and flow.

J = -D \nabla c + c\, \mathbf{u}, \qquad \mathbf{u} = \sum_j \mathbf{u}_j

Soret (thermodiffusion) SoretTerm

\mathbf{u} = -\frac{D\, Q^{*}}{k_B T^{2}} \nabla T

Electromigration ElectromigrationTerm

\mathbf{u} = -\frac{z\, D}{k_B T} \nabla \varphi

Stress-assisted diffusion

\mathbf{u} = \frac{D\, \bar{V}_\mathrm{H}}{k_B T} \nabla \sigma_h

Advection AdvectionTerm

\mathbf{u} = \mathbf{u}_\mathrm{fluid} \quad (\text{e.g. from OpenFOAM})

Long requested by users. Each drift is one more term in the weak form, so it works with multi-material, manifolds, enclosures and coupled heat transfer.

Hydride formation

IN PROGRESS

v2.2 makes reaction classes generic: hydrogen in solid solution and in hydrides become two species linked by user-defined reactions.

\partial_t c_\mathrm{ss} = \nabla \cdot (D \nabla c_\mathrm{ss}) - S, \qquad \partial_t c_\mathrm{hyd} = S = S_\mathrm{nucleation} + S_\mathrm{growth} - S_\mathrm{dissolution}

HNGD model written as custom Reaction classes, no hydride-specific solver. FESTIM runs of the three test cases of Passelaigue et al., J. Nucl. Mater. 544 (2021).

Getters and storage beds are natural next targets.

Work by Chirag Khurana (MIT) | festim-dev/FESTIM issue #1123

Multiphysics, multi-code coupling

OpenMC: tritium source

OpenFOAM: velocity

FESTIM: tritium

openmc2dolfinx and foam2dolfinx pass fields straight into FESTIM.

ARC breeding blanket: ~243 mg tritium inventory | Dark, Sircar, Bae, Dokken & Delaporte-Mathurin, arXiv:2608.05398

And up to the fuel cycle: FESTIM components plug into PathSim system models

Teaser on interfaces

In FESTIM 2, users now have several modelling options for the interface condition

Equilibrium

continuous chemical potential (Sieverts)

Kinetic

finite-rate exchange across the interface

Surface reaction

recombination, dissociation, isotope exchange

When is equilibrium wrong, and what does it change?

Next talk: James Dark, MIT PSFC

A community project

30+ contributors

30+ institutions

8k forum views / month

Apache 2.0

NumFOCUS affiliated

Interactive tutorials, nothing to install: festim-workshop.readthedocs.io

conda install -c conda-forge festim | Monthly dev meetings, open to all | Discourse and Slack

The FESTIM Fellowship

From FESTIM user to FESTIM expert in your organisation, by working on your own project with the development team.

Your project

A real application drives the learning

~10 weeks

At least 25% of your time, alongside your job

Remote or at MIT

Weekly 1:1 time with lead developers

No fees

Supported by your employer

Fellows leave with at least one of:

A robust, reproducible simulation of their application
A contribution to the FESTIM codebase, or a new V&V case
FESTIM integrated into a wider modelling workflow

"Even though it's quite nice to be the FESTIM 2 expert on site (!!!), I would absolutely recommend the programme to my colleagues."

Tez Orr, UKAEA, first FESTIM Fellow

Our 2026 Fellows

Tez Orr First Fellow

Now UKAEA's resident FESTIM expert, contributing to LIBRTI and STEP

Arpan Sircar Summer

Tritium uptake in sweep gases from lithium ceramic blankets

Ian Wojtowicz Summer

Hydrogen retention in topologically complex multi-material geometries

Emre Yildirim Summer

Macro2Micro: taking FESTIM through the length scales

Christopher Soika Fall

HCPB breeding blanket tritium transport model in FESTIM 2, on site at MIT PSFC

Andrea Di Maio Fall

Periodic boundary conditions and component-to-system coupling with PathSim

Want to join the next cohort? Come find James or me this week.

Thank you

Questions?

github.com/festim-dev/FESTIM

festim.readthedocs.io | festim-workshop.readthedocs.io

Try it in your browser: the workshop tutorials run on Binder, no install

Fellowship: festim.readthedocs.io/en/latest/fellowship.html

Next: James Dark, kinetic interface models with FESTIM