ERC project THEIA

Numerical methods

Local models calculate the stresses generated by flow over relief; global spectral methods resolve modes and instabilities in ellipsoids; direct simulations follow nonlinear fluid and magnetic evolution. THEIA, led by David Cébron at ISTerre, used these complementary approaches within the geometries and boundary conditions described in the associated papers.

ToCCo — local topographic coupling

ToCCo, developed by Rémy Monville during THEIA, calculates weakly nonlinear flows over periodic topography. The modelled configurations include rotation, buoyancy, magnetic effects, curvature and confinement. Symbolic calculations and arbitrary-precision arithmetic are used to obtain pressure, viscous and electromagnetic stresses within a perturbative approach. Fully developed turbulence over arbitrary roughness is outside its scope.

The public repository carries the CeCILL 2.1 licence. The 2024 archived release provides a persistent citation. The core–mantle application was developed by Rémy Monville, David Cébron and Dominique Jault (2025).

Ellipsoidal modes and stability

Jérémie Vidal developed and extended polynomial spectral methods for rotating fluids in ellipsoids. During THEIA, this work formed part of his research with David Cébron on modes, mechanically forced flows and magnetic induction in non-spherical cores. His numerical-tools page describes the methods and reference papers:

• SHINE calculates diffusionless hydromagnetic eigenmodes of Boussinesq fluids and non-magnetic modes of compressible fluids in co-rotating triaxial ellipsoids. THEIA extended this modelling programme from its earlier foundations. Documentation and references are available on the author’s numerical-tools page.
• SWAN performs short-wavelength linear stability analysis of Cartesian basic states, giving sufficient conditions for local instability. The public repository contains documentation and the hydrodynamic archive v0_nomag.zip in Downloads, with a CeCILL 2.1 licence specified in the README. This archive covers the hydrodynamic version; it does not supply the complete magnetic version. The method predates THEIA.
• SIREN tests the global linear stability of uniform-vorticity flows in ellipsoids using polynomial perturbations and inertial modes. The method predates THEIA. Documentation and references are available on the author’s numerical-tools page.

The 2021 kinematic dynamo paper by Vidal and Cébron gives a spectral induction method and benchmarks with local magnetic boundary conditions. Here the velocity is prescribed, without magnetic feedback. This differs both from SHINE’s diffusionless eigenmode problem and from a self-consistent nonlinear dynamo. Other applications concern precession-driven flows in stress-free ellipsoids and acoustic modes with centrifugal gravity.

XSHELLS and collaborative simulations

XSHELLS, developed by Nathanaël Schaeffer, solves rotating incompressible flows and magnetic fields in spherical shells and full spheres. It uses spherical harmonics and radial discretisation and is distributed under the CeCILL licence. Its website provides the source repository, documentation and benchmark references.

THEIA used this existing spherical solver and contributed developments and test cases for topographic and magnetohydrodynamic applications. Collaborative applications include semi-convective dynamos, studied by Paul Pružina, Nathanaël Schaeffer and David Cébron, and inner-core oscillation damping, studied by Paolo Personnettaz, David Cébron, Nathanaël Schaeffer, Renaud Deguen and Mioara Mandea.

The Giraud et al. study used the external solver Nek5000 for direct simulations at ETH Zürich.

Software and references

The software repositories and reference publications are linked above. For reuse, follow the authors’ documentation and cite the relevant software release and method papers. The Publications page provides further details of the scientific applications and full authorship.

See also the project results and experimental methods.