Numerics

Jérémie Vidal (Ph.D.)

CNRS Researcher, LGL-TPE (ENS Lyon - Univ. Lyon 1)

Email: jeremie [dot] vidal [at] ens-lyon [dot] fr

Here are the numerical codes in Computational Fluid Dynamics (CFD) I have been developing/using.

SINGE (Spherical INertia-Gravity Eigenmodes)

SINGE computes the free eigenmodes (e.g. the inertial modes) of a rotating spherical cavity (full spheres or spherical shells) filled with a Boussinesq (Newtonian) fluid. The code also determines the onset of double-diffusive convection in such geometries.

I have developped SINGE for several publications, and the code has been used worldwide:

IPGP, see in Gastine et al. (2016, JFM) & Tassin et al. (2021, GJI),
Max Planck Institute, see in Barik et al. (2018, JFM),
Royal Observatory of Belgium, see in Rekier et al. (2019, GJI).

=> To use SINGE, please cite Vidal & Schaeffer (2015, GJI) for the code.

Then, please also cite:

Kaplan et al. (2017) for thermal convection,
Monville, Vidal et al. (2019, GJI) for double-diffusive convection.

Meridional section of as singular inertial mode in the Earth's liquid core (computed with SINGE).

Download SINGE

SHINE (Solver for Hydromagnetic INviscid modes in Ellipsoids)

Angular frequency of hydromagnetic modes in co-rotating rigid ellipsoids (computed with SHINE).

SHINE computes the diffusionless hydromagnetic eigenmodes for Boussinesq fluids, or the non-magnetic eigenmodes for fully compressible fluids, enclosed in co-rotating triaxial ellipsoids. It relies on polynomial Galerkin expansions.

I have developed SHINE for several publications.

=> To use SHINE, please cite:

Vidal et al. (2020, JFM) for the general method.

Then, depending on the application, please also cite:

Vidal et al. (2019, AA) for MHD Boussinesq fluids,
Vidal & Cébron (2020, PRSA) for compressible planets,
Vidal & Cébron (2021, JASA) for acoustics.

Download SHINE

SWAN (Short-Wavelength stability ANalysis)

SWAN probes the linear hydromagnetic stability of generic Boussinesq basic states (but expressed in the Cartesian coordinates), by considering short-wavelength perturbations. This code gives sufficient conditions for local diffusionless instability.

I have developed SWAN for two publications.

To use SWAN, please cite these two papers:

Download SWAN

SIREN (Stability with IneRtial eigENmodes)

Flow instability within an ellipsoid moving on an eccentric Kepler orbit, as predicted by SIREN in Vidal & Cébron (2017, JFM).

SIREN probes the linear stability of arbitrary basic flows of uniform vorticity, forced by orbital forcings and enclosed within rigid ellipsoids. The code handles polynomial perturbations of unprecedented spatial complexity in ellipsoidal geometries. The code gives sufficient conditions for global instability.

I have used SIREN in several publications.

Work still in progress...

XSHELLS

Dynamo magnetic field amplitude within driven by tides in stratified interiors.

Temperature field within a stably stratified interior mixed by turbulent tidal flows.

The code XSHELLS, developed by my former Ph.D. advisor Dr N. Schaeffer, performs spectral direct numerical simulations (DNS) in spherical geometries.