Codes, scripts & models

– COMSOL Multiphysics
I have developed various COMSOL models, simulating magnetic fields, flows evolution, convection or aero-acoustics such as e.g.
— Axisymmetric model ( v.5.4) of the aero-acoustics (with non-zero azimuthal wavenumbers) in the experiment ZoRo

– FELINS (Free-surface Ellipsoids with LINear State)
The MATLAB code FELINS performs 3D unsteady simulations of uniform vorticity flows in unsteady free surface ellipsoids. The flow can be driven by (i) any force originating from a potential governed by a Poisson equation (e.g. self-gravity and electrostatic forces), (ii) by tidal forces, (iii) by isotropic linear elastic forces, (iii) by Lorentz force due to an imposed uniform magnetic field in the inductionless limit, and, (iv) for modest deformations, an interfacial tension can be added to simulate drops. It has been successfully benchmarked against theory for various cases such as rotating homogeneously charged drops (Rosenkilde 1967) and rotating tidally deformed self-gravitating fluid (Chandrasekhar 1963).

– SIF² (Spectral code for Inviscid Free Surface Irrotational Flow)
The MATLAB code SIF² performs 3D unsteady simulations of inviscid irrotational free surface flows in a sloshing parallelepipedic tank, based on the Fenton & Rienecker (1982) pseudo-spectral method. To do so, SIF² decomposes the potential on the tank sloshing natural modes, and then uses this spectral expansion to solve the fully non-linear problem without any approximation. SIF² has been inspired by a code written by D. Le Touzé during his PhD thesis (Nantes, 2003).

– FLIPPER (FLows at ImPosed Precession within Ellipsoids in Rotation)
The MATLAB script FLIPPER calculates the bulk uniform vorticity flows within precessing arbitrary ellipsoids in rotation (script released as supplementary data of Cebron, FDR 2015). Most of the different set of equations solved by FLIPPER are given in details in Busse (1968), Noir et al. (2003), Cebron et al. (2010), and Noir & Cebron (2013). New sets of equations, derived from the previous well-known ones, are also solved by FLIPPER. Finally, FLIPPER relies on new recasts of equations to perform very efficient and accurate solvings of these equations in a unique script.

– LEAFS (Lagrangian Extended Analysis of Flow Stability)
The MATLAB script LEAFS performs short-wavelength Lagrangian stability analysis of any 3D unsteady basic inviscid flow. To do so, LEAFS calculates the growth rate of pathlines by perturbing the equations of motion with localized plane waves along the considered pathline, and by assuming that the plane waves characteristic wavelength is very small, which is the short—wavelength hypothesis (see Lifschitz&Hameiri 1991 ; Lifschitz 1994 for details). The perturbation is thus written in the geometrical optics, or WKB (Wentzel-Kramers-Brillouin) form, and then solved using the Floquet method, i.e. by solving 15 coupled ODE formed by the trajectory equation (3 ODE), the wavenumber equation (3 ODE), and the Floquet system (monodromy matrix : 9 ODEs).

– TREFLES (TRiaxial Ellipsoid Flows and LinEar Stability)
Considering an incompressible fluid within a triaxial ellipsoidal container, the MATLAB script TREFLES calculates the bulk uniform vorticity flows for an arbitrary motion of the container. The flow is thus mechanically forced by the motions of the ellipsoid rotation axis and of the figure axes (i.e. ellipsoid inertia tensor), which are imposed independently. This allows, for instance, to calculate the flow driven by a precession/nutation (rotation axis motion) coupled to librations in longitude/latitude (figures axes motion).
TREFLES also calculates the complex linear growth rates of these flows by using polynomial velocity perturbations of degre N=1, 2, 3, 4 and 5 in space coordinates (following Gledzer&Ponomarev 1992, Wu&Roberts 2011), which takes into account the confinement effect due to the presence of an ellipsoidal boundary. The growth rate is then calculated by a a brute-force time-stepping, or by solving the associated Floquet system (monodromy matrix : the number of ODEs to solve scales as N^6 !).