  The full non-linear evolution of the tidal instability is studied numerically
in an ellipsoidal fluid domain relevant for planetary cores applications. Our
numerical model, based on a finite element method, is first validated by
reproducing some known analytical results. This model is then used to address
open questions that were up to now inaccessible using theoretical and
experimental approaches. Growth rates and mode selection of the instability are
systematically studied as a function of the aspect ratio of the ellipsoid and
as a function of the inclination of the rotation axis compared to the
deformation plane. We also quantify the saturation amplitude of the flow driven
by the instability and calculate the viscous dissipation that it causes. This
tidal dissipation can be of major importance for some geophysical situations
and we thus derive general scaling laws which are applied to typical planetary
cores.
