  We investigate separations of trapped balanced two-component atomic Fermi
gases with repulsive contact interaction. Candidates for ground-state densities
are obtained from the imaginary-time evolution of a nonlinear
pseudo-Schr\"odinger equation in three dimensions, rather than from the
cumbersome variational equations. With the underlying hydrodynamical approach,
gradient corrections to the Thomas-Fermi approximation are conveniently
included and are shown to be vital for reliable density profiles. We provide
critical repulsion strengths that mark the onset of phase transitions in a
harmonic trap. We present transitions from identical density profiles of the
two fermion species towards isotropic and anisotropic separations for various
confinements, including harmonic and double-well-type traps. Our proposed
method is suited for arbitrary trap geometries and can be straightforwardly
extended to study dynamics in the light of ongoing experiments on degenerate
Fermi gases.
