  Aims. We present the first high-resolution non-equilibrium ionization
simulation of the joint evolution of the Local Bubble (LB) and Loop I
superbubbles in the turbulent supernova-driven interstellar medium (ISM). The
time variation and spatial distribution of the Li-like ions Civ, Nv, and Ovi
inside the LB are studied in detail.
  Methods. This work uses the parallel adaptive mesh refinement code EAF-PAMR
coupled to the newly developed atomic and molecular plasma emission module
E(A+M)PEC, featuring the time-dependent calculation of the ionization structure
of H through Fe, using the latest revision of solar abundances. The finest AMR
resolution is 1 pc within a grid that covers a representative patch of the
Galactic disk (with an area of 1 kpc^2 in the midplane) and halo (extending up
to 10 kpc above and below the midplane).
  Results. The evolution age of the LB is derived by the match between the
simulated and observed absorption features of the Li-like ions Civ, Nv, and Ovi
. The modeled LB current evolution time is bracketed between 0.5 and 0.8 Myr
since the last supernova reheated the cavity in order to have N(Ovi) < 8 \times
10^12 cm-2, log[N(Civ) /N(Ovi) ] < -0.9 and log[N(Nv) /N(Ovi) ] < -1 inside the
simulated LB cavity, as found in Copernicus, IUE, GHRS-IST and FUSE
observations.
