To probe the effects of the nuclear activity on the host galaxy, it is
essential to disentangle the relative contribution of shock excitatio
n from that of photoionization. One milestone towards this goal is the
ability to model the bowshock structures created by the interaction o
f radio ejecta with their surrounding medium. We have built a bowshock
model based on TDA's one (Taylor, Dyson & Axon 1992) which was itself
derived from an earlier work on Herbig-Haro objects. Since TDA's orig
inal model supplied the astronomers with only [O III]lambda 5007 fluxe
s and profiles for various models of bowshocks, we undertook to includ
e magnetic fields and to incorporate all of the atomic data tables of
the code MAPPINGS IC for the computation of ionization states, cooling
rates and line emissivities of the gas. This new model allows us to m
ap line ratios and profiles of extragalactic bowshocks for all major l
ines of astrophysical interest. In this first paper, we present our mo
del, analyse the gas behavior along the bowshock and give some example
s of model results.