  We study time-dependent relativistic jets under the influence of radiation
field of the accretion disk. The accretion disk consists of an inner compact
corona and an outer sub-Keplerian disk. The thermodynamics of the fluid is
governed by a relativistic equation of state (EoS) for multispecies fluid which
enables to study the effect of composition on jet-dynamics. Jets originate from
the vicinity of the central black hole where the effect of gravity is
significant and traverses large distances where only special relativistic
treatment is sufficient. So we have modified the flat metric to include the
effect of gravity. In this modified relativistic framework we have developed a
new total variation diminishing (TVD) routine along with multispecies EoS for
the purpose. We show that the acceleration of jets crucially depends on flow
composition. All the results presented are transonic in nature, starting from
very low injection velocities, the jets can achieve high Lorentz factors. For
sub-Eddington luminosities, lepton dominated jets can be accelerated to Lorentz
factors > 50. The change in radiation field due to variation in the accretion
disk dynamics will be propagated to the jet in a finite amount of time. Hence
any change in radiation field due to a change in disk configuration will affect
the lower part of the jet before it affects the outer part. This can drive
shock transition in the jet flow. Depending upon the disk oscillation
frequency, amplitude and jet parameters these shocks can collide with each
other and may trigger shock cascades.
