Radio jets and the lobes they inflate are common in cool-core clusters and
are known to play a critical role in regulating the heating and cooling of the
intracluster medium (ICM). This is an inherently multi-scale problem, and much
effort has been made to understand the processes governing the inflation of
lobes and their impact on the cluster, as well as the impact of the environment
on the jet-ICM interaction, on both macro- and microphysical scales.
Developments of new numerical techniques and improving computational resources
have seen simulations of jet feedback in galaxy clusters become ever more
sophisticated. This ranges from modelling ICM plasma physics processes such as
the effects of magnetic fields, cosmic rays and viscosity to including jet
feedback in cosmologically evolved cluster environments in which the ICM
thermal and dynamic properties are shaped by large-scale structure formation.
In this review, we discuss the progress made over the last ~decade in capturing
both the macro- and microphysical processes in numerical simulations,
highlighting both the current state of the field as well as open questions and
potential ways in which these questions can be addressed in the future.Comment: 49 pages, 7 figures, Review Article accepted for publication in
Galaxies Special Issue "New Perspectives on Radio Galaxy Dynamics