  We present numerical simulations of active fluid droplets immersed in an
external fluid in 2-dimensions { using} an Immersed Boundary method to simulate
the fluid droplet interface as a Lagrangian mesh. We present results from two
example systems, firstly an active isotropic fluid boundary consisting of
particles that can bind and unbind from the interface and generate surface
tension gradients through active contractility. Secondly, a droplet filled with
an active polar fluid with { homeotropic} anchoring at the droplet interface.
These two systems demonstrate spontaneous symmetry breaking and steady state
dynamics resembling cell motility and division and show complex feedback
mechanisms with minimal degrees of freedom. The simulations outlined here will
be useful for quantifying the wide range of dynamics observable in these active
systems and modelling the effects of confinement in a consistent and adaptable
way.
