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We present numerical simulations of active fluid droplets immersed in anexternal fluid in 2-dimensions { using} an Immersed Boundary method to simulatethe fluid droplet interface as a Lagrangian mesh. We present results from twoexample systems, firstly an active isotropic fluid boundary consisting ofparticles that can bind and unbind from the interface and generate surfacetension gradients through active contractility. Secondly, a droplet filled withan active polar fluid with { homeotropic} anchoring at the droplet interface.These two systems demonstrate spontaneous symmetry breaking and steady statedynamics resembling cell motility and division and show complex feedbackmechanisms with minimal degrees of freedom. The simulations outlined here willbe useful for quantifying the wide range of dynamics observable in these activesystems and modelling the effects of confinement in a consistent and adaptableway.

Immersed Boundary Simulations of Active Fluid Droplets