Over the last decade, microfluidics has revolutionized our ability to manipulate and control flows in channels the width of a single human hair. Due to preponderant effect of surface tension, flows of two immiscible fluids in microdevices allow to create monodisperse emulsions where droplets are used as microreactors to study very fast chemical kinetics. In this paper, we present a new numerical method for immiscible incompressible bifluid flows in microfluidics. This Level Set approach allows fast and accurate simulations of droplets hydrodynamics in microchannels. We particularly focus on mixing dynamics inside microdroplets : numerical simulations are in good agreement with physical experiments. Zones, where fluid is trapped in front and at the back of the droplet, already observed experimentally, are brought to the fore numerically. In addition, we explore various mixing dynamics inside microdroplets by studying the influence of parameters such as droplet volume, injection velocity, viscosity ratio and confinement.