Numerical study of deformation and breakup of a multi-core compound droplet in simple shear flow

•Deformation and breakup of a multi-core compound droplet in shear flow is investigated by the front-tracking method.•The effects of various parameters are investigated to reveal four breakup modes and two deformation modes.•Five diagrams are proposed to show the deformation and breakup modes and the transition.•Increasing the number of the inner droplets enhances the compound droplet breakup.