Inertial confinement fusion (ICF) aims at producing energy from thermonuclear fusion reactions between low atomic-number elements. A possible approach for reaching the high densities and temperatures needed for triggering these reactions, consists in imploding a spherical capsule, filled with a mixture of fusible elements, by means of a high energy density irradiation. This irradiation induces a violent vaporization – ablation – of the capsule outer shell that drives the implosion. The finite duration of these implosions emphasize the need for investigating possible perturbation transient growth that may dominate the flow over short-time horizons. For this project, we wish to investigate such transient growth in strongly accelerated self-similar ablation flows, with planar of spherical symmetry, which are relevant to the main stage of an implosion. This work will be carried out using a direct-adjoint method of non-modal stability theory, previously devised for weakly accelerated self-similar ablation flows in planar symmetry, that will have to be adapted to handle strongly accelerated configurations. Results could be used to setup, in a more realistic setting, `multi-physics' simulations of capsule implosions.