The origin of cosmic dust grains is a hotly debated topic. For the local Universe, there is general consensus that dust production is dominated by low mass stars, and transported into the interstellar medium (ISM) via stellar winds. Enormous amounts of dust found at high redshifts make for a problematic situation, i.e., all the dust observed in galaxies cannot be accounted for as no low mass stars could have evolved to their dust producing phase when the Universe was 1-2 Gyr. This is known as the dust-budget crisis – a significant unsolved problems in contemporary astronomy. In the project proposed here, we will study supernovew (SNe) interacting with the surrounding dusty ISM to answer mainly two questions, which have proved to be particularly important: (1) are SNe net producers or net desttroyers of dust? (2) Is dust over- or under-abundent in newly formed cold molecular clouds (MCs)? We seek to answer these questions primarily by means of advanced HPC numerical simulations which go beyond the current state of the art. We will also compute spectral energy distributions and extinction curves based on known optical properties of dust to establish links between simulations and observations. Addressing the issues described above is particularly timely as the coming years will see a vast improvement in the sensitivities of infrared instrumentation (e.g. ELT, JWST), which provides a great opportunity to discriminate between possible solutions and contributing factors.