Stellar wind models are crucial in order to understand the environment around a star, and its possible impact on surrounding exoplanets. However, most models suffer from the same limitation: they compute quasi-static relaxed states that are not evolving. In order to take into account active stars that can have rapid changes of structure in their magnetic field that propagate up to the corona, we need to have time-dependent wind models that have assimilative boundary conditions. We present such a model, improving the Wind Predict model (Réville+2015, Perri+2018) based on the PLUTO code (Mignonne+2007). We start with the simple polytropic version (no Alfvén waves included). Focusing first on the solar case where we have more data, we have modified the boundary conditions of the code in order to assimilate magnetic observations at regular times. We compare first to a standard test case from Lionello+2005, and quantify the impact of various interpolation technics on the quality of the final solution. We finally show a physical case, where the time-dependent model and quantify the addition of the time-dependency for the solar case. We then discuss the impact for stellar winds and stellar models.