With the recent advent of gravitational wave-based multi-messenger astrophysics, the next decade holds an enormous promise to achieve major progress for a number of long-standing problems. To name just a few, these include the sources of the heaviest elements in the Universe, the properties of matter at extreme densities and temperature, the sources of gamma-ray bursts and potential modifications of Einstein's theory of General Relativity. With the availabiliy of a broad spectrum of observational information comes an increasing demand on the realism of the theoretical source modelling, both in terms of including physical processes and in terms of spanning large length and time scales. In this talk I will present SPHINCS_BSSN, the first Lagrangian hydrodynamics code that solves the full set of Einstein equations and I will show some of its first applications.
