We invite contributions to this session focused on the development, testing and implementation of numerical schemes currently used in astrophysics, including but not limited to methods for I) smoothed particle hydrodynamics, II) grid-based hydrodynamics and III) mesh free hydrodynamics. Although we differentiate between these three approaches based on pure hydrodynamics, we also invite contributions concerning magnetic fields, gravity, self-gravity, particles and particle tracking, PDFs and radiation transport. We particularly encourage submissions from early career researchers and graduate students, presenting latest developments to mature codes, or presenting new codes and the associated validations, or seeking guidance to overcome development issues. We will give preference to such submissions over mathematical descriptions of unimplemented new schemes. We currently have two sessions, each taking the format of an invited presentation (S1: Prof. Ant Whitworth at Cardiff, S2: Prof Sam Falle at Leeds), and five or six further presentations including one comparatively extended invited presentation from an early career researcher (S1: Dr Rowan Smith at Manchester, S2 tbc).