Active fluids offer a versatile framework for studying the dynamics of living matter under non-equilibrium conditions. However, the complex nature of the non-linear equations in three dimensions, combined with a lack of robust and scalable numerical methods, restricted most of the research to two dimensions [1]. Here, we present a novel hybrid particle-mesh method for simulating the hydrodynamics of active polar fluids in three dimensions. Our approach combines Discretization-Corrected Particle Strength Exchange (DC-PSE) with pressure correction to accurately solve the incompressible force balance on irregular particle distributions. Our method is implemented in the scalable scientific computing framework OpenFPM [2,3], enabling parallel computations on distributed computers. With our proposed method, we are able to simulate the meso-scale behavior of 3D active polar fluids and 3D active liquid crystals, leading to the discovery of novel phase transitions [4]. This opens up new possibilities for investigating the complex dynamics of living matter in three dimensions, providing insights into the emergent behaviors of active fluids in realistic and biologically relevant settings. [1] R. Ramaswamy et al., Activity induces chaos in a model actomyosin layer, Sci. Rep. 6, (2016). [2] P. Incardona, et al. OpenFPM: A scalable open framework for particle and particle-mesh codes on parallel computers, Comput. Phys. Commun., vol. 241 (2019). [3] A. Singh et al., A C++ expression system for PDEs, Eur. Phys. J. E, vol. 44, no. 9, (2021). [4] A. Singh et al., 3D Spontaneous Flow Transition in Active Polar Fluids arXiv:2302.04259 (2023).