Abstract-The main contribution of the present work consists of several parallel approaches for grid refinement based on a multi-domain decomposition for lattice-Boltzmann simulations. The proposed method for discretizing the fluid incorporates different regular Cartesian grids with no homogeneous spatial domains, which are in need to be communicated each other.Three different parallel approaches are proposed, homogeneous Multicore, homogeneous GPU, and heterogeneous Multicore-GPU. Although, the homogeneous implementations exhibit satisfactory results, the heterogeneous approach achieves up to 30% extra efficiency, in terms of Millions of Fluid Lattice Updates per Second (MFLUPS), by overlapping some of the steps on both architectures, Multicore and GPU.