Lattice Boltzmann method (LBM) is a promising approach to solving Computational Fluid Dynamics (CFD) problems, however, its nature of memory-boundness limits nearly all LBM algorithms' performance on modern computer architectures. This paper introduces novel sequential and parallel 3D memory-aware LBM algorithms to optimize its memory access performance. The introduced new algorithms combine the features of single-copy distribution, single sweep, swap algorithm, prism traversal, and merging two temporal time steps. We also design a parallel methodology to guarantee thread safety and reduce synchronizations in the parallel LBM algorithm. At last, we evaluate their performances on three high-end manycore systems and demonstrate that our new 3D memory-aware LBM algorithms outperform the state-of-the-art Palabos software (which realizes the Fuse Swap Prism LBM solver) by up to 89%.