Implicit propagation of directly addressed grids in lattice Boltzmann methods

Lattice Boltzmann methods (LBM) are well suited to highly parallel computational fluid dynamics simulations due to their separability into a perfectly parallel collision step and a propagation step that only communicates within a local neighborhood. The implementation of the propagation step provides constraints for the maximum possible bandwidth-limited performance, memory layout and usage of vector instructions. This article revisits and extends the work on implicit propagation on directly addressed grids started by A-A and its shift-swap-streaming (SSS) formulation by reconsidering them as transformations of the underlying space filling curve. In this work, a new periodic shift (PS) pattern is proposed that imposes minimal restrictions on the implementation of collision operators and utilizes virtual memory mapping to provide consistent performance across a range of targets. Various implementation approaches as well as time dependency and performance anisotropy are discussed. Benchmark results for SSS and PS on SIMD CPUs including Intel Xeon Phi as well as Nvidia GPUs are provided. Finally, the application of PS as the propagation pattern of the open source LBM framework OpenLB is summarized.