LRnLA Lattice Boltzmann Method: A Performance Comparison of Implementations on GPU and CPU

We present an implementation of the Lattice Boltzmann Method (LBM) with Locally Recursive non-Locally Asynchronous (LRnLA) algorithms on GPU and CPU. The algorithm is based on the recursive subdivision of the domain of the dD1T space-time simulation and loosens the memory-bound limit for numerical schemes with local dependencies. We show that LRnLA algorithm allows to overcome the main memory bandwidth limitations in both CPU and GPU implementations. For CPU, we find the data layout that provides alignment for the full use of AVX2/AVX512 vectorization. For GPU, we devise a procedure for pairwise CUDA-block synchronization applied to the implementation of the LRnLA algorithm, which previously worked only on CPU. The performance on GPU is higher, as it is usual in modern implementations. However, the performance gap in our implementation is smaller, thanks to a more efficient CPU version. Through a detailed comparison, we show possible future applications for both the CPU and the GPU implementations of the lattice Boltzmann method in the complex setting.