Sparse geometries handling in lattice-Boltzmann method implementation for graphic processors

We describe a high-performance implementation of the lattice-Boltzmann method (LBM) for sparse geometries on graphic processors. In our implementation we cover the whole geometry with a uniform mesh of small tiles and carry out calculations for each tile independently with a proper data synchronization at tile edges. For this method we provide both the theoretical analysis of complexity and the results for real implementations for 2D and 3D geometries. Based on the theoretical model, we show that tiles offer significantly smaller bandwidth overhead than solutions based on indirect addressing. For 2-dimensional lattice arrangements a reduction of memory usage is also possible, though at the cost of diminished performance. We reached the performance of 682 MLUPS on GTX Titan (72\% of peak theoretical memory bandwidth) for D3Q19 lattice arrangement and double precision data.