Architecture specific generation of large scale lattice Boltzmann methods for sparse complex geometries

We implement and analyse a sparse/indirect-addressing data structure for the Lattice Boltzmann Method to support efficient compute kernels for fluid dynamics problems with a high number of non-fluid nodes in the domain, as encountered in porous media flows. The data structure is integrated into a code generation pipeline to enable sparse Lattice Boltzmann Methods with a variety of stencils and collision operators and to generate efficient code for kernels on CPU as well as on AMD and NVIDIA accelerator cards. To further enhance performance, we optimize these sparse kernels with an in-place streaming pattern to save memory accesses and memory consumption and we implement a communication hiding technique to demonstrate strong scalability. We provide a comprehensive, systematic performance analysis comparing the sparse and the traditional dense data structure. We present single GPU performance results for the sparse approach with up to 99% of maximal bandwidth utilization. We integrate the optimized generated kernels in the high performance framework waLBerla and achieve a scaling efficiency of at least 82% on up to 1024 NVIDIA A100 GPUs and up to 4096 AMD MI250X GPUs on modern HPC systems. In addition, we propose a hybrid data structure that enables an adaptive choice between sparse and dense representations on a per-subdomain basis, allowing further improvements in performance and memory efficiency. We evaluate all approaches on three realistic application scenarios: flow through porous media, free flow over a particle bed, and blood flow in a coronary artery. Across these benchmarks, we demonstrate a speed-up of up to 2x and a reduction in memory consumption of up to 75% using the sparse/indirect-addressing data structure compared to the conventional direct-addressing approach.