Efficient lattice Boltzmann simulations on large scale high performance computing systems

This thesis presents efforts to attain efficient Lattice Boltzmann simulations on large-scale parallel High-Performance Computing systems. This topic is addressed from two different perspectives. One is the reduction of the computational effort through the improvement of the numerical method. The other is an efficient utilization of the parallel and distributed computing resources.The Lattice Boltzmann Method (LBM) is a numerical scheme for simulations of weakly compressible fluid flows. It is a highly efficient method because of its simple algorithm. However, its dependence on Cartesian meshes introduces issues which will be solved in this thesis.One issue is related to the efficiency when using the LBM to simulate flows in complex geometries. While the geometry can be accurately approximated by a second order boundary condition, it still requires an efficient management of flow elements versus structural (boundary and non-flow) elements. An efficient execution requires appropriate data structures, memory requirements and so on. Thus, the first focus in this thesis is put on the improvements from the computer science point of view.The second focus is the reduction of computational effort from the numerical point of view. Complex geometries imply quite a high resolution of the computational domain in the region where the geometry has detailed structures. With a restriction to uniform Cartesian meshes, this results in a fine mesh everywhere, which would lead to an extreme computational demand that cannot be satisfied even by modern supercomputers. In this thesis, hierarchical meshes are used, resulting in an octree data structure which allows for fine resolution where necessary, but coarse resolution where acceptable. This mesh hierarchy implies the need for interpolating data from coarse to fine and vice versa. An efficient compact interpolation scheme exists but only in 2D. A 3D compact interpolation scheme which maintains all relevant properties is presented and discussed in this thesis.Unfortunately, this technique again implies a computer science issue, which is the so-called load imbalance. Fine elements need to perform more time steps to arrive at the same point in simulated time than coarser ones. Thus, the required effort is much higher in fine elements than in coarse elements. The treatment of these load imbalances is the final topic of the thesis.The presented methods are implemented in the Lattice Boltzmann solver Musubi, and available under a permissive open source license