Lattice Group Models: GPU Acceleration and Numerics

Lattice group models (LGpM) are kinetic models on integer lattices derived from the automorphism group of the lattice. In the last decades it was too expensive to simulate large systems (100 1000 velocities in a 2D or 3D model), with complex physical two or three dimensional domains, on normal computers or clusters within an acceptable amount of time. That changed due to the fast growth of the computing power of modern processing units. We briefly introduce lattice group models and then describe the main parallelization and optimization strategies for an efficient implementation on NVIDIA graphics cards and INTEL processors. Afterwards we present the achieved speedups and discuss some results from numerical simulations of physical phenomena (shock waves, Knudsen pump, Karman vortex street) in two and three dimensions at high, transitional and low Knudsen numbers.