Direct solution of the Boltzmann equation for a binary mixture on GPUs

We show how to accelerate the numerical solution of the Boltzmann equation for a binary gas mixture by using Graphics Processing Units (GPUs). In order to fully exploit the computational power of the GPU, we adopt a semi-regular method of solution which combines a finite difference discretization of the free-streaming term with a Monte Carlo evaluation of the collision integral. The efficiency of the code is demonstrated by studying the propagation of plane harmonic waves of small amplitude in a binary gas mixture of hard spheres for a wide range of Knudsen numbers and wave frequencies. The GPU-based code is about two order of magnitudes faster than the CPU version thus proving that GPUs can substantially speedup the numerical solution of kinetic equations.