Solving the Boltzmann equation on GPUs

We show how to accelerate the direct solution of the Boltzmann equation using Graphics Processing Units (GPUs). In order to fully exploit the computational power of the GPU, we choose a 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 solving the two-dimensional driven cavity flow. Computational results show that it is possible to cut down the computing time of the sequential code of two order of magnitude. This makes the proposed method of solution a viable alternative to particle simulations for studying unsteady low Mach number flows.

► Direct solution of the Boltzmann equation can be accelerated by using GPUs.
► Code efficiency is demonstrated by solving the two-dimensional driven cavity flow.
► The computing time of the sequential code is cut down of two order of magnitude.
► Method of solution extendible to three dimension and/or non-equilibrium mixtures.