Solving the Boltzmann Equation on GPU

Aldo Frezzotti, Gian P. Ghiroldi, Livio Gibelli
Politecnico di Milano, Dipartimento di Matematica, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
arXiv:1005.5405v1 [physics.comp-ph] (28 May 2010)


   author={Frezzotti}, A. and {Pietro Ghiroldi}, G. and {Gibelli}, L.},

   title={“{Solving the Boltzmann Equation on GPU}”},

   journal={ArXiv e-prints},




   keywords={Physics – Computational Physics, Physics – Fluid Dynamics},




   adsnote={Provided by the SAO/NASA Astrophysics Data System}


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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 magnitudes. This makes the proposed method of solution a viable alternative to particle simulations for studying unsteady low Mach number flows.
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