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

Aldo Frezzotti, Gian Pietro Ghiroldi, Livio Gibelli
Dipartimento di Matematica del Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy
AIP Conf. Proc. 1333, pp. 884-889, 2011


   title={Direct solution of the Boltzmann equation for a binary mixture on GPUs},

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

   booktitle={American Institute of Physics Conference Series},





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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.
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