Accelerated composite distribution function methods for computational fluid dynamics using GPU

Matthew R. Smith, Yen-Chih Chen
National Cheng-Kung University No. 1, University Road, Tainan, Taiwan
The 2013 International Workshop on Computational Science and Engineering, 2013


   title={Accelerated composite distribution function methods for computational fluid dynamics using GPU},

   author={Smith, Matthew R and Chen, Yen-Chih},

   booktitle={International Workshop on Computational Science and Engineering (IWCSE 2013)},



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The Kinetic Theory of Gases has long been established as a useful tool for the solution of modern Computational Fluid Dynamics (CFD) problems. Together with the Finite Volume Method, such approaches have been popular in CFD for over 30 years, with techniques such as the Equilibrium Flux Method (EFM) or Kinetic Flux Vector Splitting (KFVS), Equilibrium Interface Method (EIM) together with more recent developments. One of the disadvantages to using such an approach are the expensive exponential (exp(-x^2)) and error function (erf(x)) evaluations often associated with the moments taken around the distribution functions for the computation of interface fluxes. One common approach for avoiding such expenses is to employ discrete velocities in the flux calculation, taking moments around these rather than a continuous distribution function. In this talk we will discuss how we can approximate the governing particle velocity distribution function with a series of Composite Distribution Functions (CDF’s) – made of more than one distribution function – to simplify the moment equations. The resulting expressions are then applied to multi-dimensional computation using Graphics Processing Units (GPU’s), to which the application is well suited due to the simplicity of the flux expressions and locality of the schemes. Very high levels of speedup are demonstrated using C2075 (Fermi) and newer Kepler GPU architectures when compared to modern Xeon E5 processing cores.
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