Extension of the uniform equilibrium flux method (UEFM) to second order accuracy and its graphics processing unit acceleration

Matthew R. Smith*, Yen Chih Chen, Ji Ye Liu, Alexander Ferguson, Jong-Shinn Wu

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review


Presented is the Uniform Equilibrium Flux Method (UEFM) extended to second order spatial accuracy and applied to Graphics Processing Unit (GPU) computation. The UEFM is an approximation of the True Direction Equilibrium Method (TDEFM), in which higher-order extension through the inclusion of gradients in primitives is very challenging due to difficulty in integrating the exponential function over space when there are temperature gradients in the flow. Since UEFM does not directly employ exponential functions-instead replacing the equilibrium velocity probability distribution function with a series of uniform step (i.e. Heaviside) step functions, no such difficulties exist in its extension to higher order accuracy. Furthermore, due to the high locality of the UEFM, the method is readily applied to GPU acceleration. No communication with the host is required due to the exclusive use of the GPU for all flux and state computations. In increase in overall computational speed of approximately 9% is demonstrated with an approximate speedup of 81x when compared to a conventional single Xeon core. We also demonstrate that the UEFM solver has better dissipative properties when compared to the Quiet Direct Simulation (QDS) method.

Original languageEnglish
Pages (from-to)70-75
Number of pages6
JournalProcedia Engineering
StatePublished - 1 Jan 2013
Event25th International Conference on Parallel Computational Fluid Dynamics, ParCFD 2013 - Changsha, China
Duration: 20 May 201324 May 2013


  • Equilibrium Flux Method
  • Euler Equations
  • GPU
  • Graphics Processing Units
  • High Resolution
  • Kinetic Theory of Gases
  • Total Variable Diminishing
  • Uniform Equilibrium Flux Method


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