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 Shin Wu

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
Publication statusPublished - 2013
Event25th International Conference on Parallel Computational Fluid Dynamics, ParCFD 2013 - Changsha, China
Duration: 2013 May 202013 May 24

All Science Journal Classification (ASJC) codes

  • General Engineering


Dive into the research topics of 'Extension of the uniform equilibrium flux method (UEFM) to second order accuracy and its graphics processing unit acceleration'. Together they form a unique fingerprint.

Cite this