Kinetic equations are used to mathematically model gas flows that are far from equilibrium due to their more general applicability than typical hydrodynamic equations. However, their complex mathematical structure requires time consuming algorithms to obtain accurate numerical solutions for realistic flow geometries. This chapter discusses the graphics processing unit (GPU)-accelerated algorithms for direct solutions of kinetic equations. The efficiency of the GPU-accelerated codes is demonstrated on the two-dimensional driven cavity flow. Experimental results show that the GPU-accelerated codes run about two orders of magnitude faster than their sequential counterparts whose execution time is comparable to those reported in the literature. The algorithms described can be extended to three-dimensional flows and gas mixtures. GPU architecture is very effective in reducing the computational effort associated with modeling nonequilibrium rarefied gas flows by the Boltzmann or model kinetic equations. Regular and semi-regular methods of solution are to be recommended in microflows modeling where the small departures from equilibrium condition and flow unsteadiness impair the efficiency of traditional direct simulation Monte Carlo particle schemes. Although the direct methods provide accurate predictions of one- and two-dimensional low Mach number flows, any future extension to more complex flows (gas mixtures, polyatomic gases, three dimensional geometries) is essentially related to the possibility of reducing the memory demand by a more efficient representation of the distribution function in the phase space.
|Title of host publication||GPU Computing Gems Jade Edition|
|Number of pages||14|
|Publication status||Published - 1 Dec 2012|