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Presented is the multi-dimensional extension of the Quiet Direct Simulation (QDS) method to general, higher order spatial accuracy. Due to the true directional nature of QDS, where volume-to-volume fluxes are computed as opposed to fluxes at cell interfaces, a volumetric reconstruction is required. In this approach, the conserved quantities are permitted to vary (according to a polynomial expression) across all simulated dimensions. Prior to flux computation, QDS particles are introduced using properties based on weighted moments taken over the polynomial reconstruction of conserved quantity fields. The resulting flux expressions are shown to exactly reproduce existing 2nd order extensions (for one-dimensional flows) while providing means for true multi-dimensional reconstruction and general higher order extensions. Here we will show a typical comparison among different spatial order extensions of QDS and other WENO (5th order accurate) based numerical scheme. The extension is demonstrated up to 5th order spatial accuracy and is shown to be comparable to or more accurate than the other higher order schemes. [ABSTRACT FROM AUTHOR]

Presented here is the QDS method modified to employ an arbitrary governing velocity probability distribution. An algorithm is presented for the computation of QDS particle 'blueprints'. The method, which employs a known continuous velocity probability distribution function, uses a set of fixed QDS particle 'weights', which can be arbitrarily selected. Provided the weights, particle 'blueprint' velocities are computed by taking multiple moments around the governing velocity probability distribution function to provide the discrete representation employed by QDS. In particular, we focus on the results obtained when the governing distribution function is the Chapman-Enskog distribution function. Results are shown for several benchmark tests including a one dimensional standing shock wave and a two dimensional lid driven cavity problem. Finally, the performance of QDS when applied to General Purpose computing on Graphics Processing Units (GPGPU) is demonstrated. [ABSTRACT FROM AUTHOR]