General Higher Order Extension to the Quiet Direct Simulation Method

Abstract

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 2(nd) 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 (5(th) order accurate) based numerical scheme. The extension is demonstrated up to 5(th) order spatial accuracy and is shown to be comparable to or more accurate than the other higher order schemes.