Adaptation methods for a new Navier-Stokes algorithm

Multilevel error estimation and adaptive h-refinement for Cartesian meshes with embedded boundaries

“…A common approach found in the literature is to set the refinement threshold to some fraction of a standard deviation above the mean of the distribution . [3][4] [26] Figure 7 shows an actual refinement histogram resulting from a coarse grid simulation (3775 cells) of flow over an ONERA M6 wing at transonic conditions [25]. This plot bears little resemblance to the idealized Gaussian-like model shown in figure 6.…”

“…A tagged ceils according to adaptation criteria, and these tags were then modified to satisfy the smoothness and mesh validity rules detailed in A. 3. In addition, the adaptation criteria used in this example was:…”

Viscous Flow Simulation Using an Upwind Method for Hexahedral Based Adaptive Meshes

“…[23]. The current work contains some important differences in the handling of surface vectors, time steps, and volumes, however, and the extension to three dimensions is completely new.…”

“…Furthermore, Ref. [23] shows that, in 2D, the overlapping secondary cells results in a discretization which is capable of recognizing and damping saw-tooth oscillations in the solution. Finally, the Appendix demonstrates that the current choice of auxiliary and secondary control volumes results in an integration which preserves a zero gradient flow on any arbitrary, nonoverlapping mesh (preserves free stream flow).…”

“…The cells tagged in the second scan are evaluated on a statistical basis as outlined in Ref. [23]. The division routine operates recursively in a direction-by-direction manner and retains the ability to divide the cells directionally when features are nearly mesh aligned.…”