Application of strand meshes to complex aerodynamic flow fields

We explore a new approach for viscous computational fluid dynamics calculations for external aerodynamics around geometrically complex bodies that incorporates nearly automatic mesh generation and efficient flow solution methods. A prismatic-like grid using “strands” is grown a short distance from the body surface to capture the viscous boundary layer, and adaptive Cartesian grids are used throughout the rest of the domain. The approach presents several advantages over established methods: nearly automatic grid generation from triangular or quadrilateral surface tessellations, very low memory overhead, automatic mesh adaptivity for time-dependent problems, and fast and efficient solvers from structured data in both the strand and Cartesian grids.The approach is evaluated for complex geometries and flow fields. We investigate the effects of strand length and strand vector smoothing to understand the effects on computed solutions. Results of three applications using the strand-adaptive Cartesian approach are given, including a NACA wing, isolated V-22 (TRAM) rotor in hover, and the DLR-F6 wing-body transport. The results from these cases show that the strand approach can successfully resolve near-body and off-body features as well as or better than established methods.     

A posteriori error estimation and error control for finite element approximations of the time-dependent Navier–Stokes equations

We present an approach to estimate numerical errors in finite element approximations of the time-dependent Navier–Stokes equations along with a strategy to control these errors. The error estimators and the error control procedure are based on the residuals of the Navier–Stokes equations, which are shown to be comparable to error components in the velocity variable. The present methodology applies to the estimation of numerical errors due to the spatial discretization only. Its performance is demonstrated for two-dimensional channel flows past a cylinder in the periodic regime.     

NOTES ON REFINABLE FUNCTIONS

1.IntroductionItiswell--knownthatrefinablefunctionsplayanimportantroleinthestudyingofwavelet.Usually,onehopesthatrefinablefunctionshavesomeparticularpropertiessuchassmoothnessandintegrability.Inthisnote,thezerosofanintegrablerefinablefunctionareobtained.Inparticalarbyexamplesoneshowsthatthelinearspaceassociatingthetranslatesoverthelatticepointsofarefinablefunctioncouldincludepolynomialspaceofdegreehigherthanitssmoothorder.LetsbeapositiveintegerandletR'(resp.C')bethes-dimensionalreal(qgmplex)…