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By Norbert Kroll (auth.), Norbert Kroll, Heribert Bieler, Herman Deconinck, Vincent Couaillier, Harmen van der Ven, Kaare Sørensen (eds.)

This quantity includes effects won from the EU-funded sixth Framework undertaking ADIGMA (Adaptive Higher-order Variational equipment for Aerodynamic functions in Industry). The objective of ADIGMA was once the improvement and usage of leading edge adaptive higher-order equipment for the compressible circulation equations permitting trustworthy, mesh autonomous numerical options for large-scale aerodynamic functions in plane undefined. The ADIGMA consortium was once produced from 22 corporations which integrated the most ecu airplane brands, the foremost ecu study institutions and a number of other universities, all with good confirmed services in Computational Fluid Dynamics (CFD). The publication provides an advent to the venture, shows companions’ tools and ap-proaches and gives a severe review of the newly built tools for commercial aerodynamic purposes. the simplest numerical suggestions for integration as significant construction blocks for the subsequent new release of commercial circulation solvers are pointed out.

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Additional info for ADIGMA - A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications: Results of a collaborative research project funded by the European Union, 2006-2009

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The DG solutions have been computed up to P3 and up to P2 polynomial approximation on two nested grids with 50618 and 404944 hexahedral elements, respectively. The coarse and fine grid computations have been run in parallel using, respectively, 128 and 512 cores of the CASE cluster facility at DLR in Braunschweig. Pressure contours and residuals convergence for the corse grid solution are shown in Figure 7, while Table 2 reports the force and pitching moment coefficients on the two grids. The discrepancy between the more accurate results on the two grids is still to be understood and no conclusion can be drawn about the asymptotic convergence of the two solutions.

Bassi et al. Fig. 2 Flat plate: skin-friction, velocity profiles and turbulence quantities The weak form of Eq. (6) reads Ω φ ∂u dx − ∂t Ω ∇φ · F(u, ∇u) dx + ∂Ω φ F(u, ∇u) · n dσ + Ω φ s(u, ∇u) dx = 0, (7) where φ denotes any arbitrary, sufficiently smooth, test function and F is the sum of the inviscid and viscous fluxes. The DG discretization of Eq. (7) is defined on a triangulation Th = {K} of an approximation Ωh of Ω , consisting of a set of non-overlapping hybrid-type elements. The following space setting of discontinuous piecewise polynomial functions for each component uhi = uh1 , .

Denote by Φ the mapping from reference triangle Tˆ to any curved triangle T (Ti or T j ) and by Φ −1 the inverse mapping, Φ (ξ , η ) = x y , Φ −1 (x, y) = ξ η . (15) Points (ξ , η ) ∈ Tˆ are transformed into points (x, y) ∈ T according to x= pb pb −m ∑ ∑ γmn ξ m η n , m=0 n=0 y= pb pb −m ∑ ∑ δmn ξ m η n , (16) m=0 n=0 where pb is the polynomial order of the boundary and γmn , δmn are constants that are computed in the preprocessor. -E. Ekstr¨om and M. Berggren will not be constant for pb > 1. The Jacobians are precomputed at each quadrature point, and are stored and used during computations.

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