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

ISBN-10: 3642037062

ISBN-13: 9783642037061

ISBN-10: 3642037070

ISBN-13: 9783642037078

This quantity comprises effects won from the EU-funded sixth Framework venture ADIGMA (Adaptive Higher-order Variational equipment for Aerodynamic purposes in Industry). The aim of ADIGMA used to be the advance and usage of cutting edge adaptive higher-order tools for the compressible circulation equations permitting trustworthy, mesh self sufficient numerical options for large-scale aerodynamic purposes in plane undefined. The ADIGMA consortium was once produced from 22 enterprises which integrated the most eu airplane brands, the foremost eu study institutions and several other universities, all with good confirmed services in Computational Fluid Dynamics (CFD). The publication offers an advent to the venture, indicates companions’ tools and ap-proaches and gives a serious evaluate of the newly built tools for business aerodynamic functions. the simplest numerical options for integration as significant development blocks for the following iteration of commercial movement solvers are pointed out.

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Extra resources 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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Without pronouncing ourselves as yet on the outcome, these results in any case indicate the need for an optimised implementation in the assessment of iterative techniques for DGM. Acknowledgements. Part of this work was supported by the Walloon Region and the European funds ERDF and ESF under contract N◦ EP1A122030000102. References 1. : Using FGMRES to obtain backward stability in mixed precision. Electronic Transactions on Numerical Analysis 33, 31–44 (2009) 2. : Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems.

Ekstr¨om and M. Berggren The DG method is obtained by multiplying equation (1) by a test function Vh ∈ Vhd+2 , integrating over each control volume, integrating by parts, and introducing the numerical flux F ∗ on the boundaries. This procedure yields that Uh ∈ Vhd+2 solves the variational problem Vh · ∂ Km ˆ ds − F ∗ (UL ,UR , n) ∇Vh · F (Uh ) dV = 0, ∀Km ⊂ Ω , Km ∀Vh ∈ Vhd+2 , (5) where subscripts L and R denote local (“left”) and remote (“right”) values on the boundary ∂ Km of control volume Km , and nˆ is the outward unit normal.

To impose the solid wall boundary condition, we have implemented two options: the first imposes symmetry and the second uses an explicitly modified flux to enforce non penetration. Both give similar results, both with respect to computational effort and accuracy. The first option uses the the same Roe or Local Lax–Friedrichs flux at the wall as everywhere else, but imposes symmetry by defining UR from UL using a reflected momentum vector: ρR = ρL , ˆ (ρ u)R = (ρ u)L − 2(nˆ · (ρ u)L )n, (ρ E)R = (ρ E)L .

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


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