By Norbert Kroll (auth.), Norbert Kroll, Heribert Bieler, Herman Deconinck, Vincent Couaillier, Harmen van der Ven, Kaare Sørensen (eds.)
This quantity comprises effects received from the EU-funded sixth Framework undertaking ADIGMA (Adaptive Higher-order Variational equipment for Aerodynamic purposes in Industry). The target of ADIGMA used to be the advance and usage of cutting edge adaptive higher-order tools for the compressible circulation equations allowing trustworthy, mesh self sustaining numerical options for large-scale aerodynamic purposes in plane undefined. The ADIGMA consortium was once constituted of 22 enterprises which integrated the most eu airplane brands, the most important ecu examine institutions and a number of other universities, all with good confirmed services in Computational Fluid Dynamics (CFD). The booklet offers an advent to the undertaking, indicates companions’ equipment and ap-proaches and gives a severe review of the newly built tools for commercial aerodynamic purposes. the simplest numerical innovations for integration as significant development blocks for the following new release of business move solvers are pointed out.
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Additional 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
Eng. 191(32), 3477–3490 (2002) 9. : Discontinuous Galerkin Methods: Theory, Computation and Applications. Springer, Heidelberg (1999) 10. : A Conservative Formulation of the Multidimensional Upwind Residual Distribution Schemes for General Nonlinear Conservation Laws. J. Comput. Phys. 179(1), 286–312 (2002) 11. : Agglomeration multigrid for the vertex-centered dual discontinuous Galerkin method. , et al. ) ADIGMA. NNFM, vol. 113, pp. 301–308. Springer, Heidelberg (2010) 12. : EDGE, a Navier–Stokes solver, for unstructured grids.
We triangulate each dual cell (bottom left) and define a macro element on each dual cell (bottom right), where the white circles are the computational nodes. Vertex-Centered Discontinuous Galerkin in Edge 45 Runge–Kutta scheme. This strategy is often combined with convergence acceleration strategies such as local time stepping and multigrid; both have been implemented and the multigrid approach is discussed in our other contribution to this volume . A crucial step in such an algorithm is the computation of the residual, which is a vector of dimension equal to the number of degrees of freedom for Vh for each equation that is solved.
The T Euler fluxes are written in a short hand notation as a row vector Fa := F1a , F2a , F3a which has as coefficients the fluxes into x, y- and z-direction: ⎞ ⎛ ρ vl ⎜ρ v1 vl + δ1l p⎟ ⎟ ⎜ a ⎟ (2) Fl (U) = ⎜ ⎜ρ v2 vl + δ2l p⎟ , l = 1, 2, 3. ⎝ρ v3 vl + δ3l p⎠ ρ evl + p vl Here, we use the usual notation of the physical quantities: ρ , v = (v1 , v2 , v3 )T , p, and e denote the density, the velocity vector, the pressure, and the specific total energy, respectively. The system is closed with the equation of state of a perfect gas 1 p = ρ RT = (γ − 1) ρ e − v · v 2 and 1 e = v · v + cv T 2 (3) c with the specific gas constant R = c p − cv .