An efficient high-order compact scheme for the unsteady compressible Euler and Navier–Stokes equations

Autor: Alain Lerat
Přispěvatelé: Laboratoire de Dynamique des Fluides (DynFluid), Conservatoire National des Arts et Métiers [CNAM] (CNAM)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)
Rok vydání: 2016
Předmět:
Zdroj: Journal of Computational Physics
Journal of Computational Physics, Elsevier, 2016, 322, pp.365-386. ⟨10.1016/j.jcp.2016.06.050⟩
ISSN: 0021-9991
1090-2716
DOI: 10.1016/j.jcp.2016.06.050
Popis: International audience; Residual-Based Compact (RBC) schemes approximate the 3-D compressible Euler equationswith a 5th- or 7th-order accuracy on a 5 × 5 × 5-point stencil and capture shocks prettywell without correction. For unsteady flows however, they require a costly algebra toextract the time-derivative occurring at several places in the scheme. A new high-ordertime formulation has been recently proposed [13] for simplifying the RBC schemes andincreasing their temporal accuracy. The present paper goes much further in this directionand deeply reconsiders the method. An avatar of the RBC schemes is presented that greatlyreduces the computing time and the memory requirements while keeping the same type ofsuccessful numerical dissipation. Two and three-dimensional linear stability are analyzedand the method is extended to the 3-D compressible Navier–Stokes equations. The newcompact scheme is validated for several unsteady problems in two and three dimension. Inparticular, an accurate DNS at moderate cost is presented for the evolution of the Taylor–Green Vortex at Reynolds 1600 and Prandtl 0.71. The effects of the mesh size and of theaccuracy order in the approximation of Euler and viscous terms are discussed.
Databáze: OpenAIRE
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