An efficient high-order compact scheme for the unsteady compressible Euler and Navier–Stokes equations
TypeArticles dans des revues avec comité de lecture
Residual-Based Compact (RBC) schemes approximate the 3-D compressible Euler equations with a 5th- or 7th-order accuracy on a 5 × 5 × 5-point stencil and capture shocks pretty well without correction. For unsteady flows however, they require a costly algebra to extract the time-derivative occurring at several places in the scheme. A new high-order time formulation has been recently proposed  for simplifying the RBC schemes and increasing their temporal accuracy. The present paper goes much further in this direction and deeply reconsiders the method. An avatar of the RBC schemes is presented that greatly reduces the computing time and the memory requirements while keeping the same type of successful numerical dissipation. Two and three-dimensional linear stability are analyzed and the method is extended to the 3-D compressible Navier–Stokes equations. The new compact scheme is validated for several unsteady problems in two and three dimension. In particular, 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 the accuracy order in the approximation of Euler and viscous terms are discussed.
Showing items related by title, author, creator and subject.
Recent Progress in High-Order Residual-Based Compact Schemes for Compressible Flow Simulations: Toward Scale-Resolving Simulations and Complex Geometries CINNELLA, Paola; GRIMICH, Karim; LERAT, Alain; OUTTIER, P. Y. (Springer International Publishing, 2015)Recent developments about the extension of high-order Residual-Based Compact schemes to unsteady flows and complex configurations are discussed, with application to scale-resolving simulations and complex turbomachinery flows.
LERAT, Alain (ELSEVIER, 2015)Residual-Based Compact (RBC) schemes can approximate the compressible Euler equations with a high space-accuracy on a very compact stencil. For instance on a 2-D Cartesian mesh, the 5th and 7th-order accuracy can be reached ...
VAN GORP, Adrien; BIGERELLE, Maxence; GRELLIER, Alain; IOST, Alain; NAJJAR, Denis (ELSEVIER, 2007)This paper proposes a new multi-scale measurement approach performed to compare the surface roughness and the visual aspect of polished surfaces. In this investigation, five specimens of glass moulds presenting different ...
Influence of chemical surface modification of cellulose nanowhiskers on thermal, mechanical, and barrier properties of poly(lactide) based ESPINO-PÉREZ, Etzael; BRAS, Julien; DUCRUET, Violette J.; GUINAULT, Alain; DUFRESNE, Alain; DOMENEK, Sandra (2013)In the aim of producing fully organic bionanocomposite based on poly(lactide) (PLA), cellulose nanowhiskers (CNW) were grafted by n-octadecyl-isocyanate (CNW-ICN) applying an in situ surface grafting method. The compatibilizing ...
MARTIN, Patrick; BAUDOUIN, Cyrille; DAILLE-LEFEVRE, Bruno; GODOT, Xavier; ETIENNE, Alain; SIADAT, Ali; MARSOT, Jacques (AIP PRIMECA, 2012)La démarche de « Prévention intégrée» consiste à appliquer au plus tôt des principes de conception sûre en termes de sécurité des opérateurs d’équipements de travail. Malgré les avancées en termes de connaissances et de ...