• français
    • English
    français
  • Login
Help
View Item 
  •   Home
  • Dynamique des Fluides (DynFluid)
  • View Item
  • Home
  • Dynamique des Fluides (DynFluid)
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

A high-order time formulation of the RBC schemes for unsteady compressible Euler equations

Article dans une revue avec comité de lecture
Author
LERAT, Alain
134975 Laboratoire de Dynamique des Fluides [DynFluid]

URI
http://hdl.handle.net/10985/18920
DOI
10.1016/j.jcp.2015.09.045
Date
2015
Journal
Journal of Computational Physics

Abstract

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 on a 5x5-point stencil. The time integration of the RBC schemes uses a fully implicit method of 2nd-order accuracy (Gear method) usually solved by a dual-time approach. This method is efficient for computing compressible flows in slow unsteady regimes, but for quick unsteady flows, it may be costly and not accurate enough. A new time-formulation is proposed in the present paper. Unusually, in a RBC scheme the time derivative occurs, through linear discrete operators due to compactness, not only in the main residual but also in the other two residuals (in 2-D) involved in the numerical dissipation. To extract the time derivative, a space-factorization method which preserves the high accuracy in space is developed for reducing the algebra to the direct solution of simple linear systems on the mesh lines. Then a time-integration of high accuracy is selected for the RBC schemes by comparing the efficiency of four classes of explicit methods. The new time-formulation is validated for the diagonal advection of a Gaussian shape, the rotation of a hump, the advection of a vortex for a long time and the interaction of a vortex with a shock.

Files in this item

Name:
DYNFLUID_JCP_2015_LERAT.pdf
Size:
653.3Kb
Format:
PDF
Description:
Article
View/Open

Collections

  • Dynamique des Fluides (DynFluid)

Related items

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 
    Ouvrage scientifique
    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.
  • An efficient high-order compact scheme for the unsteady compressible Euler and Navier–Stokes equations 
    Article dans une revue avec comité de lecture
    LERAT, Alain (Elsevier, 2016)
    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 ...
  • A multi-scale approach of roughness measurements: Evaluation of the relevant scale 
    Article dans une revue avec comité de lecture
    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 
    Article dans une revue avec comité de lecture
    ESPINO-PÉREZ, Etzael; BRAS, Julien; DUCRUET, Violette J.; GUINAULT, Alain; DUFRESNE, Alain; DOMENEK, Sandra (Elsevier, 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 ...
  • Sensitivity of a 5-phase Brushless DC machine to the 7th harmonic of the back-electromotive force 
    Communication avec acte
    SEMAIL, Eric; KESTELYN, Xavier; BOUSCAYROL, Alain (IEEE, 2004)
    This paper presents a vector control of a 5-phase drive composed of a 5-leg Pulse Width Modulation (PWM) Voltage Source Inverter (VSI) supplying a permanent-magnet Brushless DC (BLDC) machine with trapezoidal waveform of ...

Browse

All SAMCommunities & CollectionsAuthorsIssue DateCenter / InstitutionThis CollectionAuthorsIssue DateCenter / Institution

Newsletter

Latest newsletterPrevious newsletters

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors

ÉCOLE NATIONALE SUPERIEURE D'ARTS ET METIERS

  • Contact
  • Mentions légales

ÉCOLE NATIONALE SUPERIEURE D'ARTS ET METIERS

  • Contact
  • Mentions légales