A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows

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A robust, implicit, low-dissipation method suitable for LES/DNS of compressible turbulent flows is discussed. The scheme is designed such that the discrete flux of kinetic energy and its rate of change are consistent with those predicted by the momentum and continuity equations. The resulting spatial fluxes are similar to those derived using the so-called skew-symmetric formulation of the convective terms. Enforcing consistency for the time derivative results in a novel density weighted Crank-Nicolson type scheme. The method is stable without the addition of any explicit dissipation terms at very high Reynolds numbers for flows without shocks. Shock capturing is achieved by switching on a dissipative flux term which tends to zero in smooth regions of the flow. Numerical examples include a one-dimensional shock tube problem, the Taylor-Green problem, simulations of isotropic turbulence, hypersonic flow over a double-cone geometry, and compressible turbulent channel flow.

Original languageEnglish (US)
Pages (from-to)1347-1364
Number of pages18
JournalJournal of Computational Physics
Issue number5
StatePublished - Mar 20 2009

Bibliographical note

Funding Information:
The authors would like to thank Professor Gary N. Coleman for the channel flow DNS data and Dr. Ioannis Nompelis for help with the double-cone simulations. The research is supported by Air Force Office of Scientific Research (AFOSR) under Grant No. FA9550-0401-0341 and the NASA Fundamental Aeronautics Program. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the AFOSR or the US Government.


  • Compressible flow
  • Direct numerical simulation
  • Fully discrete
  • Implicit time integration
  • Kinetic energy
  • Large-eddy simulation
  • Non-dissipative


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