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Entropy Splitting for High-Order Numerical Simulation of Compressible TurbulenceA stable high-order numerical scheme for direct numerical simulation (DNS) of shock-free compressible turbulence is presented. The method is applicable to general geometries. It contains no upwinding, artificial dissipation, or filtering. Instead the method relies on the stabilizing mechanisms of an appropriate conditioning of the governing equations and the use of compatible spatial difference operators for the interior points (interior scheme) as well as the boundary points (boundary scheme). An entropy-splitting approach splits the inviscid flux derivatives into conservative and nonconservative portions. The spatial difference operators satisfy a summation-by-parts condition, leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate. A Laplacian formulation of the viscous and heat conduction terms on the right hand side of the Navier–Stokes equations is used to ensure that any tendency to odd–even decoupling associated with central schemes can be countered by the fluid viscosity. The resulting methods are able to minimize the spurious high-frequency oscillations associated with pure central schemes, especially for long time integration applications such as DNS. For validation purposes, the methods are tested in a DNS of compressible turbulent plane channel flow at low values of friction Mach number, where reference turbulence data bases exist. It is demonstrated that the methods are robust in terms of grid resolution, and in good agreement with published channel data. Accurate turbulence statistics can be obtained with moderate grid sizes. Stability limits on the range of the splitting parameter are determined from numerical tests.
Document ID
20010069675
Acquisition Source
Ames Research Center
Document Type
Preprint (Draft being sent to journal)
Authors
N.D. Sandham
(University of Southampton Southampton, United Kingdom)
Q. Li
(University of Southampton Southampton, United Kingdom)
H.C. Yee
(Ames Research Center Mountain View, California, United States)
Date Acquired
August 20, 2013
Publication Date
May 25, 2002
Publication Information
Publication: Journal of Computational Physics
Publisher: Elsevier
Volume: 178
Issue: 2
Issue Publication Date: May 20, 2002
ISSN: 0021-9991
e-ISSN: 1090-2716
Subject Category
Fluid Mechanics And Thermodynamics
Report/Patent Number
RIACS-TR-00.10
Meeting Information
Meeting: First International Conference on Computational Fluid Dynamics
Location: Kyoto
Country: JP
Start Date: July 10, 2000
End Date: July 14, 2000
Funding Number(s)
CONTRACT_GRANT: EPSRC GR/M 21546
CONTRACT_GRANT: EPSRC GR/M 84336
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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