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Entropy splitting for high-order numerical simulation of compressible turbulence

Entropy splitting for high-order numerical simulation of compressible turbulence
Entropy splitting for high-order numerical simulation of compressible turbulence
A 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.
0021-9991
307-322
Sandham, N.D.
0024d8cd-c788-4811-a470-57934fbdcf97
Li, Q.
54e51d2b-808c-42f2-95bb-62b4110df4dd
Yee, H.C.
be62329c-c041-4b20-abe8-637df86fba4b
Sandham, N.D.
0024d8cd-c788-4811-a470-57934fbdcf97
Li, Q.
54e51d2b-808c-42f2-95bb-62b4110df4dd
Yee, H.C.
be62329c-c041-4b20-abe8-637df86fba4b

Sandham, N.D., Li, Q. and Yee, H.C. (2002) Entropy splitting for high-order numerical simulation of compressible turbulence. Journal of Computational Physics, 178 (2), 307-322. (doi:10.1006/jcph.2002.7022).

Record type: Article

Abstract

A 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.

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Published date: 2002

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Local EPrints ID: 21760
URI: http://eprints.soton.ac.uk/id/eprint/21760
ISSN: 0021-9991
PURE UUID: 9c7a8c8e-f2b1-4a5c-92d4-fdc90f39b3c1
ORCID for N.D. Sandham: ORCID iD orcid.org/0000-0002-5107-0944

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Date deposited: 15 Mar 2006
Last modified: 03 Dec 2019 01:56

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Author: N.D. Sandham ORCID iD
Author: Q. Li
Author: H.C. Yee

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