Convergence Tests for the Piecewise Parabolic Method and Navier-Stokes Solutions for Homogeneous Compressible Turbulence

Igor V. Sytine; David H. Porter; Paul R. Woodward; Stephen W. Hodson; Karl Heinz Winkler

doi:10.1006/jcph.1999.6416

Convergence Tests for the Piecewise Parabolic Method and Navier-Stokes Solutions for Homogeneous Compressible Turbulence

Igor V. Sytine, David H. Porter, Paul R. Woodward, Stephen W. Hodson, Karl Heinz Winkler

Research output: Contribution to journal › Article › peer-review

75 Scopus citations

Abstract

The need to simulate fully developed turbulence with wide range of scales led us to use the Piecewise Parabolic Method (PPM) to solve the Euler equations of motions. To obtain data for 3-D homogeneous compressible decaying turbulence numerical simulations were performed on computational meshes of up to 1024³ zones. These data were compared with data obtained by solving the Navier-Stokes (NS) equations. Results of studying the kinetic energy, enstrophy, and the energy power spectra with different resolutions are presented for both the PPM and NS data. The results of the comparison show convergence of the PPM and NS solutions to the same limit.

Original language	English (US)
Pages (from-to)	225-238
Number of pages	14
Journal	Journal of Computational Physics
Volume	158
Issue number	2
DOIs	https://doi.org/10.1006/jcph.1999.6416
State	Published - Mar 1 2000

Bibliographical note

Funding Information:
The authors are pleased to acknowledge grants of computer time from the Los Alamos National Laboratory (LANL) and the National Center for Supercomputing Applications (NCSA) where the computations were performed. Very useful discussions with Tom Jones of the Astronomy Department, University of Minnesota, helped to keep us focused. The discussions and efforts of Laboratory for Computational Science and Engineering staff members Wenlong Dai and Steve Anderson were also helpful. This work was supported by the National Science Foundation, under Grand Challenge Grant ASC-9217394, by the Department of Energy by Grant DE-FG02-87ER25035, and through the Lawrence Livermore National Laboratory under the ASCI Project through Grant LLNL/B31627/DOE and the Los Alamos National Laboratory under Grant LANL/B33700016-3Y/DOE. This work was supported also by the National Center for Supercomputing Applications under Grant MCA97S006N. The LCSE, where the analysis of the data was performed, is also supported in part by a grant from the Minnesota Supercomputer Institute.

Keywords

Homogeneous compressible turbulence
Piecewise Parabolic Method
Subgrid-scale models
Turbulence modeling

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title = "Convergence Tests for the Piecewise Parabolic Method and Navier-Stokes Solutions for Homogeneous Compressible Turbulence",

abstract = "The need to simulate fully developed turbulence with wide range of scales led us to use the Piecewise Parabolic Method (PPM) to solve the Euler equations of motions. To obtain data for 3-D homogeneous compressible decaying turbulence numerical simulations were performed on computational meshes of up to 10243 zones. These data were compared with data obtained by solving the Navier-Stokes (NS) equations. Results of studying the kinetic energy, enstrophy, and the energy power spectra with different resolutions are presented for both the PPM and NS data. The results of the comparison show convergence of the PPM and NS solutions to the same limit.",

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note = "Funding Information: The authors are pleased to acknowledge grants of computer time from the Los Alamos National Laboratory (LANL) and the National Center for Supercomputing Applications (NCSA) where the computations were performed. Very useful discussions with Tom Jones of the Astronomy Department, University of Minnesota, helped to keep us focused. The discussions and efforts of Laboratory for Computational Science and Engineering staff members Wenlong Dai and Steve Anderson were also helpful. This work was supported by the National Science Foundation, under Grand Challenge Grant ASC-9217394, by the Department of Energy by Grant DE-FG02-87ER25035, and through the Lawrence Livermore National Laboratory under the ASCI Project through Grant LLNL/B31627/DOE and the Los Alamos National Laboratory under Grant LANL/B33700016-3Y/DOE. This work was supported also by the National Center for Supercomputing Applications under Grant MCA97S006N. The LCSE, where the analysis of the data was performed, is also supported in part by a grant from the Minnesota Supercomputer Institute.",

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Convergence Tests for the Piecewise Parabolic Method and Navier-Stokes Solutions for Homogeneous Compressible Turbulence

Abstract

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Keywords

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