Optimal time splitting for two- and three-dimensional navier-stokes equations with mixed derivatives

Saul Abarbanel; David Gottlieb

doi:10.1016/0021-9991(81)90077-2

Optimal time splitting for two- and three-dimensional navier-stokes equations with mixed derivatives

Saul Abarbanel
, David Gottlieb

Tel Aviv University

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

105 Scopus citations

Abstract

A new explicit, time splitting algorithm has been developed for finite difference modelling of the full two and three-dimensional time-dependent, compressible, viscous Navier-Stokes equations of fluid mechanics. The scheme is optimal in the sense that the split operators achieve their maximum allowable time step, i.e., the corresponding Courant number. The algorithm allows a conservation-form formulation. Stability is proven analytically and verified numerically. In proving stability it was shown that all nine matrix coefficients of the Navier-Stokes equations are simultaneously symmetrizable by a similarity transformation. Two such transformations and their resulting symmetric matrix coefficients are presented explicitly.

Original language	English
Pages (from-to)	1-33
Number of pages	33
Journal	Journal of Computational Physics
Volume	41
Issue number	1
DOIs	https://doi.org/10.1016/0021-9991(81)90077-2
State	Published - May 1981
Externally published	Yes

Bibliographical note

Funding Information:
*This work was supported in part by the Air Force Office of Scientific Research (NAM); the European Office of Aerospace Research, AFSC, United States Air Force, under Grant AFOSR 78.365 1, and in part by NASA Contracts NASl-14101 and NASl-15810 at ICASE, NASA Langley Research Center, Hampton, VA. 23665.

Funding

*This work was supported in part by the Air Force Office of Scientific Research (NAM); the European Office of Aerospace Research, AFSC, United States Air Force, under Grant AFOSR 78.365 1, and in part by NASA Contracts NASl-14101 and NASl-15810 at ICASE, NASA Langley Research Center, Hampton, VA. 23665.

Funders	Funder number
European Office of Aerospace Research
NASA Langley Research Center, Hampton	23665
National Aeronautics and Space Administration	NASl-14101, NASl-15810
Air Force Office of Scientific Research	78.365 1
U.S. Air Force
National Academy of Medicine
Air Force Systems Command

Access to Document

10.1016/0021-9991(81)90077-2

Cite this

@article{28bef99514e14cb68474ab6cdfda00b1,

title = "Optimal time splitting for two- and three-dimensional navier-stokes equations with mixed derivatives",

abstract = "A new explicit, time splitting algorithm has been developed for finite difference modelling of the full two and three-dimensional time-dependent, compressible, viscous Navier-Stokes equations of fluid mechanics. The scheme is optimal in the sense that the split operators achieve their maximum allowable time step, i.e., the corresponding Courant number. The algorithm allows a conservation-form formulation. Stability is proven analytically and verified numerically. In proving stability it was shown that all nine matrix coefficients of the Navier-Stokes equations are simultaneously symmetrizable by a similarity transformation. Two such transformations and their resulting symmetric matrix coefficients are presented explicitly.",

author = "Saul Abarbanel and David Gottlieb",

note = "Funding Information: *This work was supported in part by the Air Force Office of Scientific Research (NAM); the European Office of Aerospace Research, AFSC, United States Air Force, under Grant AFOSR 78.365 1, and in part by NASA Contracts NASl-14101 and NASl-15810 at ICASE, NASA Langley Research Center, Hampton, VA. 23665.",

year = "1981",

month = may,

doi = "10.1016/0021-9991(81)90077-2",

language = "אנגלית",

volume = "41",

pages = "1--33",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Optimal time splitting for two- and three-dimensional navier-stokes equations with mixed derivatives

AU - Abarbanel, Saul

AU - Gottlieb, David

N1 - Funding Information: *This work was supported in part by the Air Force Office of Scientific Research (NAM); the European Office of Aerospace Research, AFSC, United States Air Force, under Grant AFOSR 78.365 1, and in part by NASA Contracts NASl-14101 and NASl-15810 at ICASE, NASA Langley Research Center, Hampton, VA. 23665.

PY - 1981/5

Y1 - 1981/5

N2 - A new explicit, time splitting algorithm has been developed for finite difference modelling of the full two and three-dimensional time-dependent, compressible, viscous Navier-Stokes equations of fluid mechanics. The scheme is optimal in the sense that the split operators achieve their maximum allowable time step, i.e., the corresponding Courant number. The algorithm allows a conservation-form formulation. Stability is proven analytically and verified numerically. In proving stability it was shown that all nine matrix coefficients of the Navier-Stokes equations are simultaneously symmetrizable by a similarity transformation. Two such transformations and their resulting symmetric matrix coefficients are presented explicitly.

AB - A new explicit, time splitting algorithm has been developed for finite difference modelling of the full two and three-dimensional time-dependent, compressible, viscous Navier-Stokes equations of fluid mechanics. The scheme is optimal in the sense that the split operators achieve their maximum allowable time step, i.e., the corresponding Courant number. The algorithm allows a conservation-form formulation. Stability is proven analytically and verified numerically. In proving stability it was shown that all nine matrix coefficients of the Navier-Stokes equations are simultaneously symmetrizable by a similarity transformation. Two such transformations and their resulting symmetric matrix coefficients are presented explicitly.

UR - https://www.scopus.com/pages/publications/0003084153

U2 - 10.1016/0021-9991(81)90077-2

DO - 10.1016/0021-9991(81)90077-2

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0003084153

SN - 0021-9991

VL - 41

SP - 1

EP - 33

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 1

ER -

Optimal time splitting for two- and three-dimensional navier-stokes equations with mixed derivatives

Abstract

Bibliographical note

Funding

Access to Document

Other files and links

Fingerprint

Cite this