An asymptotically stable compact upwind-biased finite-difference scheme for hyperbolic systems

A. Jocksch; N. A. Adams; L. Kleiser

doi:10.1016/j.jcp.2005.01.030

An asymptotically stable compact upwind-biased finite-difference scheme for hyperbolic systems

A. Jocksch, N. A. Adams, L. Kleiser

Chair of Aerodynamics and Fluid mechanics

ETH Zurich

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

2 Scopus citations

Abstract

Asymptotic stability of high-order finite-difference schemes for linear hyperbolic systems is investigated using the Nyquist criterion of linear-system theory. This criterion leads to a sufficient stability condition which is evaluated numerically. A fifth-order compact upwind-biased finite-difference scheme is developed which is asymptotically stable, according to the Nyquist criterion, for linear 2 × 2 systems. Moreover, this scheme is optimised with respect to its dispersion properties. The suitability of the scheme for discretisation of the compressible Navier-Stokes equations is demonstrated by computing inviscid and viscous eigensolutions of compressible Couette flow.

Original language	English
Pages (from-to)	435-454
Number of pages	20
Journal	Journal of Computational Physics
Volume	208
Issue number	2
DOIs	https://doi.org/10.1016/j.jcp.2005.01.030
State	Published - 20 Sep 2005

Keywords

Compact finite-difference schemes
Stability

Access to Document

10.1016/j.jcp.2005.01.030

Cite this

@article{a05b51f740ed4feda01afd0cd169684b,

title = "An asymptotically stable compact upwind-biased finite-difference scheme for hyperbolic systems",

abstract = "Asymptotic stability of high-order finite-difference schemes for linear hyperbolic systems is investigated using the Nyquist criterion of linear-system theory. This criterion leads to a sufficient stability condition which is evaluated numerically. A fifth-order compact upwind-biased finite-difference scheme is developed which is asymptotically stable, according to the Nyquist criterion, for linear 2 × 2 systems. Moreover, this scheme is optimised with respect to its dispersion properties. The suitability of the scheme for discretisation of the compressible Navier-Stokes equations is demonstrated by computing inviscid and viscous eigensolutions of compressible Couette flow.",

keywords = "Compact finite-difference schemes, Stability",

author = "A. Jocksch and Adams, {N. A.} and L. Kleiser",

note = "Funding Information: This work was supported by the Swiss National Science Foundation. The authors would like to acknowledge helpful discussions with Prof. J. Waldvogel (ETH), Dr. B. M{\"u}ller (Uppsala), S. M{\"u}ller and F. Keiderling. ",

year = "2005",

month = sep,

day = "20",

doi = "10.1016/j.jcp.2005.01.030",

language = "English",

volume = "208",

pages = "435--454",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - An asymptotically stable compact upwind-biased finite-difference scheme for hyperbolic systems

AU - Jocksch, A.

AU - Adams, N. A.

AU - Kleiser, L.

N1 - Funding Information: This work was supported by the Swiss National Science Foundation. The authors would like to acknowledge helpful discussions with Prof. J. Waldvogel (ETH), Dr. B. Müller (Uppsala), S. Müller and F. Keiderling.

PY - 2005/9/20

Y1 - 2005/9/20

N2 - Asymptotic stability of high-order finite-difference schemes for linear hyperbolic systems is investigated using the Nyquist criterion of linear-system theory. This criterion leads to a sufficient stability condition which is evaluated numerically. A fifth-order compact upwind-biased finite-difference scheme is developed which is asymptotically stable, according to the Nyquist criterion, for linear 2 × 2 systems. Moreover, this scheme is optimised with respect to its dispersion properties. The suitability of the scheme for discretisation of the compressible Navier-Stokes equations is demonstrated by computing inviscid and viscous eigensolutions of compressible Couette flow.

AB - Asymptotic stability of high-order finite-difference schemes for linear hyperbolic systems is investigated using the Nyquist criterion of linear-system theory. This criterion leads to a sufficient stability condition which is evaluated numerically. A fifth-order compact upwind-biased finite-difference scheme is developed which is asymptotically stable, according to the Nyquist criterion, for linear 2 × 2 systems. Moreover, this scheme is optimised with respect to its dispersion properties. The suitability of the scheme for discretisation of the compressible Navier-Stokes equations is demonstrated by computing inviscid and viscous eigensolutions of compressible Couette flow.

KW - Compact finite-difference schemes

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=19744374914&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2005.01.030

DO - 10.1016/j.jcp.2005.01.030

M3 - Article

AN - SCOPUS:19744374914

SN - 0021-9991

VL - 208

SP - 435

EP - 454

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 2

ER -

An asymptotically stable compact upwind-biased finite-difference scheme for hyperbolic systems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this