Highly energy-conservative finite difference method for the cylindrical coordinate system

Koji Fukagata, Nobuhide Kasagi

Research output: Contribution to journalArticle

89 Citations (Scopus)

Abstract

A highly energy-conservative second-order-accurate finite difference method for the cylindrical coordinate system is developed. It is rigorously proved that energy conservation in discretized space is satisfied when appropriate interpolation schemes are used. This argument holds not only for an unequally spaced mesh but also for an equally spaced mesh on cylindrical coordinates but not on Cartesian coordinates. Numerical tests are undertaken for an inviscid flow with various schemes, and it turns out that the proposed scheme offers a superior energy-conservation property and greater stability than the intuitive and previously proposed methods, for both equally spaced and unequally spaced meshes.

Original languageEnglish
Pages (from-to)478-498
Number of pages21
JournalJournal of Computational Physics
Volume181
Issue number2
DOIs
Publication statusPublished - 2002 Sep 20
Externally publishedYes

Fingerprint

cylindrical coordinates
Finite difference method
mesh
Energy conservation
Computer systems
energy conservation
inviscid flow
Interpolation
Cartesian coordinates
interpolation
energy

Keywords

  • Advection
  • Body force
  • Cylindrical coordinate system
  • Energy conservation
  • Finite difference method
  • Incompressible flow
  • Pipe flow
  • Singularity

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

Highly energy-conservative finite difference method for the cylindrical coordinate system. / Fukagata, Koji; Kasagi, Nobuhide.

In: Journal of Computational Physics, Vol. 181, No. 2, 20.09.2002, p. 478-498.

Research output: Contribution to journalArticle

@article{531953aba02446e0aadc400477e315a7,
title = "Highly energy-conservative finite difference method for the cylindrical coordinate system",
abstract = "A highly energy-conservative second-order-accurate finite difference method for the cylindrical coordinate system is developed. It is rigorously proved that energy conservation in discretized space is satisfied when appropriate interpolation schemes are used. This argument holds not only for an unequally spaced mesh but also for an equally spaced mesh on cylindrical coordinates but not on Cartesian coordinates. Numerical tests are undertaken for an inviscid flow with various schemes, and it turns out that the proposed scheme offers a superior energy-conservation property and greater stability than the intuitive and previously proposed methods, for both equally spaced and unequally spaced meshes.",
keywords = "Advection, Body force, Cylindrical coordinate system, Energy conservation, Finite difference method, Incompressible flow, Pipe flow, Singularity",
author = "Koji Fukagata and Nobuhide Kasagi",
year = "2002",
month = "9",
day = "20",
doi = "10.1006/jcph.2002.7138",
language = "English",
volume = "181",
pages = "478--498",
journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",
number = "2",

}

TY - JOUR

T1 - Highly energy-conservative finite difference method for the cylindrical coordinate system

AU - Fukagata, Koji

AU - Kasagi, Nobuhide

PY - 2002/9/20

Y1 - 2002/9/20

N2 - A highly energy-conservative second-order-accurate finite difference method for the cylindrical coordinate system is developed. It is rigorously proved that energy conservation in discretized space is satisfied when appropriate interpolation schemes are used. This argument holds not only for an unequally spaced mesh but also for an equally spaced mesh on cylindrical coordinates but not on Cartesian coordinates. Numerical tests are undertaken for an inviscid flow with various schemes, and it turns out that the proposed scheme offers a superior energy-conservation property and greater stability than the intuitive and previously proposed methods, for both equally spaced and unequally spaced meshes.

AB - A highly energy-conservative second-order-accurate finite difference method for the cylindrical coordinate system is developed. It is rigorously proved that energy conservation in discretized space is satisfied when appropriate interpolation schemes are used. This argument holds not only for an unequally spaced mesh but also for an equally spaced mesh on cylindrical coordinates but not on Cartesian coordinates. Numerical tests are undertaken for an inviscid flow with various schemes, and it turns out that the proposed scheme offers a superior energy-conservation property and greater stability than the intuitive and previously proposed methods, for both equally spaced and unequally spaced meshes.

KW - Advection

KW - Body force

KW - Cylindrical coordinate system

KW - Energy conservation

KW - Finite difference method

KW - Incompressible flow

KW - Pipe flow

KW - Singularity

UR - http://www.scopus.com/inward/record.url?scp=0037144932&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037144932&partnerID=8YFLogxK

U2 - 10.1006/jcph.2002.7138

DO - 10.1006/jcph.2002.7138

M3 - Article

VL - 181

SP - 478

EP - 498

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 2

ER -