Conservative form of interpolated differential operator scheme for compressible and incompressible fluid dynamics

Yohsuke Imai, Takayuki Aoki, Kenji Takizawa

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

The proposed scheme, which is a conservative form of the interpolated differential operator scheme (IDO-CF), can provide high accurate solutions for both compressible and incompressible fluid equations. Spatial discretizations with fourth-order accuracy are derived from interpolation functions locally constructed by both cell-integrated values and point values. These values are coupled and time-integrated by solving fluid equations in the flux forms for the cell-integrated values and in the derivative forms for the point values. The IDO-CF scheme exactly conserves mass, momentum, and energy, retaining the high resolution more than the non-conservative form of the IDO scheme. A direct numerical simulation of turbulence is carried out with comparable accuracy to that of spectral methods. Benchmark tests of Riemann problems and lid-driven cavity flows show that the IDO-CF scheme is immensely promising in compressible and incompressible fluid dynamics studies.

Original languageEnglish
Pages (from-to)2263-2285
Number of pages23
JournalJournal of Computational Physics
Volume227
Issue number4
DOIs
Publication statusPublished - 2008 Feb 1
Externally publishedYes

Fingerprint

compressible fluids
differential operators
incompressible fluids
fluid dynamics
Fluid dynamics
cavity flow
Cauchy problem
Fluids
spectral methods
Direct numerical simulation
retaining
cells
direct numerical simulation
interpolation
Interpolation
Momentum
Turbulence
turbulence
Fluxes
Derivatives

Keywords

  • Computational fluid dynamics
  • Conservative form
  • DO scheme
  • High resolution

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy (miscellaneous)

Cite this

Conservative form of interpolated differential operator scheme for compressible and incompressible fluid dynamics. / Imai, Yohsuke; Aoki, Takayuki; Takizawa, Kenji.

In: Journal of Computational Physics, Vol. 227, No. 4, 01.02.2008, p. 2263-2285.

Research output: Contribution to journalArticle

@article{6fdf296c068d4e2c987b565d9c84ee36,
title = "Conservative form of interpolated differential operator scheme for compressible and incompressible fluid dynamics",
abstract = "The proposed scheme, which is a conservative form of the interpolated differential operator scheme (IDO-CF), can provide high accurate solutions for both compressible and incompressible fluid equations. Spatial discretizations with fourth-order accuracy are derived from interpolation functions locally constructed by both cell-integrated values and point values. These values are coupled and time-integrated by solving fluid equations in the flux forms for the cell-integrated values and in the derivative forms for the point values. The IDO-CF scheme exactly conserves mass, momentum, and energy, retaining the high resolution more than the non-conservative form of the IDO scheme. A direct numerical simulation of turbulence is carried out with comparable accuracy to that of spectral methods. Benchmark tests of Riemann problems and lid-driven cavity flows show that the IDO-CF scheme is immensely promising in compressible and incompressible fluid dynamics studies.",
keywords = "Computational fluid dynamics, Conservative form, DO scheme, High resolution",
author = "Yohsuke Imai and Takayuki Aoki and Kenji Takizawa",
year = "2008",
month = "2",
day = "1",
doi = "10.1016/j.jcp.2007.11.031",
language = "English",
volume = "227",
pages = "2263--2285",
journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",
number = "4",

}

TY - JOUR

T1 - Conservative form of interpolated differential operator scheme for compressible and incompressible fluid dynamics

AU - Imai, Yohsuke

AU - Aoki, Takayuki

AU - Takizawa, Kenji

PY - 2008/2/1

Y1 - 2008/2/1

N2 - The proposed scheme, which is a conservative form of the interpolated differential operator scheme (IDO-CF), can provide high accurate solutions for both compressible and incompressible fluid equations. Spatial discretizations with fourth-order accuracy are derived from interpolation functions locally constructed by both cell-integrated values and point values. These values are coupled and time-integrated by solving fluid equations in the flux forms for the cell-integrated values and in the derivative forms for the point values. The IDO-CF scheme exactly conserves mass, momentum, and energy, retaining the high resolution more than the non-conservative form of the IDO scheme. A direct numerical simulation of turbulence is carried out with comparable accuracy to that of spectral methods. Benchmark tests of Riemann problems and lid-driven cavity flows show that the IDO-CF scheme is immensely promising in compressible and incompressible fluid dynamics studies.

AB - The proposed scheme, which is a conservative form of the interpolated differential operator scheme (IDO-CF), can provide high accurate solutions for both compressible and incompressible fluid equations. Spatial discretizations with fourth-order accuracy are derived from interpolation functions locally constructed by both cell-integrated values and point values. These values are coupled and time-integrated by solving fluid equations in the flux forms for the cell-integrated values and in the derivative forms for the point values. The IDO-CF scheme exactly conserves mass, momentum, and energy, retaining the high resolution more than the non-conservative form of the IDO scheme. A direct numerical simulation of turbulence is carried out with comparable accuracy to that of spectral methods. Benchmark tests of Riemann problems and lid-driven cavity flows show that the IDO-CF scheme is immensely promising in compressible and incompressible fluid dynamics studies.

KW - Computational fluid dynamics

KW - Conservative form

KW - DO scheme

KW - High resolution

UR - http://www.scopus.com/inward/record.url?scp=62849092980&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=62849092980&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2007.11.031

DO - 10.1016/j.jcp.2007.11.031

M3 - Article

AN - SCOPUS:62849092980

VL - 227

SP - 2263

EP - 2285

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 4

ER -