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

Yohsuke Imai*, Takayuki Aoki, Kenji Takizawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


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
Issue number4
Publication statusPublished - 2008 Feb 1
Externally publishedYes


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

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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