Stable coupling between vector and scalar variables for the IDO scheme on collocated grids

Yohsuke Imai, Takayuki Aoki

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


The Interpolated Differential Operator (IDO) scheme on collocated grids provides fourth-order discretizations for all the terms of the fluid flow equations. However, computations of fluid flows on collocated grids are not guaranteed to produce accurate solutions because of the poor coupling between velocity vector and scalar variables. A stable coupling method for the IDO scheme on collocated grids is proposed, where a new representation of first-order derivatives is adopted. It is important in deriving the representation to refer to the variables at neighboring grid points, keeping fourth-order truncation error. It is clear that accuracy and stability are drastically improved for shallow water equations in comparison with the conventional IDO scheme. The effects of the stable coupling are confirmed in incompressible flow calculations for DNS of turbulence and a driven cavity problem. The introduction of a rational function into the proposed method makes it possible to calculate shock waves with the initial conditions of extreme density and pressure jumps.

Original languageEnglish
Pages (from-to)81-97
Number of pages17
JournalJournal of Computational Physics
Issue number1
Publication statusPublished - 2006 Jun 10


  • Collocated grid
  • Computational fluid dynamics
  • Higher-order accuracy
  • IDO scheme
  • Numerical coupling
  • Numerical stability

ASJC Scopus subject areas

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


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