Fourth-order accurate IDO scheme using gradient-staggered interpolation

Yohsuke Imai, Takayuki Aoki

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


An Interpolated Differential Operator (IDO) scheme using a new interpolation function is proposed. The gradient of the dependent variable is calculated at the position shifted by a half grid size from that of the physical value. A fourth-order Hermite-interpolation function is constructed locally using both the value and the gradient defined at staggered positions. The numerical solutions for the Poisson, diffusion, advection and wave equations have fourth- order accuracy in space. In particular, for the Poisson and diffusion equations, the Gradient-Staggered (G-S) IDO scheme shows better accuracy than the original IDO scheme. As a practical application, the Direct Numerical Simulation (DNS) for two-dimensional isotropic homogeneous turbulence is examined and a comparable result with that of the original IDO scheme is obtained. The G-S IDO scheme clearly contributes to high-accurate computations for solving partial differential equations in computational mechanics.

Original languageEnglish
Pages (from-to)681-689
Number of pages9
JournalJSME International Journal, Series B: Fluids and Thermal Engineering
Issue number4
Publication statusPublished - 2004 Nov


  • Fourth order accuracy
  • Gradient-staggered interpolation
  • Hermite interpolation
  • IDO scheme

ASJC Scopus subject areas

  • Mechanical Engineering
  • Physical and Theoretical Chemistry
  • Fluid Flow and Transfer Processes


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