A higher-order implicit IDO scheme and its CFD application to local mesh refinement method

Yohsuke Imai, Takayuki Aoki

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


The Interpolated Differential Operator (IDO) scheme has been developed for the numerical solution of the fluid motion equations, and allows to produce highly accurate results by introducing the spatial derivative of the physical value as an additional dependent variable. For incompressible flows, semi-implicit time integration is strongly affected by the Courant and diffusion number limitation. A high-order fully-implicit IDO scheme is presented, and the two-stage implicit Runge-Kutta time integration keeps over third-order accuracy. The application of the method to the direct numerical simulation of turbulence demonstrates that the proposed scheme retains a resolution comparable to that of spectral methods even for relatively large Courant numbers. The scheme is further applied to the Local Mesh Refinement (LMR) method, where the size of the time step is often restricted by the dimension of the smallest meshes. In the computation of the Karman vortex street problem, the implicit IDO scheme with LMR is shown to allow a conspicuous saving of computational resources.

Original languageEnglish
Pages (from-to)211-221
Number of pages11
JournalComputational Mechanics
Issue number3
Publication statusPublished - 2006 Aug


  • IDO scheme
  • Implicit Runge-Kutta method
  • Incompressible flow simulation
  • Local Mesh Refinement

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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