Accuracy study of the IDO scheme by Fourier analysis

Yohsuke Imai, Takayuki Aoki

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

The numerical accuracy of the Interpolated Differential Operator (IDO) scheme is studied with Fourier analysis for the solutions of Partial Differential Equations (PDEs): advection, diffusion, and Poisson equations. The IDO scheme solves governing equations not only for physical variable but also for first-order spatial derivative. Spatial discretizations are based on Hermite interpolation functions with both of them. In the Fourier analysis for the IDO scheme, the Fourier coefficients of the physical variable and the first-order derivative are coupled by the equations derived from the governing equations. The analysis shows the IDO scheme resolves all the wavenumbers with higher accuracy than the fourth-order Finite Difference (FD) and Compact Difference (CD) schemes for advection equation. In particular, for high wavenumbers, the accuracy is superior to that of the sixth-order Combined Compact Difference (CCD) scheme. The diffusion and Poisson equations are also more accurately solved in comparison with the FD and CD schemes. These results show that the IDO scheme guarantees highly resolved solutions for all the terms of fluid flow equations.

Original languageEnglish
Pages (from-to)453-472
Number of pages20
JournalJournal of Computational Physics
Volume217
Issue number2
DOIs
Publication statusPublished - 2006 Sep 20

Keywords

  • Computational fluid dynamics
  • Fourier analysis
  • High resolution
  • IDO scheme
  • Numerical accuracy
  • 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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