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

  • Authors:

  • Yohsuke Imai;Takayuki Aoki;Kenji Takizawa

  • Affiliations:

  • Department of Bioengineering and Robotics, Graduate School of Engineering, Tohoku University, 6-6-01 Aramaki Aza Aoba, Aoba-ku, Sendai-shi, Miyagi 980-8579, Japan;Global Scientific Information and Computing Center, Tokyo Institute of Technology, 2-12-1O-Okayama, Meguro-ku, Tokyo 152-8550, Japan;National Maritime Research Institute, 6-38-1 Shinkawa, Mitaka-shi, Tokyo 181-0004, Japan

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2008

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Abstract

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.