A new approach for error reduction in the volume penalizationmethod

Wakana Iwakami, Yuzuru Yatagai, Nozomu Hatakeyama, Yuji Hattori

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

A new approach for reducing error of the volume penalization method is proposed. The mask function is modified by shifting the interface between solid and fluid by √νη toward the fluid region, where ν and η are the viscosity and the permeability, respectively. The shift length √νη is derived from the analytical solution of the one-dimensional diffusion equation with a penalization term. The effect of the error reduction is verified numerically for the one-dimensional diffusion equation, Burgers' equation, and the two-dimensional Navier-Stokes equations. The results show that the numerical error is reduced except in the vicinity of the interface showing overall second-order accuracy, while it converges to a non-zero constant value as the number of grid points increases for the original mask function. However, the new approach is effectivewhen the grid resolution is sufficiently high so that the boundary layer, whose width is proportional to √νη, is resolved. Hence, the approach should be used when an appropriate combination of ν and η is chosen with a given numerical grid.

Original languageEnglish
Pages (from-to)1181-1200
Number of pages20
JournalCommunications in Computational Physics
Volume16
Issue number5
DOIs
Publication statusPublished - 2014 Nov 1

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grids
masks
Burger equation
fluids
Navier-Stokes equation
boundary layers
permeability
viscosity
shift

Keywords

  • Compact scheme
  • Error reduction
  • Immersed boundary method
  • Volume penalization method

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

A new approach for error reduction in the volume penalizationmethod. / Iwakami, Wakana; Yatagai, Yuzuru; Hatakeyama, Nozomu; Hattori, Yuji.

In: Communications in Computational Physics, Vol. 16, No. 5, 01.11.2014, p. 1181-1200.

Research output: Contribution to journalArticle

Iwakami, Wakana ; Yatagai, Yuzuru ; Hatakeyama, Nozomu ; Hattori, Yuji. / A new approach for error reduction in the volume penalizationmethod. In: Communications in Computational Physics. 2014 ; Vol. 16, No. 5. pp. 1181-1200.
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