### 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 language | English |
---|---|

Pages (from-to) | 1181-1200 |

Number of pages | 20 |

Journal | Communications in Computational Physics |

Volume | 16 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2014 Nov 1 |

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### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Communications in Computational Physics*,

*16*(5), 1181-1200. https://doi.org/10.4208/cicp.220513.070514a

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

Research output: Contribution to journal › Article

*Communications in Computational Physics*, vol. 16, no. 5, pp. 1181-1200. https://doi.org/10.4208/cicp.220513.070514a

}

TY - JOUR

T1 - A new approach for error reduction in the volume penalizationmethod

AU - Iwakami, Wakana

AU - Yatagai, Yuzuru

AU - Hatakeyama, Nozomu

AU - Hattori, Yuji

PY - 2014/11/1

Y1 - 2014/11/1

N2 - 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.

AB - 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.

KW - Compact scheme

KW - Error reduction

KW - Immersed boundary method

KW - Volume penalization method

UR - http://www.scopus.com/inward/record.url?scp=84907210438&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907210438&partnerID=8YFLogxK

U2 - 10.4208/cicp.220513.070514a

DO - 10.4208/cicp.220513.070514a

M3 - Article

AN - SCOPUS:84907210438

VL - 16

SP - 1181

EP - 1200

JO - Communications in Computational Physics

JF - Communications in Computational Physics

SN - 1815-2406

IS - 5

ER -