### Abstract

A surface tension model is essential to simulate multiphase flows with deformed interfaces. This study develops a contoured continuum surface force (CCSF) model for particle methods. A color function that varies sharply across the interface to mark different fluid phases is smoothed in the transition region, where the local contour curvature can be regarded as the interface curvature. The local contour passing through each reference particle in the transition region is extracted from the local profile of the smoothed color function. The local contour curvature is calculated based on the Taylor series expansion of the smoothed color function, whose derivatives are calculated accurately according to the definition of the smoothed color function. Two schemes are proposed to specify the smooth radius: Fixed scheme, where 2×r_{e} (r_{e} = particle interaction radius) is assigned to all particles in the transition region; and varied scheme, where r_{e} and 2×r_{e} are assigned to the central and edged particles in the transition region respectively. Numerical examples, including curvature calculation for static circle and ellipse interfaces, deformation of square droplet to a circle (2D and 3D), droplet deformation in shear flow, and droplet coalescence, are simulated to verify the CCSF model and compare its performance with those of other methods. The CCSF model with the fixed scheme is proven to produce the most accurate curvature and lowest parasitic currents among the tested methods.

Original language | English |
---|---|

Pages (from-to) | 280-304 |

Number of pages | 25 |

Journal | Journal of Computational Physics |

Volume | 298 |

DOIs | |

Publication status | Published - 2015 Jan 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Contoured continuum surface force model
- MPS method
- Particle method
- Surface tension

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)
- Computer Science Applications

### Cite this

*Journal of Computational Physics*,

*298*, 280-304. https://doi.org/10.1016/j.jcp.2015.06.004

**A contoured continuum surface force model for particle methods.** / Duan, Guangtao; Koshizuka, Seiichi; Chen, Bin.

Research output: Contribution to journal › Article

*Journal of Computational Physics*, vol. 298, pp. 280-304. https://doi.org/10.1016/j.jcp.2015.06.004

}

TY - JOUR

T1 - A contoured continuum surface force model for particle methods

AU - Duan, Guangtao

AU - Koshizuka, Seiichi

AU - Chen, Bin

PY - 2015/1/1

Y1 - 2015/1/1

N2 - A surface tension model is essential to simulate multiphase flows with deformed interfaces. This study develops a contoured continuum surface force (CCSF) model for particle methods. A color function that varies sharply across the interface to mark different fluid phases is smoothed in the transition region, where the local contour curvature can be regarded as the interface curvature. The local contour passing through each reference particle in the transition region is extracted from the local profile of the smoothed color function. The local contour curvature is calculated based on the Taylor series expansion of the smoothed color function, whose derivatives are calculated accurately according to the definition of the smoothed color function. Two schemes are proposed to specify the smooth radius: Fixed scheme, where 2×re (re = particle interaction radius) is assigned to all particles in the transition region; and varied scheme, where re and 2×re are assigned to the central and edged particles in the transition region respectively. Numerical examples, including curvature calculation for static circle and ellipse interfaces, deformation of square droplet to a circle (2D and 3D), droplet deformation in shear flow, and droplet coalescence, are simulated to verify the CCSF model and compare its performance with those of other methods. The CCSF model with the fixed scheme is proven to produce the most accurate curvature and lowest parasitic currents among the tested methods.

AB - A surface tension model is essential to simulate multiphase flows with deformed interfaces. This study develops a contoured continuum surface force (CCSF) model for particle methods. A color function that varies sharply across the interface to mark different fluid phases is smoothed in the transition region, where the local contour curvature can be regarded as the interface curvature. The local contour passing through each reference particle in the transition region is extracted from the local profile of the smoothed color function. The local contour curvature is calculated based on the Taylor series expansion of the smoothed color function, whose derivatives are calculated accurately according to the definition of the smoothed color function. Two schemes are proposed to specify the smooth radius: Fixed scheme, where 2×re (re = particle interaction radius) is assigned to all particles in the transition region; and varied scheme, where re and 2×re are assigned to the central and edged particles in the transition region respectively. Numerical examples, including curvature calculation for static circle and ellipse interfaces, deformation of square droplet to a circle (2D and 3D), droplet deformation in shear flow, and droplet coalescence, are simulated to verify the CCSF model and compare its performance with those of other methods. The CCSF model with the fixed scheme is proven to produce the most accurate curvature and lowest parasitic currents among the tested methods.

KW - Contoured continuum surface force model

KW - MPS method

KW - Particle method

KW - Surface tension

UR - http://www.scopus.com/inward/record.url?scp=84942085724&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84942085724&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2015.06.004

DO - 10.1016/j.jcp.2015.06.004

M3 - Article

VL - 298

SP - 280

EP - 304

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -