## Abstract

In this study we define the continuous height function to investigate the approximation of an interface line and its geometrical properties with the height function method. We show that in each mixed cell the piecewise linear interface reconstruction and the approximation of the derivatives and curvature based on three consecutive height function values are second-order accurate. We also discuss the quadratic reconstruction and fourth-order accurate expressions of the normal and curvature. We present a hierarchical algorithm to compute the normal vector and curvature of an interface line with the height function method that switches automatically between second- and fourth-order approximations and that can be applied also when the local radius of curvature is of the order of the grid spacing.

Original language | English |
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Pages (from-to) | 851-862 |

Number of pages | 12 |

Journal | Journal of Computational Physics |

Volume | 230 |

Issue number | 4 |

DOIs | |

State | Published - Feb 20 2011 |

## Keywords

- Curvature
- Height function
- Interface reconstruction
- Normal vector
- Quadratic reconstruction
- VOF/PLIC method