## Abstract

A robust numerical methodology to predict equilibrium interfaces over arbitrary solid surfaces is developed. The kernel of the proposed method is the distance regularized level set equations (DRLSE) with techniques to incorporate the no-penetration and volume-conservation constraints. In this framework, we avoid reinitialization that is typically used in traditional level set methods. This allows for a more efficient algorithm since only one advection equation is solved, and avoids numerical error associated with the re-distancing step. A novel surface tension distribution, based on harmonic mean, is prescribed such that the zero level set has the correct liquid-solid surface tension value. This leads to a more accurate prediction of the triple contact point location. The method uses second-order central difference schemes which facilitates easy parallel implementation, and is validated by comparing to traditional level set methods for canonical problems. The application of the method in the context of Gibbs free energy minimization, to obtain liquid-air interfaces is validated against existing analytical solutions. The capability of the methodology to predict equilibrium shapes over both structured and realistic rough surfaces is demonstrated.

Original language | English (US) |
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Article number | 109184 |

Journal | Journal of Computational Physics |

Volume | 406 |

DOIs | |

State | Published - Apr 1 2020 |

### Bibliographical note

Funding Information:This work is supported by the United States Office of Naval Research (ONR) under ONR Grants N00014-12-1-0874 and N00014-17-1-2676 with Dr. Ki-Han Kim as technical monitor. The computations were made possible through the Minnesota Supercomputing Institute (MSI) at the University of Minnesota.

Funding Information:

This work is supported by the United States Office of Naval Research (ONR) under ONR Grants N00014-12-1-0874 and N00014-17-1-2676 with Dr. Ki-Han Kim as technical monitor. The computations were made possible through the Minnesota Supercomputing Institute (MSI) at the University of Minnesota.

Publisher Copyright:

© 2019 Elsevier Inc.

## Keywords

- Distance regularized level set equations
- Gibbs free energy minimization
- Level set method
- Multiphase
- Roughness
- Variational level set