# A variational level set methodology without reinitialization for the prediction of equilibrium interfaces over arbitrary solid surfaces

## TL;DR

This paper introduces a novel, efficient level set method that predicts equilibrium interfaces on arbitrary solid surfaces without reinitialization, improving accuracy and computational efficiency in interface modeling.

## Contribution

The proposed method eliminates reinitialization in level set calculations, incorporates a new surface tension distribution, and demonstrates improved accuracy and efficiency in predicting equilibrium interfaces.

## Key findings

- Accurately predicts equilibrium interfaces on complex surfaces.
- Reduces computational cost by avoiding reinitialization.
- Validated against analytical solutions and traditional methods.

## 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 mass-conservation constraints. In this framework, we avoid reinitialization 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 the liquid-solid surface tension value. This leads to a more accurate 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 our current methodology to predict equilibrium shapes over both structured and realistic rough surfaces is demonstrated.