Some improvements on Moment-of-Fluid method in 3D rectangular hexahedrons

TL;DR

This paper enhances the 3D Moment-of-Fluid (MOF) method by introducing a Gauss-Newton iteration and an improved initial guess, significantly improving computational efficiency and robustness in interface reconstruction.

Contribution

The study proposes a novel acceleration technique for MOF reconstruction using Gauss-Newton iteration and an improved initial guess, advancing the computational efficiency of 3D interface modeling.

Findings

Reduced computational cost of MOF reconstruction

Enhanced robustness and efficiency of the algorithm

Open-source implementation available on Github

Abstract

The moment-of-fluid method (MOF) is an extension of the volume-of-fluid method with piecewise linear interface construction (VOF-PLIC). In MOF reconstruction, the optimized normal vector is determined from the reference centroid and the volume fraction by iteration. The state-of-art work by \citet{milcent_moment--fluid_2020} proposed an analytic gradient of the objective function, which greatly reduces the computational cost. In this study, we further accelerate the MOF reconstruction algorithm by using Gauss-Newton iteration instead of Broyden-Fletcher-Goldfarb-Shanno (BFGS) iteration. We also propose an improved initial guess for MOF reconstruction, which improves the efficiency and the robustness of the MOF reconstruction algorithm. Our implementation of the code and test cases are available on our Github repository.