  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.
