An analytic approach for the moment-of-fluid interface reconstruction method on tetrahedral meshes

This article presents an original fast and robust approach for solving the moment -of -fluid interface reconstruction problem on tetrahedral meshes. We establish an explicit parametrization of the locus of the centroids under volume constrains using the spherical coordinates on a reference tetrahedron. This parametrization allows to write the moment -of -fluid objective function and its gradient by means of analytic formulas. Then, we show that the minimization problem on arbitrary tetrahedra can be effectively solved on the reference tetrahedron by using an affine transformation. Based on this transformation, we propose a improved technique for obtaining an initial condition for the minimization algorithm. We then describe the Gauss-Newton and the BFGS minimization algorithms, both combined with a trust -region method, to solve this reconstruction problem. Finally, we perform a verification and validation process on a series of increasingly complex test cases. These tests show that the proposed analytic method, paired with the Gauss-Newton algorithm, outperforms the other methods that were tested.