Multi-plane moment-of-fluid interface reconstruction in 3D

Journal Article · Sat Jul 12 04:00:00 EDT 2025 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2025.114239· OSTI ID:2572541

Spainhour, Jacob ^[1]; Shashkov, Mikhail Jurievich ^[2]

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1. Univ. of Colorado, Boulder, CO (United States)
2. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Moment-of-fluid (MOF) methods for interface reconstruction approximate the region occupied by material in each mesh element only through reference to its geometric moments. Here, we present a 3D MOF method that represents the material (POM) in each cell as the convex intersection of the cell and multiple half-spaces, each selected to minimize the least-squares error between computed moments of the approximated material and provided reference moments. This optimization problem is highly non-linear and non-convex, making the numerical result very sensitive to the initial guess. To create an effective initial guess in each cell, we construct an ellipsoid from 0th–2nd order reference moments such that its shape corresponds with that of the POM. Within this ellipsoid we inscribe a polyhedron, and initialize the minimization problem with the half-spaces defined by each of its faces. The inscribed polyhedron has minimally 4 faces, and using up to 3rd order moments permits optimization over up to 20 unknown values. We therefore define MOF methods that utilize 4, 5, or 6 half-spaces, correspondingly initialized with the faces of a single inscribed tetrahedron, triangular prism, or hexahedron. Stability of the non-linear optimization is further improved with a prepossessing step that normalizes the reference moments according to the axes of the reference ellipsoid. Using this approach, the non-linear least-squares solver reliably converges to a near-global minimum from a single initial guess. We demonstrate accuracy and robustness using single-cell and multi-cell examples over a wide spectrum of geometry. In particular, we demonstrate our ability to exactly reproduce several important and complex features defined by up to four half-spaces, such as corners, filaments, filament tips, and embedded material in the cell.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 2572541
• Report Number(s): LA-UR--24-30258; 10.1016/j.jcp.2025.114239
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 539; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

3D interface reconstruction
97 MATHEMATICS AND COMPUTING
Convex polyhedra
Moment-of-fluid
Non-linear optimization