An Exact Geometric Method for Efficient Computation of Volume-Fraction Fields in Front-Tracking Simulations
Abstract
This work presents an exact geometric method for computing volume-fraction fields in Front-Tracking simulations on hexahedral Eulerian meshes. Such volume-fraction fields are essential for multiphase CFD simulations based on the one-fluid formulation of the conservation equations, as they describe the distribution of each phase within the Eulerian mesh. The proposed approach evaluates the volume enclosed by a Lagrangian interface within each Eulerian cell through direct geometric computation based on polyhedral intersections. Unlike commonly used approximate reconstruction techniques, the method does not rely on local approximations of the interface or on interface reconstruction from a gradient field, and preserves phase volumes up to errors on the order of floating-point precision. An algorithm is proposed to efficiently test intersections between Eulerian cells and Lagrangian facets using two bounding volume hierarchy structures. The method is designed to be used during the execution of large-scale simulations, with a naturally parallel formulation compatible with Message Passing Interface (MPI)-based Front-Tracking frameworks. The method is assessed through several validation cases, including isolated interfaces and configurations involving multiple interfaces crossing the same Eulerian cells. Comparisons with classical diffuse-interface and distance-based reconstruction approaches demonstrate improved volume conservation and accuracy while maintaining a sharp interface representation at the Eulerian level. In particular, the geometric formulation naturally handles multiple interface fronts within the same Eulerian cell, without requiring additional reconstruction or assumptions about the local interface topology.
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BibTeX
@misc{labat2026exact,
title = {{An Exact Geometric Method for Efficient Computation of Volume-Fraction Fields in Front-Tracking Simulations}},
author = {Alexandre Labat and Samuel Mer and Françoise Bataille and Adrien Toutant},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05761503v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - An Exact Geometric Method for Efficient Computation of Volume-Fraction Fields in Front-Tracking Simulations
AU - Alexandre Labat
AU - Samuel Mer
AU - Françoise Bataille
AU - Adrien Toutant
PY - 2026
DA - 2026/09/23
PB - HAL
UR - https://hal.science/hal-05761503v1
AB - This work presents an exact geometric method for computing volume-fraction fields in Front-Tracking simulations on hexahedral Eulerian meshes. Such volume-fraction fields are essential for multiphase CFD simulations based on the one-fluid formulation of the conservation equations, as they describe the distribution of each phase within the Eulerian mesh. The proposed approach evaluates the volume enclosed by a Lagrangian interface within each Eulerian cell through direct geometric computation based on polyhedral intersections. Unlike commonly used approximate reconstruction techniques, the method does not rely on local approximations of the interface or on interface reconstruction from a gradient field, and preserves phase volumes up to errors on the order of floating-point precision. An algorithm is proposed to efficiently test intersections between Eulerian cells and Lagrangian facets using two bounding volume hierarchy structures. The method is designed to be used during the execution of large-scale simulations, with a naturally parallel formulation compatible with Message Passing Interface (MPI)-based Front-Tracking frameworks. The method is assessed through several validation cases, including isolated interfaces and configurations involving multiple interfaces crossing the same Eulerian cells. Comparisons with classical diffuse-interface and distance-based reconstruction approaches demonstrate improved volume conservation and accuracy while maintaining a sharp interface representation at the Eulerian level. In particular, the geometric formulation naturally handles multiple interface fronts within the same Eulerian cell, without requiring additional reconstruction or assumptions about the local interface topology.
ER -