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arXiv · 2509.26361

A Three-dimensional Edge-Based Interface Tracking (EBIT) Method for Multiphase-flow Simulations

Abstract

The Edge-Based Interface Tracking (EBIT) method is a novel Front-Tracking method in which the markers are located on grid edges, and their connectivity is implicitly represented by a color vertex field. This localized representation simplifies topology changes and allows for automatic parallelization. In this work, we propose a simplified extension of EBIT to three dimensions (3D). The directional split scheme used for interface advection in the two-dimensional (2D) version is generalized to 3D by decomposing each 3D directional advection step into 2D advection problems on the two corresponding cube faces. The same dimension-reduction strategy is applied to connectivity representation, allowing the main 2D algorithms and data structures to be reused and thereby reducing the algorithmic and implementation complexity. For coupling with the Navier--Stokes equations, volume fractions are reconstructed from the EBIT markers and color vertex field using the Front2VOF geometric method. The resulting volume fractions are then used to compute the fluid properties and surface-tension forces with the Height-Function method. The 3D EBIT method has been implemented in the free Basilisk framework, with the documented source code available in the online repository. The method is verified against five benchmark cases: translation with uniform velocity, 3D deformation test, oscillating drop, rising bubble, and bubble merging. The results show good agreement with reference solutions and with the Volume-of-Fluid (VOF) method implemented in Basilisk, demonstrating the effectiveness of the simplified extension. In addition, the 3D EBIT method exhibits excellent weak scalability, highlighting its potential advantage over traditional front-tracking methods for large-scale parallel computations.

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Jieyun Pan, Tian Long, Ruben Scardovelli, Stéphane Popinet, Stéphane Zaleski. 2026-09-17. A Three-dimensional Edge-Based Interface Tracking (EBIT) Method for Multiphase-flow Simulations. https://arxiv.org/abs/2509.26361

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