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

TL;DR

This work extends the Edge-Based Interface Tracking (EBIT) method to three dimensions by employing a directional split advection that decomposes 3D motion into two 2D problems, enabling direct reuse of the 2D circle-fit reconstruction and the color-vertex topology framework. The EBIT-Navier–Stokes coupling is achieved through the Front2VOF geometrical volume-fraction computation and the Height-Function curvature model, implemented within the Basilisk platform with adaptive mesh refinement. Validation against five benchmarks shows EBIT delivers accurate 3D interface tracking with automatic topology changes and favorable mass-conservation and interface quality compared to PLIC-VOF, while exhibiting scalable parallel performance. The work also discusses limitations and future directions, including richer kinematic topology control (e.g., multiple markers per edge) and potential direct computation of capillary forces to further enhance subgrid-scale dynamics.

Abstract

The Edge-Based Interface Tracking (EBIT) method is a novel Front-Tracking method where the markers are located on grid edges, and their connectivity is implicitly represented by a color vertex field. This localized representation simplifies the process of topology changes and allows for almost automatic parallelization. In our previous journal articles, we have presented both the kinematic part, includes the algorithms for advection of the interface and color vertex field evolution, and the dynamic part, which couples the EBIT method with the Navier--Stokes equations for multiphase flow simulations, in the two-dimensional (2D) case. In this work, we propose a simplified strategy to extend the EBIT method to three dimensions (3D). The directional split scheme used for interface advection in 2D version is directly generalized to 3D. Specifically, the 3D advection within a given cubic cell along one direction is decomposed into two 2D advection problems on the two cube faces. The dimension reduction allows us to fully reused the 2D interface reconstruction algorithms, including the 2D circle fit and the evolution rules for the color vertex field. For coupling with the Navier--Stokes equations, we first calculate volume fractions from the position of the markers and the color vertex field using the Front2VOF geometrical method, then viscosity and density fields from the computed volume fractions, and finally surface tension stresses with the Height-Function method. The 3D EBIT method has been implemented in the free Basilisk platform and validated against five benchmark cases: translation with uniform velocity, 3D deformation test, oscillating drop, rising bubble, and bubble merging. The results are compared with those obtained using the Volume-of-Fluid (VOF) method already implemented in Basilisk.

Figures (20)

• Figure 1: One-dimensional advection of the EBIT method along the $x$-axis: (a) initial interface line; (b) advection of the markers on the grid lines aligned with the velocity component (blue points); (c) advection of the unaligned markers (gray points) and computation of the intersections with the grid lines (red points); (d) interface line after the 1D advection.
• Figure 2: Circle fit to compute the position of the unaligned marker (red point).
• Figure 3: Two color vertex configurations (brown and green squares) to select a different connectivity in the same set of markers.
• Figure 4: Update of the Color Vertex value on a cell corner: its value changes, from green to brown, as the marker is advected across the grid lines intersection.
• Figure 5: Topology change mechanism.