Jieyun Pan | Searcharxiv

arXiv2026

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

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.

physics.flu-dyn↗

arXiv2026

Applying contact angles based on a continuously moving contact line in 2D VOF simulations

A height-function-based numerical approach is developed for enforcing contact angles on flat and curved solid surfaces within two-dimensional volume-of-fluid simulations. This method incorporates the contact line position into the curvature estimation in the contact line cell, where the interface normal is constrained to the prescribed angle to ensure smooth contact line motion. On flat solid surfaces, the proposed model achieves higher accuracy than the conventional vertical height-function method for enforcing very small and very large contact angles. Moreover, it extends naturally to curved solid surfaces represented by the embedded boundary method, enabling the imposition of arbitrary contact angles without inducing significant spurious currents near the contact line. Numerical validations confirm the accuracy and robustness of the proposed method, demonstrating its applicability to multiphase flows involving complex wall geometries and contact-line dynamics.

physics.flu-dyn↗

arXiv2025

An Unsplit Scheme for Interface Advection in the Edge-based Interface Tracking (EBIT) Method

We propose an unsplit scheme for interface advection in a novel Front-Tracking method, called the Edge-Based Interface Tracking (EBIT) method. In the EBIT method, the markers are placed on the grid edges, and their connectivity is implicitly represented using a color vertex field. In our previous publications, a split scheme was used to advect the interface in the EBIT method. Although the split scheme facilitates the extension of the EBIT method to three dimensions, it also imposes some limitations. First, implementing high-order time integration methods for interface advection becomes challenging. Second, in multiscale simulations using Front-Tracking methods with a boundary layer model applied to the interface, the redistribution of physical quantities inside the boundary layer, such as a scalar concentration, along the interface becomes difficult due to the loss of correspondence between interface segments before and after each advection step, caused by the operator split. Here, we present an unsplit scheme for interface advection to enhance the capability of the EBIT method. In the unsplit scheme, a reconstruction step based on a circle fit, similar to that used in the split scheme, is performed to reposition markers on the cell edges. Furthermore, the algorithm used to update the color vertex field, which implicitly represents marker connectivity and distinguishes among ambiguous topology configurations, is modified to achieve consistent connectivity results. An EBIT method based on an unsplit scheme has been implemented in the free Basilisk platform, and validated with four kinematic test cases: translation with uniform velocity, solid body rotation, Zalesak's disk rotation, and single vortex test. The results are compared with those obtained using the original EBIT method based on a split scheme.

physics.flu-dyn↗

arXiv2025

Direct numerical simulation of nucleate boiling with a resolved microlayer and conjugate heat transfer

In this paper, a phase-change model based on a geometric Volume-of-Fluid (VOF) framework is extended to simulate nucleate boiling with a resolved microlayer and conjugate heat transfer. Heat conduction in both the fluid and solid domains is simultaneously solved, with Interfacial Heat-Transfer Resistance (IHTR) imposed. The present model is implemented in the open-source software Basilisk with adaptive mesh refinement (AMR), which significantly improves computational efficiency. However, the approximate projection method required for AMR introduces strong oscillations within the microlayer due to intense heat and mass transfer. This issue is addressed using a ghost fluid method, allowing nucleate boiling experiments to be successfully replicated. Compared to previous literature studies, the computational cost is reduced by three orders of magnitude. The influence of contact angle is further investigated, revealing consistent thermodynamic effects across different contact angles. Finally, a complete bubble cycle from nucleation to detachment is simulated, which, to our knowledge, has not been reported in the open literature. Reasonable agreement with experimental data is achieved, enabling key factors affecting nucleate boiling simulations in the microlayer regime to be identified, which were previously obscured by limited simulation time.

physics.flu-dyn↗

arXiv2025

Exact computation of the color function for triangular element interfaces

The calculation of the volume enclosed by curved surfaces discretized into triangular elements, and a cube is of great importance in different domains, such as computer graphics and multiphase flow simulations. We propose a robust algorithm, the Front2VOF (F2V) algorithm, to address this problem. The F2V algorithm consists of two main steps. First, it identifies the polygons within the cube by segmenting the triangular elements on the surface, retaining only the portions inside the cube boundaries. Second, it computes the volume enclosed by these polygons in combination with the cube faces. To validate the algorithm's accuracy and robustness, we tested it using a range of synthetic configurations with known analytical solutions.

cs.GR↗

arXiv2024

An Edge-based Interface Tracking (EBIT) Method for Multiphase Flows with Phase Change

We present a novel Front-Tracking method, the Edge-Based Interface Tracking (EBIT) method for multiphase flow simulations. In the EBIT method, the markers are located on the grid edges and the interface can be reconstructed without storing the connectivity of the markers. This feature makes the process of marker addition or removal easier than in the traditional Front-Tracking method. The EBIT method also allows almost automatic parallelization due to the lack of explicit connectivity. In a previous journal article we have presented the kinematic part of the EBIT method, that includes the algorithms for piecewise linear reconstruction and advection of the interface. Here, we complete the presentation of the EBIT method and combine the kinematic algorithm with a Navier--Stokes solver. A circle fit is now implemented to improve the accuracy of mass conservation in the reconstruction phase. Furthermore, to identify the reference phase and to distinguish ambiguous topological configurations, we introduce a new feature: the Color Vertex. For the coupling with the Navier--Stokes equations, we first calculate volume fractions from the position of the markers and the Color Vertex, then viscosity and density fields from the computed volume fractions and finally surface tension stresses with the Height-Function method. In addition, an automatic topology change algorithm is implemented into the EBIT method, making it possible the simulation of more complex flows. The two-dimensional version of the EBIT method has been implemented in the free Basilisk platform, and validated with seven standard test cases: stagnation flow, translation with uniform velocity, single vortex, Zalesak's disk, capillary wave, Rayleigh-Taylor instability and rising bubble. The results are compared with those obtained with the Volume-of-Fluid (VOF) method already implemented in Basilisk.

physics.flu-dyn↗

arXiv2024

An Edge-based Interface Tracking (EBIT) Method for Multiphase-flows Simulation with Surface Tension

We present a novel Front-Tracking method, the Edge-Based Interface Tracking (EBIT) method for multiphase flow simulations. In the EBIT method, the markers are located on the grid edges and the interface can be reconstructed without storing the connectivity of the markers. This feature makes the process of marker addition or removal easier than in the traditional Front-Tracking method. The EBIT method also allows almost automatic parallelization due to the lack of explicit connectivity. In a previous journal article we have presented the kinematic part of the EBIT method, that includes the algorithms for piecewise linear reconstruction and advection of the interface. Here, we complete the presentation of the EBIT method and combine the kinematic algorithm with a Navier--Stokes solver. A circle fit is now implemented to improve the accuracy of mass conservation in the reconstruction phase. Furthermore, to identify the reference phase and to distinguish ambiguous topological configurations, we introduce a new feature: the Color Vertex. For the coupling with the Navier--Stokes equations, we first calculate volume fractions from the position of the markers and the Color Vertex, then viscosity and density fields from the computed volume fractions and finally surface tension stresses with the Height-Function method. In addition, an automatic topology change algorithm is implemented into the EBIT method, making it possible the simulation of more complex flows. The two-dimensional version of the EBIT method has been implemented in the free Basilisk platform, and validated with seven standard test cases: stagnation flow, translation with uniform velocity, single vortex, Zalesak's disk, capillary wave, Rayleigh-Taylor instability and rising bubble. The results are compared with those obtained with the Volume-of-Fluid (VOF) method already implemented in Basilisk.

physics.flu-dyn↗