Sharp front tracking with geometric interface reconstruction

Journal Article · Thu May 08 04:00:00 EDT 2025 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2025.114059· OSTI ID:2566448

Gorges, Christian ^[1]; Evrard, Fabien ^[2]; Chiodi, Robert ^[3]; van Wachem, Berend ^[1]; Denner, Fabian ^[4]

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1. Otto-von-Guericke-Universität Magdeburg (Germany)
2. University of Illinois at Urbana-Champaign, IL (United States)
3. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
4. Polytechnique Montréal, QC (Canada)

Here, this paper presents a novel sharp front-tracking method designed to address limitations in classical front-tracking approaches, specifically their reliance on smooth interpolation kernels and extended stencils for coupling the front and fluid mesh. In contrast, the proposed method employs exclusively sharp, localized interpolation and spreading kernels, restricting the coupling to the interfacial fluid cells–those containing the interface/front. This localized coupling is achieved by integrating a divergence-preserving velocity interpolation method with a piecewise parabolic interface calculation (PPIC) and a polyhedron intersection algorithm to compute the indicator function and local interface curvature. Surface tension is computed using the Continuum Surface Force (CSF) method, maintaining consistency with the sharp representation. Additionally, we propose an efficient local roughness smoothing implementation to account for surface mesh undulations, which is easily applicable to any triangulated surface mesh. Building on our previous work, the primary innovation of this study lies in the localization of the coupling for both the indicator function and surface tension calculations. By reducing the interface thickness on the fluid mesh to a single cell, as opposed to the 4–5 cell spans typical in classical methods, the proposed sharp front-tracking method achieves a highly localized and accurate representation of the interface. This sharper representation mitigates parasitic currents and improves force balancing, making it particularly suitable for scenarios where the interface plays a critical role, such as microfluidics, fluid-fluid interactions, and fluid-structure interactions. The proposed method is comprehensively validated and tested on canonical interfacial flow problems, including stationary and translating Laplace equilibria, oscillating droplets, and rising bubbles. The presented results demonstrate that the sharp front-tracking method significantly outperforms the classical approach in terms of accuracy, stability, and computational efficiency. Notably, parasitic currents are reduced by approximately two orders of magnitude and stable results are obtained for parameter ranges where classical front tracking fails to converge.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); German Research Foundation (DFG); Marie Skłodowska-Curie Actions (MSCA)
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 2566448
• Report Number(s): LA-UR--24-23114
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 535; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
Interfacial flows
Parabolic interface reconstruction
Roughness smoothing
Sharp front tracking