Garcke, Harald and Nürnberg, Robert and Zhao, Quan (2026) A variational front-tracking method for multiphase flow with triple junctions. MATHEMATICS OF COMPUTATION, 95 (358). pp. 647-682. ISSN 0025-5718, 1088-6842
Full text not available from this repository. (Request a copy)Abstract
We present and analyze a variational front-tracking method for a sharp-interface model of multiphase flow. The fluid interfaces between different phases are represented by curve networks in two space dimensions (2d) or surface clusters in three space dimensions (3d) with triple junctions where three interfaces meet, and boundary points/lines where an interface meets a fixed planar boundary. The model is described by the incompressible Navier-Stokes equations in the bulk domains, with classical interface conditions on the fluid interfaces, and appropriate boundary conditions at the triple junctions and boundary points/lines. We propose a weak formulation for the model, which combines a parametric formulation for the evolving interfaces and an Eulerian formulation for the bulk equations. We employ an unfitted discretization of the coupled formulation to obtain a fully discrete finite element method, where the existence and uniqueness of solutions can be shown under weak assumptions. The constructed method admits an unconditional stability result in terms of the discrete energy. Furthermore, we adapt the introduced method so that an exact volume preservation for each phase can be achieved for the discrete solutions. Numerical examples for three-phase flow and four-phase flow are presented to show the robustness and accuracy of the introduced methods.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FINITE-ELEMENT APPROXIMATION; LEVEL SET APPROACH; NUMERICAL APPROXIMATION; SPURIOUS VELOCITIES; BOUNDARY MOTION; SURFACE-TENSION; 2-PHASE FLOW; SIMULATION; MODEL; DISCRETIZATION; Multiphase flow; Navier-Stokes; surface tension; triple junctions; parametric finite element method; unconditional stability; volume preservation |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 23 Jun 2026 07:46 |
| Last Modified: | 23 Jun 2026 07:46 |
| URI: | https://pred.uni-regensburg.de/id/eprint/66413 |
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