Garcke, Harald and Nurnberg, Robert and Zhao, Quan (2024) Arbitrary Lagrangian-Eulerian finite element approximations for axisymmetric two-phase flow. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 155. pp. 209-223. ISSN 0898-1221, 1873-7668
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We analyze numerical approximations for axisymmetric two-phase flow in the arbitrary Lagrangian-Eulerian (ALE) framework. We consider a parametric formulation for the evolving fluid interface in terms of a one-dimensional generating curve. For the two-phase Navier-Stokes equations, we introduce both conservative and nonconservative ALE weak formulations in the 2d meridian half-plane. Piecewise linear parametric elements are employed for discretizing the moving interface, which is then coupled to a moving finite element approximation of the bulk equations. This leads to a variety of ALE methods, which enjoy either an equidistribution property or unconditional stability. Furthermore, we adapt these introduced methods with the help of suitable time-weighted discrete normals, so that the volume of the two phases is exactly preserved on the discrete level. Numerical results for rising bubbles and oscillating droplets are presented to show the efficiency and accuracy of these introduced methods.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DIFFUSE-INTERFACE MODEL; NAVIER-STOKES EQUATIONS; FRONT-TRACKING METHOD; LEVEL SET; SURFACE-TENSION; MESH METHOD; DISCRETIZATION; VOLUME; COMPUTATIONS; FORMULATION; Arbitrary Lagrangian-Eulerian; Finite element method; Energy stability; Equidistribution; Volume preservation |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 May 2024 13:43 |
| Last Modified: | 04 Mar 2025 09:18 |
| URI: | https://pred.uni-regensburg.de/id/eprint/62350 |
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