Barrett, John W. and Garcke, Harald and Nuernberg, Robert (2015) A Stable Parametric Finite Element Discretization of Two-Phase Navier-Stokes Flow. JOURNAL OF SCIENTIFIC COMPUTING, 63 (1). pp. 78-117. ISSN 0885-7474, 1573-7691
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We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Navier-Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel variational formulation for the interface evolution gives rise to a natural discretization of the mean curvature of the interface. The parametric finite element approximation of the evolving interface is then coupled to a standard finite element approximation of the two-phase Navier-Stokes equations in the bulk. Here enriching the pressure approximation space with the help of an XFEM function ensures good volume conservation properties for the two phase regions. In addition, the mesh quality of the parametric approximation of the interface in general does not deteriorate over time, and an equidistribution property can be shown for a semidiscrete continuous-in-time variant of our scheme in two space dimensions. Moreover, our finite element approximation can be shown to be unconditionally stable. We demonstrate the applicability of our method with some numerical results in two and three space dimensions.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | 2-DIMENSIONAL BUBBLE DYNAMICS; DIFFUSE-INTERFACE MODEL; FRONT-TRACKING METHOD; MULTI-FLUID FLOWS; SURFACE-TENSION; BENCHMARK COMPUTATIONS; INCOMPRESSIBLE-FLOW; SPURIOUS VELOCITIES; APPROXIMATION; VOLUME; Finite elements; XFEM; Two-phase flow; Navier-Stokes; Free boundary problem; Surface tension; Interface tracking |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 22 Jul 2019 14:00 |
| Last Modified: | 22 Jul 2019 14:00 |
| URI: | https://pred.uni-regensburg.de/id/eprint/5759 |
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