Volume 17, Issue 5
Fitted Front Tracking Methods for Two-Phase Incompressible Navier–Stokes Flow: Eulerian and Ale Finite Element Discretizations

Marco AgneseRobert Nürnberg

Int. J. Numer. Anal. Mod., 17 (2020), pp. 613-642.

Published online: 2020-08

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  • Abstract

We investigate novel fitted finite element approximations for two-phase Navier–Stokes flow. In particular, we consider both Eulerian and Arbitrary Lagrangian–Eulerian (ALE) finite element formulations. The moving interface is approximated with the help of parametric piecewise linear finite element functions. The bulk mesh is fitted to the interface approximation, so that standard bulk finite element spaces can be used throughout. The meshes describing the discrete interface in general do not deteriorate in time, which means that in numerical simulations a smoothing or a remeshing of the interface mesh is not necessary. We present several numerical experiments, including convergence experiments and benchmark computations, for the introduced numerical methods, which demonstrate the accuracy and robustness of the proposed algorithms. We also compare the accuracy and efficiency of the Eulerian and ALE formulations.

  • Keywords

Incompressible two-phase flow, Navier–Stokes equations, ALE method, free boundary problem, surface tension, finite elements, and front tracking.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-17-613, author = {Agnese , Marco and Nürnberg , Robert}, title = {Fitted Front Tracking Methods for Two-Phase Incompressible Navier–Stokes Flow: Eulerian and Ale Finite Element Discretizations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {5}, pages = {613--642}, abstract = {

We investigate novel fitted finite element approximations for two-phase Navier–Stokes flow. In particular, we consider both Eulerian and Arbitrary Lagrangian–Eulerian (ALE) finite element formulations. The moving interface is approximated with the help of parametric piecewise linear finite element functions. The bulk mesh is fitted to the interface approximation, so that standard bulk finite element spaces can be used throughout. The meshes describing the discrete interface in general do not deteriorate in time, which means that in numerical simulations a smoothing or a remeshing of the interface mesh is not necessary. We present several numerical experiments, including convergence experiments and benchmark computations, for the introduced numerical methods, which demonstrate the accuracy and robustness of the proposed algorithms. We also compare the accuracy and efficiency of the Eulerian and ALE formulations.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/17872.html} }
TY - JOUR T1 - Fitted Front Tracking Methods for Two-Phase Incompressible Navier–Stokes Flow: Eulerian and Ale Finite Element Discretizations AU - Agnese , Marco AU - Nürnberg , Robert JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 613 EP - 642 PY - 2020 DA - 2020/08 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/17872.html KW - Incompressible two-phase flow, Navier–Stokes equations, ALE method, free boundary problem, surface tension, finite elements, and front tracking. AB -

We investigate novel fitted finite element approximations for two-phase Navier–Stokes flow. In particular, we consider both Eulerian and Arbitrary Lagrangian–Eulerian (ALE) finite element formulations. The moving interface is approximated with the help of parametric piecewise linear finite element functions. The bulk mesh is fitted to the interface approximation, so that standard bulk finite element spaces can be used throughout. The meshes describing the discrete interface in general do not deteriorate in time, which means that in numerical simulations a smoothing or a remeshing of the interface mesh is not necessary. We present several numerical experiments, including convergence experiments and benchmark computations, for the introduced numerical methods, which demonstrate the accuracy and robustness of the proposed algorithms. We also compare the accuracy and efficiency of the Eulerian and ALE formulations.

Marco Agnese & Robert Nürnberg. (2020). Fitted Front Tracking Methods for Two-Phase Incompressible Navier–Stokes Flow: Eulerian and Ale Finite Element Discretizations. International Journal of Numerical Analysis and Modeling. 17 (5). 613-642. doi:
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