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.

Fitted front tracking methods for two-phase incompressible Navier--Stokes flow: Eulerian and ALE finite element discretizations / Agnese, Marco; Nürnberg, Robert. - In: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING. - ISSN 1705-5105. - 17:5(2020), pp. 613-642.

Fitted front tracking methods for two-phase incompressible Navier--Stokes flow: Eulerian and ALE finite element discretizations

Nürnberg, Robert
2020-01-01

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.
2020
5
Agnese, Marco; Nürnberg, Robert
Fitted front tracking methods for two-phase incompressible Navier--Stokes flow: Eulerian and ALE finite element discretizations / Agnese, Marco; Nürnberg, Robert. - In: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING. - ISSN 1705-5105. - 17:5(2020), pp. 613-642.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/283517
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