Fitted Front Tracking Methods for Two-Phase Incompressible Navier–Stokes Flow: Eulerian and ALE Finite Element Discretizations
Year: 2020
Author: Marco Agnese, Robert Nürnberg
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 5 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2020-IJNAM-17872
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 5 : pp. 613–642
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Incompressible two-phase flow Navier–Stokes equations ALE method free boundary problem surface tension finite elements and front tracking.