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Fitted front tracking methods for two-phase ncompressible Navier-Stokes flow: Eulerian and ALE finite element discretizations. (English) Zbl 1471.76084

Summary: 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.

MSC:

76T99 Multiphase and multicomponent flows
76M10 Finite element methods applied to problems in fluid mechanics
35Q30 Navier-Stokes equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
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