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A cut finite element method for incompressible two-phase Navier–Stokes flows
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0002-4911-467X
2019 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 384, p. 77-98Article in journal (Refereed) Published
Abstract [en]

We present a space–time Cut Finite Element Method (CutFEM) for the time-dependent Navier–Stokes equations involving two immiscible incompressible fluids with different viscosities, densities, and with surface tension. The numerical method is able to accurately capture the strong discontinuity in the pressure and the weak discontinuity in the velocity field across evolving interfaces without re-meshing processes or regularization of the problem. We combine the strategy proposed in P. Hansbo et al. (2014) [14] for the Stokes equations with a stationary interface and the space–time strategy presented in P. Hansbo et al. (2016) [20]. We also propose a strategy for computing high order approximations of the surface tension force by computing a stabilized mean curvature vector. The presented space–time CutFEM uses a fixed mesh but includes stabilization terms that control the condition number of the resulting system matrix independently of the position of the interface, ensure stability and a convenient implementation of the space–time method based on quadrature in time. Numerical experiments in two and three space dimensions show that the numerical method is able to accurately capture the discontinuities in the pressure and the velocity field across evolving interfaces without requiring the mesh to be conformed to the interface and with good stability properties.

Place, publisher, year, edition, pages
Academic Press, 2019. Vol. 384, p. 77-98
Keywords [en]
Level set method, Navier–Stokes, Sharp interface method, Space–time CutFEM, Surface tension, Unfitted finite element method
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-246430DOI: 10.1016/j.jcp.2019.01.028ISI: 000460888400005Scopus ID: 2-s2.0-85062103309OAI: oai:DiVA.org:kth-246430DiVA, id: diva2:1300733
Note

QC 20190329

Available from: 2019-03-29 Created: 2019-03-29 Last updated: 2019-04-03Bibliographically approved

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Frachon, ThomasZahedi, Sara

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