Arbitrary Lagrangian–Eulerian finite element method for curved and deforming surfaces: General theory and application to fluid interfaces

Sahu, Amaresh; Omar, Yannick A. D.; Sauer, Roger A.; Mandadapu, Kranthi K.

doi:10.1016/j.jcp.2020.109253

Arbitrary Lagrangian–Eulerian finite element method for curved and deforming surfaces: General theory and application to fluid interfaces

Journal Article · Mon Jan 13 00:00:00 EST 2020 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2020.109253· OSTI ID:1603642

^[1]; Omar, Yannick A. D. ^[1]; ^[2]; Mandadapu, Kranthi K. ^[3]

Univ. of California, Berkeley, CA (United States)
Aachen Univ. (Germany)
Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

An arbitrary Lagrangian–Eulerian (ALE) finite element method for arbitrarily curved and deforming two-dimensional materials and interfaces is presented here. An ALE theory is developed by endowing the surface with a mesh whose in-plane velocity need not depend on the in-plane material velocity, and can be specified arbitrarily. A finite element implementation of the theory is formulated and applied to curved and deforming surfaces with in-plane incompressible flows. Numerical inf–sup instabilities associated with in-plane incompressibility are removed by locally projecting the surface tension onto a discontinuous space of piecewise linear functions. The general isoparametric finite element method, based on an arbitrary surface parametrization with curvilinear coordinates, is tested and validated against several numerical benchmarks. A new physical insight is obtained by applying the ALE developments to cylindrical fluid films, which are computationally and analytically found to be stable to non-axisymmetric perturbations, and unstable with respect to long-wavelength axisymmetric perturbations when their length exceeds their circumference. Finally, a Lagrangian scheme is attained as a special case of the ALE formulation. Though unable to model fluid films with sustained shear flows, the Lagrangian scheme is validated by reproducing the cylindrical instability. However, relative to the ALE results, the Lagrangian simulations are found to have spatially unresolved regions with few nodes, and thus larger errors.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: German Rsearch Foundation (DFG); National Institutes of Health (NIH); USDOE; USDOE Office of Science (SC); Univ. of California, Berkeley

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1603642

Alternate ID(s):: OSTI ID: 1592820

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 407; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
arbitrary Lagrangian-Eulerian
differential geometry
finite element method
fluid film
interfacial flows
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Arbitrary Lagrangian–Eulerian finite element method for curved and deforming surfaces: General theory and application to fluid interfaces

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