# Arbitrary Lagrangian-Eulerian finite element method for curved and deforming surfaces: I. General theory and application to fluid interfaces

@article{Sahu2020ArbitraryLF, title={Arbitrary Lagrangian-Eulerian finite element method for curved and deforming surfaces: I. General theory and application to fluid interfaces}, author={Amaresh Kumar Sahu and Yannick Azhri Din Omar and Roger A. Sauer and Kranthi K. Mandadapu}, journal={J. Comput. Phys.}, year={2020}, volume={407}, pages={109253} }

Abstract 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… CONTINUE READING

2

Twitter Mentions

#### Citations

##### Publications citing this paper.

SHOWING 1-3 OF 3 CITATIONS

## Dynamic Analysis of a Francis Turbine

VIEW 1 EXCERPT

CITES METHODS

## Fluid deformable surfaces

VIEW 1 EXCERPT

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 129 REFERENCES

## A stabilized finite element method for the Stokes problem based on polynomial pressure projections

VIEW 8 EXCERPTS

HIGHLY INFLUENTIAL

## Irreversible thermodynamics of curved lipid membranes.

VIEW 10 EXCERPTS

## The Theory of Shells and Plates

VIEW 6 EXCERPTS

HIGHLY INFLUENTIAL

## The Finite Element Method: Its Basis and Fundamentals (Butterworth-Heinemann

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Mechanics and Thermodynamics of Biomembranes (CRC Press

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL