The stability of two-dimensional, steady flows of Newtonian liquid with free boundaries affected by surface tension to small, three-dimensional disturbances is calculated by the finite-element method. The only simplification made is the neglect of the time partial derivative in each component of the Navier-Stokes equation, which leads to a major reduction in the order of the resulting matrix eigenvalue problem. The disturbances introduced vary sinusoidally in the third dimension and exponentially in time, and as a result the two-dimensional finite-element grid used for the base flow calculations can be used also for the stability calculations. Stability predictions for a stationary layer and for air displacing liquid in a Hele-Shaw cell show that the method can be effective.
%0 Journal Article
%1 RUSCHAK1983391
%A Ruschak, Kenneth J.
%D 1983
%J Computers & Fluids
%K 76d27-other-free-boundary-flows-hele-shaw-flows 76e17-interfacial-stability
%N 4
%P 391–401
%R 10.1016/0045-7930(83)90023-3
%T A three-dimensional linear stability analysis for two-dimensional free boundary flows by the finite-element method
%U http://www.sciencedirect.com/science/article/pii/0045793083900233
%V 11
%X The stability of two-dimensional, steady flows of Newtonian liquid with free boundaries affected by surface tension to small, three-dimensional disturbances is calculated by the finite-element method. The only simplification made is the neglect of the time partial derivative in each component of the Navier-Stokes equation, which leads to a major reduction in the order of the resulting matrix eigenvalue problem. The disturbances introduced vary sinusoidally in the third dimension and exponentially in time, and as a result the two-dimensional finite-element grid used for the base flow calculations can be used also for the stability calculations. Stability predictions for a stationary layer and for air displacing liquid in a Hele-Shaw cell show that the method can be effective.
@article{RUSCHAK1983391,
abstract = {The stability of two-dimensional, steady flows of Newtonian liquid with free boundaries affected by surface tension to small, three-dimensional disturbances is calculated by the finite-element method. The only simplification made is the neglect of the time partial derivative in each component of the Navier-Stokes equation, which leads to a major reduction in the order of the resulting matrix eigenvalue problem. The disturbances introduced vary sinusoidally in the third dimension and exponentially in time, and as a result the two-dimensional finite-element grid used for the base flow calculations can be used also for the stability calculations. Stability predictions for a stationary layer and for air displacing liquid in a Hele-Shaw cell show that the method can be effective.},
added-at = {2019-10-22T01:04:20.000+0200},
author = {Ruschak, Kenneth J.},
biburl = {https://www.bibsonomy.org/bibtex/208f436f9c0b9a0759c345bdf2f3db821/gdmcbain},
doi = {10.1016/0045-7930(83)90023-3},
interhash = {24453215bb0804b9e431d584b3d8ab96},
intrahash = {08f436f9c0b9a0759c345bdf2f3db821},
issn = {0045-7930},
journal = {Computers & Fluids},
keywords = {76d27-other-free-boundary-flows-hele-shaw-flows 76e17-interfacial-stability},
number = 4,
pages = {391–401},
timestamp = {2019-10-22T01:04:20.000+0200},
title = {A three-dimensional linear stability analysis for two-dimensional free boundary flows by the finite-element method},
url = {http://www.sciencedirect.com/science/article/pii/0045793083900233},
volume = 11,
year = 1983
}