%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 }