A threedimensional linear stability analysis for twodimensional free boundary flows by the finiteelement method
Abstract
The stability of twodimensional, steady flows of Newtonian liquid with free boundaries affected by surface tension to small, threedimensional disturbances is calculated by the finiteelement method. The only simplification made is the neglect of the time partial derivative in each component of the NavierStokes 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 twodimensional finiteelement 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 HeleShaw cell show that the method can be effective.
 Publication:

Computers and Fluids
 Pub Date:
 1983
 Bibcode:
 1983CF.....11..391R
 Keywords:

 Finite Element Method;
 Flow Stability;
 Free Boundaries;
 Two Dimensional Flow;
 Computational Fluid Dynamics;
 Newtonian Fluids;
 Steady Flow;
 Fluid Mechanics and Heat Transfer