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Solution to the orr–sommerfeld equation for liquid film flowing down an inclined plane: An optimal approach
Author(s) -
Lam T. T.,
Bayazitoglu Y.
Publication year - 1986
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650061203
Subject(s) - eigenfunction , eigenvalues and eigenvectors , plane (geometry) , action (physics) , mathematics , stability (learning theory) , mathematical analysis , inclined plane , geometry , mechanics , physics , computer science , quantum mechanics , machine learning
The Orr–Sommerfeld equation is solved numerically for a layer of liquid film flowing down an inclined plane under the action of gravity using the sequential gradient‐restoration algorithm (SGRA) The method consists of solving the governing equation as it is a Bolza problem in the calculus of variations. The neutral stability curves, eigenvalues and eigenfunctions to the stability problem can be determined simultaneously during the process.