Fluid flow processes that have a two-dimensional structure can be subjected to disturbances in the third (transverse) direction as well as the two primary flow directions. Therefore, a complete linear stability analysis of such a process entails verification of stability in all directions. This work focuses on the general implementation of an algorithm for use with a finite element program to enable two-dimensional flow simulations to be combined with linear stability analysis in all three directions. Here, transverse disturbances are modeled and analyzed by normal mode analysis. The algorithm is validated against a simple cylindrical static liquid layer problem by demonstrating agreement with analytical solutions. Results are also presented and discussed for simple Rayleigh-Benard convection and for a slot coaler problem.
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