The present thesis is a compendium of seven studies devoted to the numerical analysis of nonlinear dynamics and global linear stability of two-fluid flows separated by a continuous interface. The computationally efficient numerical technique developed by Herrada and Montanero [J. Comput. Phys., vol. 306, pp. 137–147, Feb. 2016] is implemented to study the dynamics of capillary one-fluid systems. Instead of using approximation techniques to simplify the two-fluid flows Navier-Stokes equations, the application of this method has the capability of modelling the complete set of governing equations for both fluids in order to obtain the hydrodynamics behavior and the global linear stability analysis.
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