• contact angle
• contact line
• Faraday instability
• sloshing waves
• static meniscus
• three-dimensional
• two-dimensional
• wedge geometry

The present thesis has been focused on the numerical study of sloshing waves and Faraday instability in presence of a curved static meniscus. After a review of the literature about this topic, a set of numerical tools to study how the static meniscus modifies the inviscid natural sloshing frequencies within the context of a three-dimensional wedge geometry have been firstly implemented. A realistic simple model with contact angle hysteresis able to describe the contact line behavior is introduced. The effect of the curved meniscus on the resulting damping coefficient and finite time of arrest is studied. The results show the presence of corners, leading to significant meniscus in those regions, mainly changes diagonal sloshing modes, while pure one-direction waves are well described by a two-dimensional geometry. In the second part of this work the Faraday instability in presence of an initially curved free surface is analyzed. Through a weakly nonlinear analysis, a mathematical model leading to an amplitude equation has been developed; the final equation allows to study this type of instability in the space of small external parameters. Focusing on a two-dimensional framework, proper numerical tools have been implemented, to study how the linear marginal stability curves are affected by the meniscus,. The fluid viscosity is introduced and the results are compared with the inviscid case. Finally, a brief description of the phenomenon in a three-dimensional configuration has been provided.