Computational Modeling of Free Surface Flows

In order to describe correctly the dynamic evolution of a fluid/fluid interface, a number of boundary conditions have to be implemented into the computational models. 

The kinematic condition requires that no fluid can transverse the interface, i.e. the local flow velocity Wj relative to the velocity of the interface should be zero 

The dynamic condition requires that the net force on any portion of the interface has to vanish. In a local coordinate frame attached to an interfacial position, three constraints are derived expressing the force balance for each of the three coordinate directions  

(132) states that the interfacial tension has to be balanced by a pressure difference between the two phases. The terms containing derivatives of crin Eqs. (133) and (134) are non-zero only if there are local variations of the interfacial tension, which might be due to differences in concentration or temperature. The flow induced by such an effect is known as Marangoni convection. 

Among interface capturing methods, one of the most popular and most successful schemes is the volume-of-fluid (VOF) method dating back to the work of Hirt and Nichols [174]. The VOF method is based on a volume-fraction field c, assuming values between 0 and 1. A value of c = 1 indicates cells that are filled with phase 1, and phase 2 corresponds to c= 0. Intermediate values of c indicate the position of the interface between the phases however, the goal is to maintain a sharp interface in order to identify the different fluid phases uniquely. Volumes assigned to the different phases are moving with the local flow velocity W , and therefore the evolution of c is determined by a convection equation  

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