VOF method in Lagrangian frameworks

104 FINITE ELEMENT MODELLENG OF POLYMERIC FLOW PROCESSES 3.5.3 VOF method in Lagrangian frameworks 

Consider the position of a material point in a flow field described by the following position vector 

Any given material point can only occupy a single position at a time and hence Equation (3.75) can be used to find the position of the point as 

The substitution for p from Equation (3.76) into Equation (3.74) gives 

If the reference time f and the current time t coincide then the reference and current positions will also coincide and the right-hand side of Equation (3.77) can be replaced by the reference position defined as x in Equation (3.76). In a velocity field given as = u x,t ) the motion of a material point can be described 

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