  In this paper I will revisit the construction of a global weak solution to
the volume preserving mean curvature flow via discrete minimizing movement
scheme by Mugnai-Seis-Spadaro (2016). This method is based on the gradient flow
approach due to Almgren-Taylor-Wang (1993) and Luckhaus-Strurzenhecker (1995)
and my aim is to replace the volume penalization by implementing the volume
constraint directly in the discrete scheme, which from practical point of view
is perhaps more natural. A technical novelty is the proof of the density
estimate which is based on the second variation condition of the energy.
