  In this paper, we review the computational aspects of a multiscale
dissipative particle dynamics model for complex fluid simulations based on the
feature-rich geometry of the Voronoi tessellation. The geometrical features of
the model are critical since the mesh is directly connected to the physics by
the interpretation of the Voronoi volumes of the tessellation as coarse-grained
fluid clusters. The Voronoi tessellation is maintained dynamically in time to
model the fluid in the Lagrangian frame of reference, including imposition of
periodic boundary conditions. Several algorithms to construct and maintain the
periodic Voronoi tessellations are reviewed in two and three spatial dimensions
and their parallel performance discussed. The insertion of polymers and
colloidal particles in the fluctuating hydrodynamic solvent is described using
surface boundaries.
