A model of sedimentation-consolidation processes in
so-called clarifier-thickener units is given by a
parabolic equation describing the evolution of the local
solids concentration coupled with a version of the Stokes
system for an incompressible fluid describing the motion
of the mixture. In cylindrical coordinates, and if an
axially symmetric solution is assumed, the original
problem reduces to two space dimensions. This poses the
difficulty that the subspaces for the construction of a
numerical scheme involve weighted Sobolev spaces. A novel
finite volume element method is introduced for the
spatial discretization, where the velocity field and the
solids concentration are discretized on two different
dual meshes. The method is based on a stabilized
discontinuous Galerkin formulation for the concentration
field, and a multiscale stabilized pair of
$\mathbbP_1$-$\mathbbP_1$ elements for velocity and
pressure, respectively. Numerical experiments illustrate
properties of the model and the satisfactory performance
of the proposed method.