A relaxation scheme forcontinuous sedimentation in ideal clarifier-thickener units

We prove convergence for a simple relaxation scheme for a scalar conservation law modeling the settling of particles in an ideal clarifier-thickener unit. The conservation law has a flux which is spatially dependent on two discontinuous parameters. We prove convergence of the relaxation approximations to a weak solution of the clarifier-thickener model, and present numerical examples using our scheme.