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A relaxation scheme for continuous sedimentation in ideal clarifier-thickener units. (English) Zbl 1122.76063
Summary: 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.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76T20 Suspensions
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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