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Control of a surface of discontinuity in continuous thickness. (English) Zbl 0758.35009
Summary: This paper examines the control of an interface between a suspension of sedimenting particles in liquid and a bed of dense-packed particles at the bottom of the suspension. The problem arises in the operation of continuous thickeners (e.g. in mineral processing) and is here mathematically described by a first order inhomogeneous partial differential equation for the concentration \(C(x,t)\) of particles. The controlled variable is the height \(H^*\) of the bed, and the control variables are the volume fluxes injected at the feed level and removed at the bed. A strategy to control the interface is devised, and control is confirmed and demonstrated by a series of numerical experiments.

MSC:
35B37 PDE in connection with control problems (MSC2000)
76T99 Multiphase and multicomponent flows
35F30 Boundary value problems for nonlinear first-order PDEs
35R35 Free boundary problems for PDEs
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
76M20 Finite difference methods applied to problems in fluid mechanics
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