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Strongly degenerate parabolic-hyperbolic systems modeling polydisperse sedimentation with compression. (English) Zbl 1047.35071
Mathematical models for the controlled sedimentation of polydisperse suspensions of small particles, which belong to a finite number of special differing in size or density are suspended in viscous fluid, are important in many theoretical and practical applications. In this work it is shown how existing models for the sedimentation of monodisperse flocculated suspensions and of polydisperse suspensions of rigid spheres differing in size can be combined to yield a new theory of the sedimentation processes of polydisperse suspensions forming compressible sediments.
For \(N\) solid particle species the problem reduces in one space dimension to an \( N\times N\) coupled system of nonlinear strongly degenerate parabolic-hyperbolic equations. Bounds for the convective flux vector and diffusion matrix are derived. The mathematical model for \(N=3\) is illustrated by a numerical calculation with central difference scheme for the conversion- diffusion system and the results of the numerical simulations are discussed.

MSC:
35K65 Degenerate parabolic equations
35L40 First-order hyperbolic systems
35L65 Hyperbolic conservation laws
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
86A05 Hydrology, hydrography, oceanography
76T20 Suspensions
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