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 \section*{Mathematical Model and Viscous Splitting Approximation
 for Sedimentation-Consolidation Processes}
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 \begin{center} W.L. Wendland and  R. B\"{u}rger
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 Mathematisches Institut~A, Universit\"{a}t Stuttgart, Pfaffenwaldring~57, 70569 Stuttgart,
 Germany, Fax~++49-711-6855599, E-Mail {\tt wendland@mathematik.uni-stuttgart.de}
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 {\small{\bf Abstract.} The phenomenological theory of sedimentation
 leads to a mathematical model
 describing the settling and con\-so\-li\-da\-tion
 behaviour of flocculated suspensions in
 solid-liquid separation vessels, so-called thickeners. In two
 or three space dimensions, solvability
 of these equations depends on
 the choice of  phase and  mixture
 viscosities. In one space dimension,
 this
 model reduces to an initial-boun\-dary
 value problem of a quasilinear
 strongly degenerate pa\-ra\-bo\-lic equation, for
 which existence, uniqueness and entropy
 boun\-dary conditions are presented. Simulations
 of batch and continuous sedimentation processes
 have been obtained by numerical solution of this
 problem has by a viscous splitting algorithm. Results
 of current research work including
 convergence of the numerical method,
 the addition of a singular
 source term modelling thickening with
 a submerged feeding source and
 numerical solution in two dimensions
 are addressed in this contribution.
 }
 }
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