Entropy solutions and flux identification of a scalar conservation law modelling centrifugal sedimentation

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TY - JOUR

T1 - Entropy solutions and flux identification of a scalar conservation law modelling centrifugal sedimentation

AU - Careaga, Julio

AU - Diehl, Stefan

PY - 2020

Y1 - 2020

N2 - Centrifugal sedimentation of an ideal suspension in a rotating tube or basket can be modelled by an initial-boundary-value problem for a scalar conservation law with a nonconvex flux function. The sought unknown is the volume fraction of solids as function of radial distance and time for constant initial data. The method of characteristics is used to construct entropy solutions. The qualitatively different solutions, which depend on the initial value and the vessel radial coordinates, are presented in detail along with numerical simulations. Based on the entropy solutions, a new method of flux identification, which does not require any prescribed functional expression, is presented and illustrated with synthetic data.

AB - Centrifugal sedimentation of an ideal suspension in a rotating tube or basket can be modelled by an initial-boundary-value problem for a scalar conservation law with a nonconvex flux function. The sought unknown is the volume fraction of solids as function of radial distance and time for constant initial data. The method of characteristics is used to construct entropy solutions. The qualitatively different solutions, which depend on the initial value and the vessel radial coordinates, are presented in detail along with numerical simulations. Based on the entropy solutions, a new method of flux identification, which does not require any prescribed functional expression, is presented and illustrated with synthetic data.

KW - hindered settling

KW - inverse problem

KW - Kynch constitutive assumption

KW - method of characteristics

KW - nonconvex flux function

KW - nonlinear hyperbolic PDE

KW - separation process

U2 - 10.1002/mma.6212

DO - 10.1002/mma.6212

M3 - Article

AN - SCOPUS:85083534730

VL - 43

SP - 4530

EP - 4557

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 1099-1476

IS - 7

ER -