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

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.