Numerical methods for the simulation of the settling of flocculated suspensions

For one space dimension, the phenomenological theory of sedimentation of fl occulated suspensions yields a model that consists of an initial-boundary v alue problem for a second order partial differential equation of mixed hype rbolic-parabolic type. Due to the mixed hyperbolic-parabolic nature of the model, its solutions may be discontinuous and difficulties arise if one tri es to construct these solutions by classical numerical methods. In this pap er we present and elaborate on numerical methods that can be used to correc tly simulate this model, i.e. conservative methods satisfying a discrete en tropy principle. Included in our discussion are finite difference methods a nd methods based on operator splitting. In particular, the operator splitti ng methods are used to simulate the settling of flocculated suspensions. (C ) 2000 Elsevier Science B.V. All rights reserved.