Preprint 2000-010

On Some Upwind Difference Schemes for the Phenomenological Sedimentation-Consolidation Model

R. Bürger and K. Hvistendahl Karlsen

Abstract: In one space dimension, the phenomenological sedimentation-consolidation model reduces to an initial-boundary value problem (IBVP) for a nonlinear strongly degenerate convection-diffusion equation with a non-convex, time dependent flux function. Due to the mixed hyperbolic-parabolic nature of the model, its solutions are discontinuous and entropy solutions must be sought. In this paper, we first give a (short) guided visit to the mathematical (entropy solution) framework in which the well posedness of this and a related IBVP can be established. This also includes a short discussion of recent existence and uniqueness results for entropy solutions of IBVPs. The entropy solution framework constitutes the point of departure from which numerical methods can be designed and analysed. The main purpose of this paper is to present and demonstrate several finite difference schemes which can be used to correctly simulate the sedimentation-consolidation model, i.e., conservative schemes satisfying a discrete entropy principle. Here, we focus on finite difference schemes of upwind type. To some extent, we discuss also stability and convergence properties of the proposed schemes. Performance of the proposed schemes is demonstrated by simulation of two cases of batch settling and one of continuous thickening of flocculated suspensions. The numerical examples focus on a detailed error study, an illustration of the effect of varying the initial datum, and on simulation of practically important thickener operations, respectively.

Available as PostScript (1.3 Mbytes) or gzipped PostScript (374 Kbytes; uncompress using gunzip).
Raimund Bürger, <>
Kenneth Hvistendahl Karlsen, <>
Publishing information:
Preprint 2000/05, Sonderforschungsbereich 404, University of Stuttgart. Submitted to special issue of J. Eng. Math.
Submitted by:
<> March 8 2000.

[ 1996 | 1997 | 1998 | 1999 | 2000 | All Preprints | Preprint Server Homepage ]
© The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

Conservation Laws Preprint Server <>
Last modified: Fri Mar 10 16:22:36 2000