Modeling and numerical simulation of secondary settlers: A Method of Lines strategy

• Published in: Water research (Oxford) Vol. 43; no. 2; pp. 319 - 330
• Main Authors: David, R., Saucez, P., Vasel, J.-L., Vande Wouwer, A.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-02-2009; Elsevier
• Subjects: Applied sciences; Exact sciences and technology; Geologic Sediments; Mathematical modeling; Method of Lines; Models, Theoretical; Numerical simulation; Other industrial wastes. Sewage sludge; Partial differential equations; Pollution; Secondary settlers; Wastes; Wastewater treatment; Water Purification - methods; Water treatment and pollution; Numerical simulation; Mathematical modeling; Partial differential equations; Wastewater treatment; Secondary settlers; Method of Lines; Numerical method; Boundary value; Boundary condition; Waste water purification; Modeling; Partial differential equation
• ISSN: 0043-1354; 1879-2448
• DOI: 10.1016/j.watres.2008.10.037

In this paper, attention is focused on a parabolic partial differential equation (PDE) modeling sedimentation in a secondary settler and the proper formulation of the problem boundary conditions (i.e., the conditions prevailing at the feed, clear water and sludge outlets). The presence of a diffusion term in the equation not only allows the reproduction of experimental observations, as reported in a number of works, but also makes the numerical solution of the initial-boundary value problem significantly easier than the original conservation law (which is a nonlinear hyperbolic PDE problem requiring advanced numerical techniques). A Method of Lines (MOL) solution strategy is then proposed, based on the use of finite differences or spectral methods, and on readily available time integrators. The efficiency and flexibility of the general procedure are demonstrated with various numerical simulation results.