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- Raimund Bürger, Kenneth H. Karlsen, Nils Henrik Risebro, John D. Towers
- Numerische Mathematik
- 2004

- Raimund Bürger, Kenneth H. Karlsen, John D. Towers
- SIAM Journal of Applied Mathematics
- 2005

The chief purpose of this paper is to formulate and partly analyze a new mathematical model for continuous sedimentation-consolidation processes of flocculated suspensions in clarifier-thickener units. This model appears in two variants for cylindrical and variable cross-sectional area units, respectively (Models 1 and 2). In both cases, the governing… (More)

The extension of Kynch's kinematic theory of sedimentation of monodisperse suspensions to polydisperse mixtures leads to a nonlinear system of conservation laws for the volume fractions of each species. In this paper, we show that a second order central (Riemann solver free) scheme for the solution of systems of conservation laws can be employed as an… (More)

- Elmer M. Tory, Kenneth H. Karlsen, Raimund Bürger, Stefan Berres
- SIAM Journal of Applied Mathematics
- 2003

We show how existing models for the sedimentation of monodisperse flocculated suspensions and of polydisperse suspensions of rigid spheres differing in size can be combined to yield a new theory of the sedimentation processes of polydisperse suspensions forming compressible sediments (" sedimentation with compression " or " sedimentation-consolidation… (More)

- Raimund Bürger, Kenneth H. Karlsen, John D. Towers
- SIAM J. Numerical Analysis
- 2009

We consider scalar conservation laws with the spatially varying flux H(x)f (u)+(1−H(x))g(u), where H(x) is the Heaviside function and f and g are smooth nonlinear functions. Adimurthi, Mishra, and Veerappa Gowda [J. Hyperbolic Differ. Equ. 2:783–837, 2005] pointed out that such a conservation law admits many L 1 contraction semigroups, one for each… (More)

The well-known Lighthill-Whitham-Richards kinematic traffic flow model for uni-directional flow on a single-lane highway is extended to include both abruptly changing road surface conditions and drivers' reaction time and anticipation length. The result is a strongly degenerate convection-diffusion equation, where the diffusion term, accounting for the… (More)

- Raimund Bürger, Alice J. Kozakevicius
- J. Comput. Physics
- 2007

Multi-species kinematic flow models lead to strongly coupled, nonlinear systems of first-order, spatially one-dimensional conservation laws. The number of unknowns (the concentrations of the species) may be arbitrarily high. Models of this class include a multi-species generalization of the Lighthill–Whitham–Richards traffic model and a model for the… (More)

We study a zero-flux type initial-boundary value problem for scalar conservation laws with a genuinely nonlinear flux. We suggest a notion of entropy solution for this problem and prove its well-posedness. The asymptotic behavior of entropy solutions is also discussed.

- Raimund Bürger, Rosa Donat, Pep Mulet, Carlos A. Vega
- J. Comput. Physics
- 2011