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- John D. Towers
- SIAM J. Numerical Analysis
- 2000

The subject of this paper is a scalar finite difference algorithm, based on the Godunov or Engquist-Osher flux, for scalar conservation laws where the flux is spatially dependent through a possiblyâ€¦ (More)

- Raimund BÃ¼rger, 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)+(1âˆ’H(x))g(u), where H(x) is the Heaviside function and f and g are smooth nonlinear functions. Adimurthi, Mishra, andâ€¦ (More)

- John D. Towers
- SIAM J. Numerical Analysis
- 2001

- Raimund BÃ¼rger, 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 clarifierthickenerâ€¦ (More)

- Raimund BÃ¼rger, Kenneth H. Karlsen, Nils Henrik Risebro, John D. Towers
- Numerische Mathematik
- 2004

R. BÃ¼rger1, K.H. Karlsen2, N.H. Risebro3, J.D. Towers4 1 Institute ofAppliedAnalysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany; e-mail:â€¦ (More)

- John D. Towers
- J. Comput. Physics
- 2009

We present a finite difference method for discretizing a Heaviside function H(u(~x)), where u is a level set function u : Rn 7â†’ R that is positive on a bounded region Î© âŠ‚ R. There are two variants ofâ€¦ (More)

The classical Lighthill-Whitham-Richards (LWR) kinematic traffic model is extended to a unidirectional road on which the maximum density a(x) represents road inhomogeneities, such as variable numbersâ€¦ (More)

We study the Cauchy problem for the nonlinear (possibly strongly) degenerate parabolic transport-diffusion equation âˆ‚tu+ âˆ‚x ( Î³(x)f(u) ) = âˆ‚ xA(u), A â€²(Â·) â‰¥ 0, where the coefficient Î³(x) is possiblyâ€¦ (More)

We propose and prove convergence of a front tracking method for scalar conservation laws with source term. The method is based on writing the single conservation law as a 2 Ã— 2 quasilinear systemâ€¦ (More)

- Raimund BÃ¼rger, A. GarÄ‡Ä±a, Kenneth H. Karlsen, John D. Towers
- 2006

A one-dimensional clarifier-thickener (CT) model, which includes a singular feed source, can be expressed as a conservation law with a flux that is discontinuous with respect to the spatial variable.â€¦ (More)