Papers/Publications

A fixed grid, shifted stencil scheme for inviscid fluid-particle interaction.

John D. Towers

Preprint - pdf file

On some difference schemes and entropy conditions for a class of multi-species kinematic flow models with discontinuous flux.

R. Bürger, K. H. Karlsen, and J. D. Towers
Preprint - pdf file Networks and Heterogeneous Media

Finite difference methods for discretizing singular source terms in a Poisson interface problem.

Preprint - pdf file Contemporary Mathematics

A conservation law with discontinuous flux modeling traffic flow with abruptly changing road surface conditions.

R. Bürger, K. H. Karlsen, and J. D. Towers
Preprint - pdf file Hyperbolic Problems: Theory, Numerics and Applications. Proceedings of Symposia in Applied Mathematics.

Finite difference methods for approximating Heaviside functions.
Preprint - pdf file Journal of Computational Physics

Some matlab/octave programs related to this paper

A convergence rate theorem for finite difference approximations to delta functions.
Preprint - pdf file Journal of Computational Physics 

Difference schemes, entropy solutions, and speedup impulse for an inhomogeneous kinematic traffic flow model.

R. Bürger, A. Garcia, K. H. Karlsen, and J. D. Towers
Preprint - pdf file Networks and Heterogeneous Media

Discretizing delta functions via finite differences and gradient normalization.
Preprint - pdf file Journal of Computational Physics

An Engquist-Osher-type scheme for conservation laws with discontinuous flux

Adapted to flux connections.
R. Bürger, K. H. Karlsen, and J. D. Towers
Preprint - pdf file SIAM Journal of Numerical Analysis

A family of schemes for kinematics flows with discontinuous flux.
R. Bürger, A. Garcia, K. H. Karlsen, and J. D. Towers
Preprint - pdf file Journal of Engineering Mathematics

A kinematic model of continuous separation and classification of polydisperse suspensions.
R. Bürger, A. Garcia, K. H. Karlsen, and J. D. Towers
Preprint - pdf file Computers and Chemical Engineering

A note on an extended clarifier-thickener model with singular source and sink terms.
R. Bürger, A. Garcia, K. H. Karlsen, and J. D. Towers
Scientia, Series A: Mathematical Sciences  Preprint - pdf file

Two methods for discretizing a delta function supported on a level set.
Journal of Computational Physics Preprint - pdf file

Some matlab/octave programs related to this paper

A mathematical model of clarifier-thickener units.
R. Bürger, K. H. Karlsen, and J. D. Towers PAMM Proc. Appl. Math
Preprint - pdf file

On an extended clarifier-thickener model with singular source and sink terms.
R. Bürger, A. Garcia, K. H. Karlsen, and J. D. Towers
European Journal of Applied Mathematics  Preprint - pdf file

On Conservation laws with discontinuous flux.
R. Bürger, K. H. Karlsen, S. Mishra, and J. D. Towers
In: Y. Wang and K. Hutter (Eds.), Trends in Applications of Mathematics to Mechanics , Shaker Verlag, Aachen, 75-84 (2005).
Preprint - pdf file

Mathematical model and numerical simulation of the dynamics of flocculated suspensions in
clarifier-thickeners.
R. Bürger, K. H. Karlsen, and J. D. Towers
Preprint - pdf file
Chemical Engineering Journal

A model of continuous sedimentation of flocculated suspensions in
clarifier-thickener units.
R. Bürger, K. H. Karlsen, and J. D. Towers
Preprint - pdf file
Society for Industrial and Applied Mathematics Journal on Applied Mathematics 

Closed-form and finite difference solutions to a population balance model
of grinding mills.
R. Bürger, K. H. Karlsen, and J. D. Towers
Preprint - pdf file
Journal of Engineering Mathematics

Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a
discontinuous space-time dependent flux.
K.H. Karlsen and J.D. Towers
Preprint - pdf file
Chinese Annals of Mathematics, Ser.B.

L¹ stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion
equations with discontinuous coefficients.
K. H. Karlsen, N. H. Risebro, and J. D. Towers
Transactions of the Royal Norwegian Society of Science and Letters DKNVS
Preprint - pdf file

Front tracking for scalar balance equations.
K. H. Karlsen, N. H. Risebro, and J. D. Towers
Journal of hyperbolic differential equations
Preprint - PDF file

Well-posedness in BV_t and convergence of a difference scheme for continuous sedimentation
in ideal clarifier-thickener units.
R. Bürger, K. H. Karlsen, N. H. Risebro, and J. D. Towers
Numerische Mathematik
Preprint .pdf file

Monotone difference approximations for the simulation of clarifier-thickener units.
R. Bürger, K. H. Karlsen, N. H. Risebro, and J. D. Towers
Computing and Visualization in Science
Preprint .pdf file

On a model for continuous sedimentation in a vessel with discontinuously varying cross sectional area.
R. Bürger, K. H. Karlsen, N. H. Risebro, and J. D. Towers
Hyperbolic problems: theory, numerics, applications. Springer, Berlin, 2003.
Preprint - PDF file
Photo - HYP2002 conference - Caltech March, 2002

Numerical Methods for the Simulation of Continuous Sedimentation in
Ideal Clarifier-Thickener Units.
R. Bürger, K. H. Karlsen, N. H. Risebro, and J. D. Towers
International Journal of Mineral Processing
Preprint - PDF file

Upwind difference approximations  for degenerate parabolic
convection-diffusion equations with a discontinuous coefficient.
K. H. Karlsen, N. H. Risebro, and J. D. Towers.
Institute for Mathematics and Applications Journal on Numerical Analysis IMAJNA
Preprint

On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous
 coefficient.
K. H. Karlsen, N. H. Risebro, and J. D. Towers.
Electronic Journal of Differential Equations
Preprint

A difference scheme for conservation laws with a discontinuous flux - the nonconvex case.
Society for Industrial and Applied Mathematics Journal on Numerical Analysis
PDF file

John responds to some questions about this paper.

Convergence of a difference scheme for conservation laws with a discontinuous flux.
Society for Industrial and Applied Mathematics Journal on Numerical Analysis
PDF file PDF file - An early version.

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Slides from Presentations

COMCA – Iquique, Chile (2008): Slides for multiclass entropy talk

ICIAM07 - Zurich: Slides for delta function talk Slides for traffic model talk

Workshop on nonlinear evolution equations, NTNU, Trondheim, Oct 5-6, 2000.
PDF file
Workshop info

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Other links of interest.

Second Chilean Conference on Numerical Analysis of Partial Differential Equations

WONAPDE 2007 - Photos

ICIAM 07

Centre for Advanced Study - Research group in Nonlinear PDE

Preprint Server for Conservation Laws

Comp. & Applied Math Reports - UCLA

Kenneth Karlsen's home page

Raimund

Burger's home page

Analysis and Numerics for Nonlinear Waves

HYP2002 - 9th International Conference on Hyperbolic Problems (at Cal Tech)

Back to my homepage.