Stefan Diehl
Associate
Professor in Applied Mathematics (Docent i tillämpad matematik)
Centre for Mathematical Sciences
Lund University/Lund Institute of Technology
P.O. Box 118
SE221 00 Lund
SWEDEN
Room: 551A
Direct phone: +46 46 222 0920
Dept phone: +46 46 222 8537
Fax: +46 46 222 4010
Email: stefan.diehl@math.lth.se
Miscellaneous (in
Swedish/English)
Introduction to the scalar nonlinear
conservation law
Min docentföreläsning om modellering av trafikflöde,
september 2006
Jag har skrivit en bok Inledande geometri för högskolestudier (innehåll) som ges ut av Studentlitteratur.
Proposals of thesis projects for Master of Science degree
Modelling and simulation of flotation
Simulation of a wastewater treatment plant with positivitypreserving numerical methods
Modelling, simulation and flux identification of traffic flow
Optimization of pedestrian evacuation modelled by PDE
Research
Interests
 nonlinear conservation laws
and convectiondiffusion equations with discontinuous coefficients
 identification of constitutive
relations in PDE models
 modelling, simulation and
control of the separation process continuous sedimentation, which
can be found in, for example, most wastewater treatment plants, the
mineral, pulpandpaper, food and chemical industries
 modelling, simulation and
control of the activated sludge process, which can be found in most
wastewater treatment plants
 modelling of flotation
 modelling of traffic flow
 modelling of processes in life science
Supervision of PhD students
 Sebastian Farås 2010–2015
 Erik Henningsson 2011–2016 (cosupervisor)
 Camilo Mejías 2015– (cosupervisor)
 Julio Careaga 2017–
Theses
S. Diehl:
Shock behaviour of sedimentation in wastewater treatment, Lund University,
1988:13/ISSN 03278475 (1988) (Master's thesis)
S. Diehl:
Scalar conservation laws with source term and discontinuous flux function, Lund
University, 1992:8/ISSN 03278475 (1992) (Licentiate's thesis)
S. Diehl:
Conservation Laws with Application to Continuous Sedimentation, Lund University,
ISBN 9162816322 (1995) (PhD thesis)
Journal publications
If
you are interested in a publication that you cannot find in the links below,
please send me an email.
 S. Diehl: On scalar conservation
laws with point source and discontinuous flux function. SIAM J. Math.
Anal., 26(6), 1425–1451, 1995. Submitted version.
 S. Diehl: Scalar conservation
laws with discontinuous flux function: I. The viscous profile condition.
Comm. Math. Phys., 176, 23–44, 1996. Submitted version.
 S. Diehl, NilsOlof Wallin: Scalar
conservation laws with discontinuous flux function: II. On the stability
of the viscous profiles. Comm. Math. Phys., 176, 45–71, 1996.
 S. Diehl: A
conservation law with point source and discontinuous flux function
modelling continuous sedimentation. SIAM J. Appl. Math.,
56(2), 388–419,
1996.
 U. Jeppsson
and S. Diehl: An evaluation of a dynamic model of the secondary
clarifier. Water Sci. Tech., 34(5–6), 19–26, 1996.
 U. Jeppsson
and S. Diehl: On the modelling of the dynamic propagation of
biological components in the secondary clarifier. Water Sci. Tech., 34(5–6), 85–92, 1996.
 S. Diehl: Dynamic
and steadystate behaviour of continuous
sedimentation. SIAM J. Appl. Math., 57(4), 991–1018, 1997.
 S. Diehl: Continuous
sedimentation of multicomponent particles. Math. Meth. Appl. Sci., 20, 1345–1364, 1997.
 S. Diehl and U. Jeppsson: A model of the settler coupled to the
biological reactor. Water
Res.,
32(2), 331–342, 1998.
 S. Diehl: On boundary
conditions and solutions for ideal clarifierthickener units. Chem.
Eng. J., 80, 119–133, 2000. (A conference talk in 1999.)
 S. Diehl: Operating charts
for continuous sedimentation I: Control of steady states. J. Eng. Math.,
41, 117–144, 2001. (Final draft)
 S. Diehl: Operating charts
for continuous sedimentation II: Step responses. J. Eng. Math., 53, 139–185, 2005. (Final draft)
 S. Diehl: Operating charts
for continuous sedimentation III: Control of step inputs. J.
Eng. Math., 54, 225–259, 2006. (Final draft)
 S. Diehl: Estimation of
the batchsettling flux function for an ideal suspension from only two
experiments. Chem. Eng. Sci., 62, 4589–4601, 2007. http://dx.doi.org/10.1016/j.ces.2007.05.025
 S. Diehl: Operating charts
for continuous sedimentation IV: Limitations for control of dynamic behaviour. J. Eng. Math.,
60, 249–264,
2008. (Final draft)
 S. Diehl: A regulator for
continuous sedimentation in ideal clarifierthickener units. J.
Eng. Math. 60, 265–291, 2008. (Final draft)
 S. Diehl: The solidsflux
theory – confirmation and extension by using partial differential
equations. Water Res. 42,
4976–4988, 2008. http://dx.doi.org/10.1016/j.watres.2008.09.005
 S. Diehl: A uniqueness
condition for nonlinear convectiondiffusion equations with discontinuous
coefficients. J. Hyperbolic
Differential Equations, 6, 127–159, 2009. (submitted version)
 R. Bürger, S.
Diehl and I. Nopens: A consistent
modelling methodology for secondary settling tanks in wastewater
treatment. Water Res. 45,
2247–2260, 2011. http://dx.doi.org/10.1016/j.watres.2011.01.020
 E. Torfs,
R. Bürger, S. Diehl, S. Farås
and I. Nopens: A reliable numerical method for
secondary settling modelling. Comm. Appl. Biol. Sci. 77(1),
151–156, 2012.
 R. Bürger, S.
Diehl, S. Farås and I. Nopens: On
reliable and unreliable numerical methods for the simulation of secondary
settling tanks in wastewater treatment. Computers
Chem. Eng. 41, 93–105, 2012.
 S. Diehl and S. Farås: Fundamental nonlinearities of the
reactorsettler interaction in the activated sludge process. Water Sci.
Tech. 66(1), 28–35, 2012.
 S. Diehl and S. Farås: A reducedorder ODEPDE model for the activated
sludge process in wastewater treatment: Classification and stability
of steady states. Math. Models Meth. Appl. Sci., 23(3), 369–405,
2013.
 S. Diehl and S. Farås: Control of an ideal activated sludge
process in wastewater treatment via an ODEPDE model. J. Process
Control. 23, 359–381, 2013. (submitted
version)
 R. Bürger
and S. Diehl: Convexitypreserving flux identification for scalar
conservation laws modelling sedimentation. Inverse Problems. 29(4),
045008, 2013.
 R. Bürger, S.
Diehl, S. Farås, I. Nopens
and E. Torfs: A consistent modelling
methodology for secondary settling tanks: A reliable numerical
method. Water Sci. Tech., 68(1), 192–208, 2013.
 F. Betancourt, R. Bürger, S. Diehl and S. Farås:
Modelling and controlling clarifierthickeners fed by suspensions
with timedependent properties. Minerals Eng., 62,
91–101, 2014.
 F. Betancourt, R. Bürger, S. Diehl and C. Mejías:
Advanced methods of flux identification for clarifierthickener simulation
models. Minerals Eng., 63, 2–15, 2014.
 S. Diehl, E. Henningsson, A. Heyden and
S. Perna: A onedimensional movingboundary
model for tubulindriven axonal growth. J. Theor.
Biol., 358, 194–207, 2014.
 S. Diehl: Numerical
identification of constitutive functions in scalar nonlinear
convectiondiffusion equations with application to batch sedimentation. Appl.
Num. Math., 95, 154–172, 2015.
 E. Torfs,
T. Maere, R. Bürger,
S. Diehl and I. Nopens: Impact on sludge
inventory and control strategies using the benchmark simulation model no.
1 with the BürgerDiehl settler model. Water
Sci. Tech., 71(10), 1524–1535, 2015.
 J. Zambrano, B. Carlsson and S. Diehl: Optimal steadystate design of
zone volumes of bioreactors with Monod growth kinetics. Biochem. Eng. J., 100, 59–66, 2015.
 S. Diehl , S. Farås and G. Mauritsson:
Fast reliable simulations of secondary settling tanks
in wastewater treatment with semiimplicit time discretization, Computers
Math. Appl., 70(4), 459–477, 2015.
 S. Diehl and J. Zambrano and B.
Carlsson: Steadystate analysis of activated
sludge processes with a settler model including sludge compression. Water
Res. 88C, 104–116,
2016.
 R.
Bürger, S. Diehl and C. Mejías: On time discretizations for the simulation
of the batch settlingcompression process in one dimension. Water Sci. Tech. 73(5), 1010–1017, 2016.
 S. Diehl, E. Henningsson and A. Heyden:
Efficient simulations of tubulindriven axonal growth. J. Comp. Neurosci. 1–19, 2016.
 R.
Bürger, J. Careaga, S. Diehl, C. Mejías, I. Nopens, E. Torfs and P.
A.Vanrolleghem: Simulations of reactive settling of activated sludge with
reduced biokinetic model. Computers Chem. Eng. 92,
216–229, 2016.
 S.
Diehl, J. Zambrano and B.
Carlsson: Steadystate analyses of activated
sludge processes with plugflow reactor. J. Env.
Chem. Eng. 5(1), 795–809, 2017.
 E. Torfs, F.
Locatelli, S. Balemans, J. Laurent, P. A.Vanrolleghem, R. Bürger, S. Diehl, P. François and I. Nopens: Concentrationdriven models revisited: Towards
a unified framework to model settling tanks in WRRFs. Water Sci. Tech. 75(3), 539–551, 2017.
 E. Torfs,
S. Balemans, F. Locatelli, S. Diehl, R. Bürger, J. Laurent, P. François and I. Nopens: On constitutive functions for hindered
settling velocity in 1D settler models: selection of appropriate
model structure. Water Res. 110, 38–47, 2017.
 R. Bürger,
J. Careaga and S. Diehl: Entropy solutions of a
scalar conservation law modelling sedimentation in vessels with varying
crosssectional area. SIAM J. Appl. Math. 77(2), 789–811, 2017.
 R. Bürger,
S. Diehl, M. C. Martí, P. Mulet;
I. Nopens, E. Torfs,
P. A. Vanrolleghem: Numerical solution of a
multiclass model for batch settling in water resource recovery
facilities. Appl. Math. Modelling 49, 415–436, 2017.
 R. Bürger,
J. Careaga and S. Diehl: A simulation model for settling
tanks with varying crosssectional area. Chem. Eng. Commun. 204, 1270–1281, 2017.
 F.
Betancourt, R. Bürger, C. Chalons, S. Diehl and S. Farås: A random
sampling method for a family of Templeclass systems of conservation laws. Numer. Math.138, 37–73, 2018.
 R. Bürger,
S. Diehl and C. Mejías: A difference scheme for
a degenerating convectiondiffusionreaction system modelling continuous
sedimentation. To appear in ESAIM: Math. Modelling Num. Anal.
 R. Bürger, S. Diehl and M. C. Martí: A conservation law with multiply discontinuous flux modelling a flotation column. To appear in Netw. Heterog. Media.
Conference publications
 S. Diehl, G. Sparr and G. Olsson: Analytical and numerical
description of the settling process in the activated sludge operation. In
R. Briggs, editor, Instrumentation, Control and Automation of Water and
Wastewater Treatment and Transport Systems, pages 471478. IAWPRC, Pergamon Press, 1990.
 U. Jeppsson
and S. Diehl: Validation of a robust model of continuous
sedimentation. Proc. 9th Forum for Applied Biotechnology (FAB), Med. Fac. Landbouww. Univ. Gent, 60/4b, 1995, pp 24032414.
 R. Bürger, S.
Diehl, S. Farås and I. Nopens:
Simulations of the secondary settling process with consistent numerical methods.WATERMATEX 2011: 8th IWA Symposium on Systems
Analysis and Integrated Assessment, San Sebastian, Spain, 2011.
 S. Diehl and S. Farås: Fundamental nonlinearities of the
reactorsettler interaction in the activated sludge process. WATERMATEX
2011: 8th IWA Symposium on Systems Analysis and Integrated Assessment, San
Sebastian, Spain, 2011.
 S. Diehl. Shockwave behaviour of sedimentation in wastewater treatment: a
rich problem. Analysis for Science, Engineering and Beyond. The
Tribute Workshop in Honour of Gunnar Sparr held in Lund, May 89, 2008. Åström,
K.; Persson, L.E.; Silvestrov, S. D. (Eds.). Springer Proceedings
in Mathematics, Springer Berlin Heidelberg.Vol.
6, 175–214, 2012.
 S.
Gedda, C. Andersson, J. Åkesson and S. Diehl: Derivativefree Parameter
Optimization of Functional Mockup Units. Proceedings of the 9th International
MODELICA Conference, September 35, 2012, Munich, Germany.
 E.
Torfs, T. Maere, R. Bürger, S. Diehl, S. Farås and I. Nopens: Towards
improved 1D settler modelling: impact on control strategies using the
Benchmark Simulation Model. In: Proceedings of Instrumentation Control
and Automation, 11th IWA conference, International Water Association
(IWA), Narbonne, France, Sep 1820, 2013.
 E.
Torfs, P. Vlasschaert, Y. Amerlinck, R. Bürger, S. Diehl, S. Farås and I.
Nopens: Towards improved 1D settler modelling: calibration of the
Bürger model and case study. Proceedings of 86th Annual Water
Environment Federation Technical Exhibition and Conference (WEFTEC),
Mc Cormick Place South, Chicago, IL, USA, 59 October 2013.
 E. Torfs, F. Locatelli, S. Balemans, S. Diehl, R. Bürger, P. François, J. Laurent, I. Nopens. Impact of the flocculation state on hindered and compression settling: experimental evidence and overview of available modelling frameworks. 9th IWA Symposium on Systems Analysis and Integrated Assessment (Watermatex), 1417 June, 2015, Gold Coast, Australia. 2015.
 E. Torfs, S. Balemans, F. Locatelli,J. Laurent, P. François, R. Bürger, S. Diehl, I. Nopens. Critical analysis of constitutive functions for hindered settling velocity in 1D settler models. 9th IWA Symposium on Systems Analysis and Integrated Assessment (Watermatex), 1417 June, 2015, Gold Coast, Australia. 2015.
 B. Carlsson, S. Diehl, J. Zambrano. Analyses of activated sludge processes consisting of a plugflow reactor and a nonideal settler. 9th IWA Symposium on Systems Analysis and Integrated Assessment (Watermatex), 1417 June, 2015, Gold Coast, Australia. 2015.
 S. Diehl, J. Zambrano and B. Carlsson. Steadystate analysis and design of activated sludge processes including compressive settling. 9th IWA Symposium on Systems Analysis and Integrated Assessment (Watermatex), 1417 June, 2015, Gold Coast, Australia. 2015.
 R. Bürger and S. Diehl. On time discretizations for the simulation of the settlingcompression process. 9th IWA Symposium on Systems Analysis and Integrated Assessment (Watermatex), 1417 June, 2015, Gold Coast, Australia. 2015.

C. Garneau., S. Diehl, E.
Torfs E, R. Bürger F. A. Claeys P. A. Vanrolleghem P.A. The
BürgerDiehl model: The right integrator for the right model. 9th IWA Symposium on Systems Analysis and Integrated Assessment (Watermatex), 1417 June, 2015, Gold Coast, Australia. 2015.
 E. Torfs,
F. Locatelli, S. Balemans, J. Laurent, P.
A.Vanrolleghem, R. Bürger, S. Diehl, P. François, R. Mosse
and I. Nopens: Concentrationdriven models
revisited: Towards a unified framework to model settling tanks in
WWTPs. Proceedings 5th IWA/WEF Wastewater Treatment Modelling Seminar
(WWTmod2016). Annecy, France, April 26, 2016. 109118. 2016.
 J. Zambrano, B. Carlsson, S. Diehl and E. Nehrenheim:
A simplified model of an activated sludge process with a plugflow
reactor. Proceedings of The 9th Eurosim
Congress on Modelling and Simulation, Oulu Finland, 1216 September 2016.
 R. Bürger,
S. Diehl and C. Mejías:
A Model for Continuous Sedimentation with Reactions for Wastewater
Treatment. Lecture Notes in Civil Engineering 4. G. Mannina (ed.). Springer International
Publishing. 596601. 2017.
Submitted manuscripts
 R. Bürger,
J. Careaga and S. Diehl: Flux identification of scalar conservation laws from sedimentation in a cone.
 S. Diehl, J. Zambrano and B. Carlsson: Analysis of photobioreactors in series.
 R. Bürger,
J. Careaga, S. Diehl, R. Merckel and J. Zambrano: Estimating the hinderedsettling flux function from a batch test in a cone.