Previous Courses

FINITE VOLUME METHODS FOR HYPERBOLIC CONSERVATION LAWS.

With applications to compressible flow and environmental problems.

Date: 25 - 28 March 2002
Place: Barcelona, SPAIN

Lecturer: Professor E F Toro OBE
Department of Computing and Mathematics
Manchester Metropolitan University Manchester UK
Emails: e.f.toro@mmu.ac.uk; toro@hyperbolica.co.uk

INTRODUCTION

Finite volume high-resolution upwind methods for hyperbolic conservation laws and their extensions
have been the subject of intensive research for more than half a century, with remarkable advances in the
last two decades or so. These methods have by now reached a stage of maturity and have started to play
a central role in the process of numerical technology transfer to industrial and research centres concerned
with the solution of engineering and scientific problems.

This short course is intended for scientists and engineers from Industry, Research Laboratories, Consultancy
and Software Organizations and Academic Institutions, who are interested in solving practical problems involving
hyperbolic partial differential equations such as compressible single and multi-phase flows, free-surface water flows,
debris flows and heavy-gas dispersion. The techniques are also applicable to other advection-dominated processes
encountered in environmental sciences. Scientists in managerial and decision-making positions will also benefit from
this intensive course on new trends and modern numerical techniques for solving practical problems.

COURSE CONTENT

Lecture 1: Basics on Hyperbolic Conservation Laws
Lecture 2: The Euler and Shallow Water Equations: Properties
Lecture 3: Exact Solution of the Riemann Problem
Lecture 4: Basics on Numerical Methods for Hyperbolic Equations
Lecture 5: Higher-Order Methods for Scalar Problems
Lecture 6: TVD Methods for Scalar Problems
Lecture 7: Godunov’s Method and Approximate Riemann Solvers I
Lecture 8: Godunov’s Method and Approximate Riemann Solvers II
Lecture 9: TVD Methods for the Non-Linear Systems
Lecture 10: Treatment of Sources Terms and Multiple Space Dimensions
Lecture 11: Very-High-Order Approaches I: ENO and WENO Methods
Lecture 12: Very-High-Order Approaches II: ADER Methods

TUTORIALS

Tutorial 1: Introduction to NUMERICA Numerical Experiments with Scalar Problems Using HYPER-LIN
Tutorial 2: Numerical Experiments with TVD Methods for Scalar Problems Using HYPER-LIN
Tutorial 3: Numerical Experiments with Godunov’s Method Using HYPER-WAT
Tutorial 4: Numerical Experiments with TVD Methods Using HYPER-EUL

SELECTED REFERENCES

Toro, E F Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer-Verlag. First Edition 1997. Second Edition 1999. See Amazon Book Review.
Toro, E F Shock-Capturing Methods for Free-Surface Shallow Flows, Wiley and Sons, 2001
Toro, E F NUMERICA, a Library of Source Codes for Teaching Research and Applications. Numeritek Ltd 1999
Toro, E F (Editor) Godunov Methods: Theory and Applications. Edited Review. Kluwer Academic/Plenum Publishers 2001

OTHER RELEVANT REFERENCES

LeVeque R J Numerical Methods for Conservation Laws.Birkhauser, 1992
Laney C B Computational Gas Dynamics. Cambridge University Press, 1998
Godlewski E and Raviart P A Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer-Verlag 1996

COST

Students £500, Academics £600, Others £1200 - if registered by 31st January 2002
Students £550, Academics £660, Others £1300 - if registered after 31st January 2002

Included in the cost are: Four days of tuition, tutorials, two coffee breaks/day, and for each participant a special version of:
" NUMERICA, a Library of Source Codes for Teaching, Research and Applications".
Prices exclusive of VAT.
Details of NUMERICA are found on http://www.numeritek.com

REGISTRATION FORM

WHO SHOULD ATTEND

Participants who would benefit from the course include: Research scientists and engineers from industry,
research laboratories, consultancy and academic organisations; post-doctoral research assistants and PhD students;
academics involved in teaching and research on numerical methods, fluid dynamics and mathematical modelling.
The course may also be useful to scientists in managerial positions, who would benefit from exposure to modern
computational techniques and their potential benefits to industry.

ACCOMMODATION

Accommodation is available at the Hotel Avenida Palace at the rate of Euro 118,70 per night (plus 7% tax), including buffet breakfast, for a standard single room. The cost for a Double room is Euro 178,70 per night (plus 7% tax). The reservation is to be sent directly to the hotel by the participants. Please click here for a copy of the hotel's reservation form. Deadline for hotel bookings at the discounted rate: 10th February 2002. After this date room reservations may be available on request.

For participants who wish to make their own arrangements for accommodation please see List of Hotels in Barcelona.

FINITE VOLUME UPWIND AND CENTRED METHODS FOR HYPERBOLIC CONSERVATION LAWS.
by

Lecturer: Professor E. F. Toro, OBE
Date: Monday 2nd to Friday 6th April 2001
Place: Hotel Avenida Palace, Barcelona, Spain

The course was attended by thirty participants from ten countries - Spain, Italy, Portugal, France, Czech Republic, Germany, Sweden, United Kingdom, Canada, USA.

The participants have fully evaluated the course and here are some of the results and comments:

 

'The time is too short. Thank you very much!!'

'Excellent course for advanced scientists. The course is very compact, that means too much information in a very short time.'

'The course taken place in Barcelona had a perfect organization and it can be qualified as excellent.'

'It was a pleasure for me to attend this course. It was organized very well and the lectures of Prof. Toro were very interesting and understanding also for an engineer.'

'I enjoyed it.'