NPA
27 January 2003 to 11 July 2003
Quasilinear hyperbolic systems in divergence form, commonly called 'hyperbolic conservation laws', govern a broad spectrum of physical phenomena in compressible fluid dynamics, nonlinear material science, etc. Such equations admit solutions that may exhibit various kinds of shocks and other nonlinear waves (propagating phase boundaries, fluid interfaces, etc.) which play a dominant role in multiple areas of physics; astrophysics, cosmology, dynamics of (solid-solid) material interfaces, multiphase (liquid-vapor) flows, combustion theory, etc.
In recent years, major progress has been made in both theoretical and the numerical aspects of the field, while the number of applications has skyrocketed. The time is ripe for building a bridge between the most recent developments in the general mathematical theory and the areas of applications that have developed most actively in the last few years. Hyperbolic problems in astrophysics and cosmology (relativistic compressible fluid models, the Einstein Field equations of general relativity) are particularly challenging for the applied mathematician; they are essential in order to uncover the structure and formation of the Universe. Hyperbolic problems arising in nonlinear material science (propagating phase boundaries in solids undergoing phase transitions of the austenite-martensite type, for instance) face serious mathematical difficulties (failure of strict hyperbolicity, elliptic regions in phase space); these models are an essential component for understanding the dynamics of shape memory alloys (also called smart materials). To describe the dynamics of phase boundaries, the notion of a kinetic relation was proposed and investigated by material scientists and applied mathematicians in recent years. Recent developments on the theory of systems of conservation laws will be covered; L1 well-posedness, singular limits based on diffusion-dispersion or relaxation, multidimensional hyperbolic problems, degenerate shock wave structure, failure of strict hyperbolicity, etc.
The programme will also have a computational component; numerical schemes for multiphase flows and fluids with non-convex equation of state, exact or approximate Riemann solvers for relativistic and non-relativistic flows, etc. Short-courses, theme weeks and conferences will provide a valuable opportunity for reviewing the state of the art on the physical models, the techniques of mathematical analysis, and the numerical analysis, and for discussing open problems among the participants.
January to February:
Kinetic Relations for Nonclassical Shocks and Phase Boundaries
February to March:
General Theory of Hyperbolic Conservation Laws
March to April:
Shock Waves having Anomalous Structure and Multi-dimensional Problems
April to May:
Multiphase Flows in Fluids
June to July:
Hyperbolic Problems from Astrophysics and Cosmology.
Click here to download the programme's final scientific report
Title | Year | Programme | |
---|---|---|---|
TVD fluxes for the high-order ADER schemesAuthors: Vladimir Titarev, Eleuterio Toro |
2002 | NPA | 21 October 2016 |
Hyperbolicity of the non-linear models of Maxwell's equationsAuthors: D Serre |
2002 | NPA | 21 October 2016 |
Nonclassical Riemann solvers with nucleationAuthors: M Shearer, PG Lefloch |
2002 | NPA | 21 October 2016 |
Steady transonic shocks and free boundary problems in infinite cylinders for the Euler equationsAuthors: M Feldman, Gui-Qiang Chen |
2002 | NPA | 21 October 2016 |
Advances in turbulent flow computations using high-resolution methodsAuthors: D Drikakis |
2002 | NPA | 21 October 2016 |
Existence and asymptotic behavior of multi-dimensional quantum hydrodynamic model for semiconductorsAuthors: Pierangelo Marcati, Tong Li |
2002 | NPA | 21 October 2016 |
Hyperbolic conservative model for compressible two-phase flowAuthors: Dia Zeidan, A Slaouti, ET Al, Eugene Romenski |
2002 | NPA | 21 October 2016 |
The Riemann problem for fluid flows in a nozzle with discontinuous cross-sectionAuthors: Mai Duc Thanh, PG Lefloch |
2002 | NPA | 21 October 2016 |
The Riemann problem for a class of resonant hyperbolic systems of balance lawsAuthors: PG Lefloch, Paola Goatin |
2002 | NPA | 21 October 2016 |
Shock waves in compressible two-phase flowsAuthors: Eleuterio Toro, Eugene Romenski |
2002 | NPA | 21 October 2016 |
Towards fully conservative numerical methods for the nonlinear model Boltzmann equationAuthors: Vladimir Titarev |
2002 | NPA | 21 October 2016 |
Multi-stage predictor-corrector fluxes for hyperbolic equationsAuthors: Eleuterio Toro |
2002 | NPA | 21 October 2016 |
Centred schemes for nonlinear hyperbolic equationsAuthors: Gui-Qiang Chen, Eleuterio Toro |
2002 | NPA | 21 October 2016 |
Eno and Weno schemes based on upwind centred TVD fluxesAuthors: Eleuterio Toro, Vladimir Titarev |
2002 | NPA | 21 October 2016 |
Free boundary problems and transonic shocks for the Euler equations in unbounded domainsAuthors: M Feldman, Gui-Qiang Chen |
2002 | NPA | 21 October 2016 |
Finite-volume weno schemes for three-dimensional conservation lawsAuthors: Eleuterio Toro, Vladimir Titarev |
2002 | NPA | 21 October 2016 |
ADER schemes for scalar hyperbolic conservation laws in three space dimensionsAuthors: Vladimir Titarev, Eleuterio Toro |
2002 | NPA | 21 October 2016 |
Shock-turbulence interaction an exhaustively classifying linearized approachAuthors: LF Dinu |
2002 | NPA | 21 October 2016 |
A geometric level-set formulation of a plasma-sheath interfaceAuthors: M Feldman, S-Y Ha, Marshall Slemrod |
2002 | NPA | 21 October 2016 |
ADER schemes for three-dimensional nonlinear hyperbolic systemsAuthors: Eleuterio Toro, Vladimir Titarev |
2002 | NPA | 21 October 2016 |
MUSTA: A multi-stage numerical fluxAuthors: Eleuterio Toro |
2002 | NPA | 21 October 2016 |
Compressible two-phase flows: Two-pressure models and numerical methodsAuthors: Eleuterio Toro, Eugene Romenski |
2002 | NPA | 21 October 2016 |
MUSTA schemes for multi-dimensional hyperbolic systems: analysis and improvementsAuthors: Eleuterio Toro, Vladimir Titarev |
2002 | NPA | 21 October 2016 |
MUSTA schemes for systems of conservation lawsAuthors: Vladimir Titarev, Eleuterio Toro |
2002 | NPA | 21 October 2016 |
Conservative hyperbolic model for compressible two-phase flow with different phase pressures and temperaturesAuthors: Eleuterio Toro, AD Resnyansky, Eugene Romenski |
2002 | NPA | 21 October 2016 |
A Riemann solver and upwind methods for a two-phase flow model in non-conservative formAuthors: Eleuterio Toro, CE Castro |
2002 | NPA | 21 October 2016 |
Riemann solvers with evolved initial conditionsAuthors: Eleuterio Toro |
2002 | NPA | 21 October 2016 |
Derivative Riemann solvers for systems of conservation laws and ADER methodsAuthors: Eleuterio Toro, Vladimir Titarev |
2002 | NPA | 21 October 2016 |
Exact Riemann problem solutions and upwind fluxes for nonlinear elasticityAuthors: Eugene Romenski, Eleuterio Toro, Vladimir Titarev |
2002 | NPA | 21 October 2016 |
Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometryAuthors: Eleuterio Toro, R Bernetti, Vladimir Titarev |
2002 | NPA | 21 October 2016 |
Multidimensional wave-wave regular interactions and genuine nonlinearity: some remarksAuthors: LF Dinu |
2002 | NPA | 21 October 2016 |
ADER schemes for the shallow water equations in channel with irregular bottom elevationAuthors: Vladimir Titarev, Eleuterio Toro, G Vignoli |
2002 | NPA | 21 October 2016 |
Alternative solvers for the derivative Riemann problem for hyperbolic balance lawsAuthors: Eleuterio Toro, CE Castro |
2002 | NPA | 21 October 2016 |
Injectivity radius of Lorentzian manifoldsAuthors: PG Lefloch, Gui-Qiang Chen |
2002 | NPA | 21 October 2016 |
Entropy solutions of the Eular equations for isothermal relativistic fluidsAuthors: M Yamazaki, PG Lefloch |
2002 | NPA | 21 October 2016 |
Explicit finite volume schemes of arbitrary high order of accuracy for hyperbolic systems with stiff source termsAuthors: Eleuterio Toro, Michael Dumbser, C Enaux |
2002 | NPA | 21 October 2016 |
ADER finite volume schemes for nonlinear diffusion-reaction equationsAuthors: Eleuterio Toro, A Hidalgo |
2002 | NPA | 21 October 2016 |
Nondegeneracy, from the prospect of wave-wave regular interactions of a gasdynamic type: some remarksAuthors: MI Dinu, LF Dinu |
2002 | NPA | 21 October 2016 |
A unified framework for the construction of one-step finite-volume and discontinuous Galerkin schemes on unstructured meshesAuthors: D Balsara, Michael Dumbser, C Munz, Eleuterio Toro |
2002 | NPA | 21 October 2016 |
FORCE schemes on unstructured meshes I: conservative hyperbolic systemsAuthors: A Hidalgo, Michael Dumbser, Eleuterio Toro |
2002 | NPA | 21 October 2016 |
Martin's "differential" approach: some classifying remarksAuthors: MI Dinu, LF Dinu |
2002 | NPA | 21 October 2016 |
Well-balanced high-order centred schemes for non-conservative hyperbolic systems. Applications to shallow water equations with fixed and mobile bed.Authors: Eleuterio Toro, A Siviglia, A Canestrelli, Michael Dumbser |
2002 | NPA | 21 October 2016 |
A global multi-scale mathematical model for the human circulation with emphasis on the venous systemAuthors: LO Muller, Eleuterio Toro |
2002 | NPA | 21 October 2016 |
Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemesAuthors: GI Montecinos, LO Muller, Eleuterio Toro |
2002 | NPA | 21 October 2016 |
Enhanced global mathematical model for studying cerebral venous blood flowAuthors: LO Muller, Eleuterio Toro |
2002 | NPA | 21 October 2016 |
On Riemann solutions to weakly hyperbolic systems part 1. Modelling subcritical flows in arteriesAuthors: E Han, G Warnecke, Eleuterio Toro, A Siviglia |
2002 | NPA | 21 October 2016 |
On Riemann solutions to weakly hyperbolic systems part 2. Modelling subcritical flows in arteriesAuthors: E Han, G Warnecke, Eleuterio Toro, A Siviglia |
2002 | NPA | 21 October 2016 |
10 February 2003 to 10 February 2003
23 March 2003 to 29 March 2003
31 March 2003 to 4 April 2003
2 June 2003 to 2 June 2003
22 June 2003 to 28 June 2003
Tuesday 28th January 2003 | |||
---|---|---|---|
14:00 to 15:00 |
James Knowles CALTECH (California Institute of Technology) |
Room 1 | |
16:00 to 17:00 |
Nabil Bedjaoui Université de Picardie Jules Verne |
Room 1 |
Wednesday 29th January 2003 | |||
---|---|---|---|
14:00 to 15:00 |
James Knowles CALTECH (California Institute of Technology) |
Room 1 | |
16:00 to 17:00 |
Nabil Bedjaoui Université de Picardie Jules Verne |
Room 1 |
Thursday 30th January 2003 | |||
---|---|---|---|
14:00 to 15:00 |
James Knowles CALTECH (California Institute of Technology) |
Room 1 | |
16:00 to 17:00 |
Nabil Bedjaoui Université de Picardie Jules Verne |
Room 1 |
Monday 3rd February 2003 | |||
---|---|---|---|
11:00 to 12:00 |
Andrea Corli |
Room 1 |
Wednesday 5th February 2003 | |||
---|---|---|---|
11:00 to 12:00 | Room 1 |
Thursday 6th February 2003 | |||
---|---|---|---|
11:00 to 12:00 | Room 1 |
Friday 14th February 2003 | |||
---|---|---|---|
11:00 to 12:00 |
Arkadi Berezovski |
Room 2 |
Tuesday 18th February 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Fumioki Asakura Osaka Electro-Communication University |
Room 1 |
Monday 3rd March 2003 | |||
---|---|---|---|
14:00 to 15:00 |
Konstantina Trivisa University of Maryland, College Park |
Room 1 |
Thursday 6th March 2003 | |||
---|---|---|---|
11:00 to 12:00 | Room 1 |
Monday 10th March 2003 | |||
---|---|---|---|
11:00 to 12:00 | Room 1 |
Tuesday 11th March 2003 | |||
---|---|---|---|
10:00 to 11:00 |
Pierangelo Marcati |
Room 1 | |
11:30 to 12:30 | Room 1 | ||
14:30 to 15:30 |
Constantine Dafermos Brown University |
Room 1 |
Wednesday 12th March 2003 | |||
---|---|---|---|
10:00 to 11:00 | Room 1 | ||
11:30 to 12:30 |
Constantine Dafermos Brown University |
Room 1 | |
14:30 to 15:30 |
Pierangelo Marcati |
Room 1 |
Thursday 13th March 2003 | |||
---|---|---|---|
10:00 to 11:00 |
Constantine Dafermos Brown University |
Room 1 | |
11:30 to 12:30 |
Pierangelo Marcati |
Room 1 | |
14:30 to 15:30 | Room 1 |
Wednesday 19th March 2003 | |||
---|---|---|---|
10:00 to 11:00 |
Alberto Bressan SISSA |
Room 1 | |
11:30 to 12:30 |
Tai-Ping Liu Stanford University |
Room 1 | |
14:30 to 15:30 |
Well-posedness theory for hyperbolic systems of conservation laws |
Room 1 |
Thursday 20th March 2003 | |||
---|---|---|---|
10:00 to 11:00 |
Tai-Ping Liu Stanford University |
Room 1 | |
11:30 to 12:30 |
Well-posedness theory for hyperbolic systems of conservation laws |
Room 1 | |
14:30 to 15:30 |
Alberto Bressan SISSA |
Room 1 |
Friday 21st March 2003 | |||
---|---|---|---|
10:00 to 11:00 |
Well-posedness theory for hyperbolic systems of conservation laws |
Room 1 | |
11:30 to 12:30 |
Alberto Bressan SISSA |
Room 1 | |
14:30 to 15:30 |
Tai-Ping Liu Stanford University |
Room 1 |
Thursday 10th April 2003 | |||
---|---|---|---|
10:00 to 11:00 |
Sergei Godunov Sobolev Institute of Mathematics |
Room 2 |
Tuesday 15th April 2003 | |||
---|---|---|---|
10:00 to 11:00 |
Peter Lax Courant Institute of Mathematical Sciences |
Room 2 | |
11:30 to 12:30 |
Cathleen Morawetz Courant Institute of Mathematical Sciences |
Room 2 | |
14:00 to 15:00 |
Barbara Lee Keyfitz University of Houston |
Room 2 | |
15:30 to 16:30 |
Shuxing Chen Fudan University |
Room 2 |
Wednesday 16th April 2003 | |||
---|---|---|---|
10:00 to 11:00 |
Peter Lax Courant Institute of Mathematical Sciences |
Room 2 | |
11:30 to 12:30 |
Cathleen Morawetz Courant Institute of Mathematical Sciences |
Room 2 | |
14:00 to 15:00 |
Barbara Lee Keyfitz University of Houston |
Room 2 | |
15:30 to 16:30 |
Shuxing Chen Fudan University |
Room 2 |
Thursday 17th April 2003 | |||
---|---|---|---|
10:00 to 11:00 |
Peter Lax Courant Institute of Mathematical Sciences |
Room 2 | |
11:30 to 12:30 |
Cathleen Morawetz Courant Institute of Mathematical Sciences |
Room 2 | |
14:00 to 15:00 |
Barbara Lee Keyfitz University of Houston |
Room 2 | |
15:30 to 16:30 |
Shuxing Chen Fudan University |
Room 2 |
Monday 28th April 2003 | |||
---|---|---|---|
09:30 to 11:00 |
Eleuterio Toro University of Trento |
Room 1 | |
11:30 to 13:00 |
Randall LeVeque University of Washington |
Room 1 | |
14:00 to 15:30 |
Randall LeVeque University of Washington |
Room 1 | |
16:00 to 17:30 |
Eleuterio Toro University of Trento |
Room 2 |
Tuesday 29th April 2003 | |||
---|---|---|---|
09:30 to 11:00 |
Eleuterio Toro University of Trento |
Room 1 | |
11:30 to 13:00 |
Eleuterio Toro University of Trento |
Room 1 | |
14:00 to 15:30 |
Randall LeVeque University of Washington |
Room 1 | |
16:00 to 17:30 |
Randall LeVeque University of Washington |
Room 1 |
Wednesday 30th April 2003 | |||
---|---|---|---|
09:30 to 11:00 |
Chi-Wang Shu Brown University |
Room 1 | |
11:30 to 13:00 |
Chi-Wang Shu Brown University |
Room 1 |
Thursday 1st May 2003 | |||
---|---|---|---|
09:30 to 11:00 |
Chi-Wang Shu Brown University |
Room 1 | |
11:30 to 13:00 |
Eleuterio Toro University of Trento |
Room 1 | |
14:00 to 15:30 |
Chi-Wang Shu Brown University |
Room 1 | |
16:00 to 17:30 |
Chi-Wang Shu Brown University |
Room 1 |
Friday 2nd May 2003 | |||
---|---|---|---|
09:30 to 11:00 |
Chi-Wang Shu Brown University |
Room 1 | |
11:30 to 13:00 |
Eleuterio Toro University of Trento |
Room 1 | |
14:00 to 15:30 |
Randall LeVeque University of Washington |
Room 1 |
Tuesday 6th May 2003 | |||
---|---|---|---|
14:00 to 15:00 | Room 1 |
Wednesday 7th May 2003 | |||
---|---|---|---|
10:00 to 11:00 | Room 1 | ||
11:30 to 12:30 | Room 1 |
Tuesday 20th May 2003 | |||
---|---|---|---|
10:00 to 11:00 |
Ash Kapila |
Room 1 | |
11:30 to 12:30 |
Ash Kapila |
Room 1 |
Wednesday 21st May 2003 | |||
---|---|---|---|
10:00 to 11:00 |
Eugene Romenski |
Room 1 | |
11:30 to 12:30 |
Walter Craig McMaster University |
Room 1 |
Friday 23rd May 2003 | |||
---|---|---|---|
10:00 to 11:00 |
Shi Jin University of Wisconsin-Madison |
Room 1 |
Tuesday 27th May 2003 | |||
---|---|---|---|
09:55 to 10:00 |
Eleuterio Toro University of Trento |
Room 1 | |
10:00 to 11:00 |
Peter Sweby University of Reading |
Room 1 | |
11:30 to 12:30 |
Hp-adaptive finite element approximations of hyperbolic problems |
Room 1 | |
14:00 to 15:00 |
John Bell |
Room 1 | |
15:30 to 16:30 |
High-order time discretisation methods for hyperbolic systems with relaxation |
Room 1 | |
16:30 to 17:30 |
Gabriella Puppo |
Room 1 |
Wednesday 28th May 2003 | |||
---|---|---|---|
10:00 to 11:00 |
Chi-Wang Shu Brown University |
Room 1 | |
11:30 to 12:30 |
Eleuterio Toro University of Trento |
Room 1 | |
14:00 to 15:00 |
Giovanni Russo |
Room 1 | |
15:30 to 16:30 |
Vladimir Titarev University of Trento |
Room 1 | |
16:30 to 17:30 |
Discretisation of mean field vortex density models in Type II superconductors |
Room 1 |
Thursday 29th May 2003 | |||
---|---|---|---|
10:00 to 11:00 |
Martin Kaeser Munich University of Technology |
Room 1 | |
11:30 to 12:30 |
Michael Dumbser |
Room 1 | |
14:00 to 15:00 |
Miloslav Feistauer Charles University, Prague |
Room 1 | |
15:30 to 16:30 |
Yoko Takakura |
Room 1 | |
16:30 to 17:30 |
Knut-Andreas Lie SINTEF Applied Mathematics |
Room 1 |
Friday 30th May 2003 | |||
---|---|---|---|
10:00 to 11:00 |
Discontinuous Galerkin finite element methods for hyperbolic PDE's |
Room 1 | |
11:30 to 12:30 |
Matthew Hubbard Aalborg Universitet |
Room 1 | |
14:00 to 15:00 |
Limiters for very high-order schemes - part of the problem or part of the solution? |
Room 1 | |
15:30 to 16:30 |
Nikolaos Nikiforakis University of Cambridge |
Room 1 | |
16:30 to 17:30 |
Marshall Slemrod |
Room 1 |
Wednesday 4th June 2003 | |||
---|---|---|---|
10:00 to 11:00 | Room 1 |
Tuesday 10th June 2003 | |||
---|---|---|---|
11:00 to 12:00 | Room 1 |
Wednesday 11th June 2003 | |||
---|---|---|---|
11:00 to 12:00 | Room 1 |
Thursday 12th June 2003 | |||
---|---|---|---|
11:00 to 12:00 | Room 1 |
Friday 13th June 2003 | |||
---|---|---|---|
11:00 to 12:00 |
Sijue Wu University of Maryland, College Park |
Room 1 |
Tuesday 17th June 2003 | |||
---|---|---|---|
11:00 to 12:00 |
Blake Temple University of California |
Room 1 |
Wednesday 18th June 2003 | |||
---|---|---|---|
11:00 to 12:00 |
Blake Temple University of California |
Room 1 |
Thursday 19th June 2003 | |||
---|---|---|---|
11:00 to 12:00 |
Blake Temple University of California |
Room 1 |
Tuesday 1st July 2003 | |||
---|---|---|---|
11:00 to 12:00 |
Asymptotic behavior of the Riemann tensor in a class of vacuum Einstein spacetimes |
Room 1 |
Wednesday 2nd July 2003 | |||
---|---|---|---|
11:00 to 12:00 |
Helmut Friedrich |
Room 1 |
Thursday 3rd July 2003 | |||
---|---|---|---|
11:00 to 12:00 |
Seiji Ukai |
Room 1 |
Friday 4th July 2003 | |||
---|---|---|---|
10:00 to 11:00 |
Jinghua Wang Chinese Academy of Sciences |
Room 1 | |
11:00 to 12:00 | Room 1 |
Monday 7th July 2003 | |||
---|---|---|---|
11:00 to 12:00 |
Felix Finster |
Room 1 |
Tuesday 8th July 2003 | |||
---|---|---|---|
11:00 to 12:00 |
Felix Finster |
Room 1 |
Wednesday 9th July 2003 | |||
---|---|---|---|
11:00 to 12:00 |
Felix Finster |
Room 1 | |
14:00 to 15:00 |
Eleuterio Toro University of Trento |
Room 1 |
Thursday 10th July 2003 | |||
---|---|---|---|
11:00 to 12:00 |
Felix Finster |
Room 1 | |
14:00 to 15:00 |
Yuri Trakhinin University of Hull |
Room 1 |
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