Nonlinear hyperbolic waves in phase dynamics and astrophysics

Programme theme

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.

Programme Outline

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

Preprints

Title	Year	Programme
TVD fluxes for the high-order ADER schemes Authors: Vladimir Titarev, Eleuterio Toro Download PDF	2002	NPA	21 October 2016
Hyperbolicity of the non-linear models of Maxwell's equations Authors: D Serre Download PDF	2002	NPA	21 October 2016
Nonclassical Riemann solvers with nucleation Authors: M Shearer, PG Lefloch Download PDF	2002	NPA	21 October 2016
Steady transonic shocks and free boundary problems in infinite cylinders for the Euler equations Authors: M Feldman, Gui-Qiang Chen Download PDF	2002	NPA	21 October 2016
Advances in turbulent flow computations using high-resolution methods Authors: D Drikakis Download PDF	2002	NPA	21 October 2016
Existence and asymptotic behavior of multi-dimensional quantum hydrodynamic model for semiconductors Authors: Pierangelo Marcati, Tong Li Download PDF	2002	NPA	21 October 2016
Hyperbolic conservative model for compressible two-phase flow Authors: Dia Zeidan, A Slaouti, ET Al, Eugene Romenski Download PDF	2002	NPA	21 October 2016
The Riemann problem for fluid flows in a nozzle with discontinuous cross-section Authors: Mai Duc Thanh, PG Lefloch Download PDF	2002	NPA	21 October 2016
The Riemann problem for a class of resonant hyperbolic systems of balance laws Authors: PG Lefloch, Paola Goatin Download PDF	2002	NPA	21 October 2016
Shock waves in compressible two-phase flows Authors: Eleuterio Toro, Eugene Romenski Download PDF	2002	NPA	21 October 2016
Towards fully conservative numerical methods for the nonlinear model Boltzmann equation Authors: Vladimir Titarev Download PDF	2002	NPA	21 October 2016
Multi-stage predictor-corrector fluxes for hyperbolic equations Authors: Eleuterio Toro Download PDF	2002	NPA	21 October 2016
Centred schemes for nonlinear hyperbolic equations Authors: Gui-Qiang Chen, Eleuterio Toro Download PDF	2002	NPA	21 October 2016
Eno and Weno schemes based on upwind centred TVD fluxes Authors: Eleuterio Toro, Vladimir Titarev Download PDF	2002	NPA	21 October 2016
Free boundary problems and transonic shocks for the Euler equations in unbounded domains Authors: M Feldman, Gui-Qiang Chen Download PDF	2002	NPA	21 October 2016
Finite-volume weno schemes for three-dimensional conservation laws Authors: Eleuterio Toro, Vladimir Titarev Download PDF	2002	NPA	21 October 2016
ADER schemes for scalar hyperbolic conservation laws in three space dimensions Authors: Vladimir Titarev, Eleuterio Toro Download PDF	2002	NPA	21 October 2016
Shock-turbulence interaction an exhaustively classifying linearized approach Authors: LF Dinu Download PDF	2002	NPA	21 October 2016
A geometric level-set formulation of a plasma-sheath interface Authors: M Feldman, S-Y Ha, Marshall Slemrod Download PDF	2002	NPA	21 October 2016
ADER schemes for three-dimensional nonlinear hyperbolic systems Authors: Eleuterio Toro, Vladimir Titarev Download PDF	2002	NPA	21 October 2016
MUSTA: A multi-stage numerical flux Authors: Eleuterio Toro Download PDF	2002	NPA	21 October 2016
Compressible two-phase flows: Two-pressure models and numerical methods Authors: Eleuterio Toro, Eugene Romenski Download PDF	2002	NPA	21 October 2016
MUSTA schemes for multi-dimensional hyperbolic systems: analysis and improvements Authors: Eleuterio Toro, Vladimir Titarev Download PDF	2002	NPA	21 October 2016
MUSTA schemes for systems of conservation laws Authors: Vladimir Titarev, Eleuterio Toro Download PDF	2002	NPA	21 October 2016
Conservative hyperbolic model for compressible two-phase flow with different phase pressures and temperatures Authors: Eleuterio Toro, AD Resnyansky, Eugene Romenski Download PDF	2002	NPA	21 October 2016
A Riemann solver and upwind methods for a two-phase flow model in non-conservative form Authors: Eleuterio Toro, CE Castro Download PDF	2002	NPA	21 October 2016
Riemann solvers with evolved initial conditions Authors: Eleuterio Toro Download PDF	2002	NPA	21 October 2016
Derivative Riemann solvers for systems of conservation laws and ADER methods Authors: Eleuterio Toro, Vladimir Titarev Download PDF	2002	NPA	21 October 2016
Exact Riemann problem solutions and upwind fluxes for nonlinear elasticity Authors: Eugene Romenski, Eleuterio Toro, Vladimir Titarev Download PDF	2002	NPA	21 October 2016
Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry Authors: Eleuterio Toro, R Bernetti, Vladimir Titarev Download PDF	2002	NPA	21 October 2016
Multidimensional wave-wave regular interactions and genuine nonlinearity: some remarks Authors: LF Dinu Download PDF	2002	NPA	21 October 2016
ADER schemes for the shallow water equations in channel with irregular bottom elevation Authors: Vladimir Titarev, Eleuterio Toro, G Vignoli Download PDF	2002	NPA	21 October 2016
Alternative solvers for the derivative Riemann problem for hyperbolic balance laws Authors: Eleuterio Toro, CE Castro Download PDF	2002	NPA	21 October 2016
Injectivity radius of Lorentzian manifolds Authors: PG Lefloch, Gui-Qiang Chen Download PDF	2002	NPA	21 October 2016
Entropy solutions of the Eular equations for isothermal relativistic fluids Authors: M Yamazaki, PG Lefloch Download PDF	2002	NPA	21 October 2016
Explicit finite volume schemes of arbitrary high order of accuracy for hyperbolic systems with stiff source terms Authors: Eleuterio Toro, Michael Dumbser, C Enaux Download PDF	2002	NPA	21 October 2016
ADER finite volume schemes for nonlinear diffusion-reaction equations Authors: Eleuterio Toro, A Hidalgo Download PDF	2002	NPA	21 October 2016
Nondegeneracy, from the prospect of wave-wave regular interactions of a gasdynamic type: some remarks Authors: MI Dinu, LF Dinu Download PDF	2002	NPA	21 October 2016
A unified framework for the construction of one-step finite-volume and discontinuous Galerkin schemes on unstructured meshes Authors: D Balsara, Michael Dumbser, C Munz, Eleuterio Toro Download PDF	2002	NPA	21 October 2016
FORCE schemes on unstructured meshes I: conservative hyperbolic systems Authors: A Hidalgo, Michael Dumbser, Eleuterio Toro Download PDF	2002	NPA	21 October 2016
Martin's "differential" approach: some classifying remarks Authors: MI Dinu, LF Dinu Download PDF	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 Download PDF	2002	NPA	21 October 2016
A global multi-scale mathematical model for the human circulation with emphasis on the venous system Authors: LO Muller, Eleuterio Toro Download PDF	2002	NPA	21 October 2016
Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes Authors: GI Montecinos, LO Muller, Eleuterio Toro Download PDF	2002	NPA	21 October 2016
Enhanced global mathematical model for studying cerebral venous blood flow Authors: LO Muller, Eleuterio Toro Download PDF	2002	NPA	21 October 2016
On Riemann solutions to weakly hyperbolic systems part 1. Modelling subcritical flows in arteries Authors: E Han, G Warnecke, Eleuterio Toro, A Siviglia Download PDF	2002	NPA	21 October 2016
On Riemann solutions to weakly hyperbolic systems part 2. Modelling subcritical flows in arteries Authors: E Han, G Warnecke, Eleuterio Toro, A Siviglia Download PDF	2002	NPA	21 October 2016

Workshops

NPAW04

Seminars

Tuesday 28th January 2003
14:00 to 15:00	James Knowles CALTECH (California Institute of Technology) Kinetic relations for continuum mechanical models of evolutionary structural transformations	Room 1
16:00 to 17:00	Nabil Bedjaoui Université de Picardie Jules Verne Kinetic relations generated by diffusive-dispersive traveling waves	Room 1

Wednesday 29th January 2003
14:00 to 15:00	James Knowles CALTECH (California Institute of Technology) Kinetic relations for continuum mechanical models of evolutionary structural transformations	Room 1
16:00 to 17:00	Nabil Bedjaoui Université de Picardie Jules Verne Kinetic relations generated by diffusive-dispersive travelling waves	Room 1

Thursday 30th January 2003
14:00 to 15:00	James Knowles CALTECH (California Institute of Technology) Kinetic relations for continuum mechanical models of evolutionary structural transformations	Room 1
16:00 to 17:00	Nabil Bedjaoui Université de Picardie Jules Verne Kinetic relations generated by diffusive-dispersive traveling waves	Room 1

Monday 3rd February 2003
11:00 to 12:00	Andrea Corli A general approach to the operator splitting method	Room 1

Wednesday 5th February 2003
11:00 to 12:00	The dynamics of thin liquid films and contact lines	Room 1

Thursday 6th February 2003
11:00 to 12:00	Dynamic aspects of nucleation phenomena	Room 1

Friday 14th February 2003
11:00 to 12:00	Arkadi Berezovski A thermomechanical model of phase-transition front propagation	Room 2

Tuesday 18th February 2003
14:00 to 15:00	Fumioki Asakura Osaka Electro-Communication University Wave-front tracking for the equations of isentropic gas dynamics	Room 1

Monday 3rd March 2003
14:00 to 15:00	Konstantina Trivisa University of Maryland, College Park On models for the dynamic combustion of compressible reacting fluids	Room 1

Thursday 6th March 2003
11:00 to 12:00	Ambipolar flows in molecular clouds: another fine mess?	Room 1

Monday 10th March 2003
11:00 to 12:00	Systems of conservation laws and congruences of lines	Room 1

Tuesday 11th March 2003
10:00 to 11:00	Pierangelo Marcati Diffusive singular limits for hyperbolic systems	Room 1
11:30 to 12:30	L1 stability of diffuse waves for conservation laws	Room 1
14:30 to 15:30	Constantine Dafermos Brown University Conservation laws: from continuum mechanics to analysis	Room 1

Wednesday 12th March 2003
10:00 to 11:00	L1 stability of diffuse waves for conservation laws	Room 1
11:30 to 12:30	Constantine Dafermos Brown University Conservation laws: from continuum mechanics to analysis	Room 1
14:30 to 15:30	Pierangelo Marcati Diffusive singular limits for hyperbolic systems	Room 1

Thursday 13th March 2003
10:00 to 11:00	Constantine Dafermos Brown University Conservation laws: from continuum mechanics to analysis	Room 1
11:30 to 12:30	Pierangelo Marcati Diffusive singular limits for hyperbolic systems	Room 1
14:30 to 15:30	L1 stability of diffuse waves for conservation laws	Room 1

Wednesday 19th March 2003
10:00 to 11:00	Alberto Bressan SISSA Vanishing viscosity solutions for systems of conservation laws	Room 1
11:30 to 12:30	Tai-Ping Liu Stanford University Boltzmann equation and Euler and Navier-Stokes equations in gas dynamics	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 Boltzmann equation and Euler and Navier-Stokes equations in gas dynamics	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 Vanishing viscosity solutions for systems of conservation laws	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 Vanishing viscosity solutions for systems of conservation laws	Room 1
14:30 to 15:30	Tai-Ping Liu Stanford University Boltzmann equation and Euler and Navier-Stokes equations in gas dynamics	Room 1

Thursday 10th April 2003
10:00 to 11:00	Sergei Godunov Sobolev Institute of Mathematics The conservation laws compatible with hyperbolic equations: chemical reaction modeling,fluid with thermodynamical model of bubble vibration	Room 2

Tuesday 15th April 2003
10:00 to 11:00	Peter Lax Courant Institute of Mathematical Sciences Zero dispersion limit	Room 2
11:30 to 12:30	Cathleen Morawetz Courant Institute of Mathematical Sciences Mixed equations in fluid dynamics	Room 2
14:00 to 15:00	Barbara Lee Keyfitz University of Houston Self-similar solutions to multidimensional conservation laws	Room 2
15:30 to 16:30	Shuxing Chen Fudan University Some recent methods for multidimensional conservation laws	Room 2

Wednesday 16th April 2003
10:00 to 11:00	Peter Lax Courant Institute of Mathematical Sciences Zero dispersion limit	Room 2
11:30 to 12:30	Cathleen Morawetz Courant Institute of Mathematical Sciences Mixed equations in fluid dynamics	Room 2
14:00 to 15:00	Barbara Lee Keyfitz University of Houston Self-similar solutions to multidimensional conservation laws	Room 2
15:30 to 16:30	Shuxing Chen Fudan University Some recent methods for multidimensional conservation laws	Room 2

Thursday 17th April 2003
10:00 to 11:00	Peter Lax Courant Institute of Mathematical Sciences Zero dispersion limit	Room 2
11:30 to 12:30	Cathleen Morawetz Courant Institute of Mathematical Sciences Mixed equations in fluid dynamics	Room 2
14:00 to 15:00	Barbara Lee Keyfitz University of Houston Self-similar solutions to multidimensional conservation laws	Room 2
15:30 to 16:30	Shuxing Chen Fudan University Some recent methods for multidimensional conservation laws	Room 2

Monday 28th April 2003
09:30 to 11:00	Eleuterio Toro University of Trento Scalar conservation laws and linear systems	Room 1
11:30 to 13:00	Randall LeVeque University of Washington Numerical methods I	Room 1
14:00 to 15:30	Randall LeVeque University of Washington Numerical methods II	Room 1
16:00 to 17:30	Eleuterio Toro University of Trento Non-linear systems	Room 2

Tuesday 29th April 2003
09:30 to 11:00	Eleuterio Toro University of Trento Godunov methods and Riemann solvers I	Room 1
11:30 to 13:00	Eleuterio Toro University of Trento Godunov methods and Riemann solvers II	Room 1
14:00 to 15:30	Randall LeVeque University of Washington Wave-propagation methods for systems	Room 1
16:00 to 17:30	Randall LeVeque University of Washington Wave-propagation methods for multidimensional problems	Room 1

Wednesday 30th April 2003
09:30 to 11:00	Chi-Wang Shu Brown University ENO and WENO methods I	Room 1
11:30 to 13:00	Chi-Wang Shu Brown University ENO and WENO methods II	Room 1

Thursday 1st May 2003
09:30 to 11:00	Chi-Wang Shu Brown University ENO and WENO methods III	Room 1
11:30 to 13:00	Eleuterio Toro University of Trento ADER methods	Room 1
14:00 to 15:30	Chi-Wang Shu Brown University Discontinuous Galerkin finite element methods I	Room 1
16:00 to 17:30	Chi-Wang Shu Brown University Discontinuous Galerkin finite element methods II	Room 1

Friday 2nd May 2003
09:30 to 11:00	Chi-Wang Shu Brown University Application to traffic flow problems	Room 1
11:30 to 13:00	Eleuterio Toro University of Trento Application to environmental flows	Room 1
14:00 to 15:30	Randall LeVeque University of Washington Application to astrophysics	Room 1

Tuesday 6th May 2003
14:00 to 15:00	Global shocks structure for random forced Burgers equation	Room 1

Wednesday 7th May 2003
10:00 to 11:00	Mechanics of fluids with internal inertia	Room 1
11:30 to 12:30	Two-fluid hyperbolic models: a variational approach	Room 1

Tuesday 20th May 2003
10:00 to 11:00	Ash Kapila Models of evolution to detonation in high-energy explosives I	Room 1
11:30 to 12:30	Ash Kapila Models of evolution to detonation in high-energy explosives II	Room 1

Wednesday 21st May 2003
10:00 to 11:00	Eugene Romenski Hyperbolic conservative model for compresible 2-phase flow	Room 1
11:30 to 12:30	Walter Craig McMaster University Travelling surface water waves	Room 1

Friday 23rd May 2003
10:00 to 11:00	Shi Jin University of Wisconsin-Madison Computation of multi-valued solutions in non-linear PDEs	Room 1

Tuesday 27th May 2003
09:55 to 10:00	Eleuterio Toro University of Trento Opening	Room 1
10:00 to 11:00	Peter Sweby University of Reading TVD schemes	Room 1
11:30 to 12:30	Hp-adaptive finite element approximations of hyperbolic problems	Room 1
14:00 to 15:00	John Bell High-order methods for reacting flows	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 Adaptive algorithms for conservation laws	Room 1

Wednesday 28th May 2003
10:00 to 11:00	Chi-Wang Shu Brown University High order WENO schemes	Room 1
11:30 to 12:30	Eleuterio Toro University of Trento The ADER approach	Room 1
14:00 to 15:00	Giovanni Russo High order central Runge-Kutta schemes for conservation laws	Room 1
15:30 to 16:30	Vladimir Titarev University of Trento A class of centred WENO schemes for multidimensional hyperbolic conservation laws	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 ADER schemes on adaptive unstructured meshes	Room 1
11:30 to 12:30	Michael Dumbser Improvements of the ADER approach for finite volume and discontinuous Galerkin schemes	Room 1
14:00 to 15:00	Miloslav Feistauer Charles University, Prague Discontinuous Galerkin methods, a natural way to obtain higher order schemes for conservation laws and compressible flow	Room 1
15:30 to 16:30	Yoko Takakura Various forms of the ADER approach	Room 1
16:30 to 17:30	Knut-Andreas Lie SINTEF Applied Mathematics New limiter based smoothness indicators and artificial compression	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 Positivity preserving finite element methods for hyperbolic problems	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 A multiple Riemann problem based approach for global atmospheric tracer-transport modelling	Room 1
16:30 to 17:30	Marshall Slemrod Initial-boundary value problems for plasmas	Room 1

Wednesday 4th June 2003
10:00 to 11:00	Numerical analysis of nematic liquid crystals	Room 1

Tuesday 10th June 2003
11:00 to 12:00	The Cauchy problem for the Einstein vacuum equations	Room 1

Wednesday 11th June 2003
11:00 to 12:00	The Cauchy problem for the Einstein vacuum equations	Room 1

Thursday 12th June 2003
11:00 to 12:00	The Cauchy problem for the Einstein vacuum equations	Room 1

Friday 13th June 2003
11:00 to 12:00	Sijue Wu University of Maryland, College Park Water waves	Room 1

Tuesday 17th June 2003
11:00 to 12:00	Blake Temple University of California Shock wave solutions of the Einstein equations	Room 1

Wednesday 18th June 2003
11:00 to 12:00	Blake Temple University of California Shock wave solutions of the Einstein equations	Room 1

Thursday 19th June 2003
11:00 to 12:00	Blake Temple University of California Shock wave solutions of the Einstein equations	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 The initial boundary value problem for Einstein's field equations	Room 1

Thursday 3rd July 2003
11:00 to 12:00	Seiji Ukai Recent topics on the half-space problem of the Boltzmann equation	Room 1

Friday 4th July 2003
10:00 to 11:00	Jinghua Wang Chinese Academy of Sciences On the large time step (LTS) schemes for hyperbolic conservation laws	Room 1
11:00 to 12:00	An example of interaction between two gasdynamic objects: a shock discontinuity and a model of turbulence	Room 1

Monday 7th July 2003
11:00 to 12:00	Felix Finster Linear hyperbolic equations in a black hole geometry	Room 1

Tuesday 8th July 2003
11:00 to 12:00	Felix Finster Linear hyperbolic equations in a black hole geometry	Room 1

Wednesday 9th July 2003
11:00 to 12:00	Felix Finster The Dirac sea and the principle of the fermionic projector	Room 1
14:00 to 15:00	Eleuterio Toro University of Trento Some developments on numerical fluxes for solving hyperbolic equations	Room 1

Thursday 10th July 2003
11:00 to 12:00	Felix Finster The Dirac sea and the principle of the fermionic projector	Room 1
14:00 to 15:00	Yuri Trakhinin University of Hull Stability of MHD shock discontinuities: recent results for fast shocks	Room 1

Nonlinear hyperbolic waves in phase dynamics and astrophysics

Organisers

Constantine Dafermos Brown University
Philippe LeFloch Centre de Physique Théorique de l’Ecole Polytechnique (CPHT)
Eleuterio Toro University of Trento

Speakers

Fumioki Asakura Osaka Electro-Communication University
Nabil Bedjaoui Université de Picardie Jules Verne
John Bell
Arkadi Berezovski
Alberto Bressan SISSA
Shuxing Chen Fudan University
Andrea Corli
Walter Craig McMaster University
Constantine Dafermos Brown University
Michael Dumbser
Miloslav Feistauer Charles University, Prague
Felix Finster
Helmut Friedrich
Sergei Godunov Sobolev Institute of Mathematics
Matthew Hubbard Aalborg Universitet
Shi Jin University of Wisconsin-Madison
Martin Kaeser Munich University of Technology
Ash Kapila
Barbara Lee Keyfitz University of Houston
James Knowles CALTECH (California Institute of Technology)
Peter Lax Courant Institute of Mathematical Sciences
Randall LeVeque University of Washington
Knut-Andreas Lie SINTEF Applied Mathematics
Tai-Ping Liu Stanford University
Pierangelo Marcati
Cathleen Morawetz Courant Institute of Mathematical Sciences
Nikolaos Nikiforakis University of Cambridge
Gabriella Puppo
Eugene Romenski
Giovanni Russo
Chi-Wang Shu Brown University
Marshall Slemrod
Peter Sweby University of Reading
Yoko Takakura
Blake Temple University of California
Vladimir Titarev University of Trento
Eleuterio Toro University of Trento
Yuri Trakhinin University of Hull
Konstantina Trivisa University of Maryland, College Park
Seiji Ukai
Jinghua Wang Chinese Academy of Sciences
Sijue Wu University of Maryland, College Park

Show All

Nonlinear hyperbolic waves in phase dynamics and astrophysics

Programme theme

Programme Outline

Preprints

TVD fluxes for the high-order ADER schemes

Hyperbolicity of the non-linear models of Maxwell's equations

Nonclassical Riemann solvers with nucleation

Steady transonic shocks and free boundary problems in infinite cylinders for the Euler equations

Advances in turbulent flow computations using high-resolution methods

Existence and asymptotic behavior of multi-dimensional quantum hydrodynamic model for semiconductors

Hyperbolic conservative model for compressible two-phase flow

The Riemann problem for fluid flows in a nozzle with discontinuous cross-section

The Riemann problem for a class of resonant hyperbolic systems of balance laws

Shock waves in compressible two-phase flows

Towards fully conservative numerical methods for the nonlinear model Boltzmann equation

Multi-stage predictor-corrector fluxes for hyperbolic equations

Centred schemes for nonlinear hyperbolic equations

Eno and Weno schemes based on upwind centred TVD fluxes

Free boundary problems and transonic shocks for the Euler equations in unbounded domains

Finite-volume weno schemes for three-dimensional conservation laws

ADER schemes for scalar hyperbolic conservation laws in three space dimensions

Shock-turbulence interaction an exhaustively classifying linearized approach

A geometric level-set formulation of a plasma-sheath interface

ADER schemes for three-dimensional nonlinear hyperbolic systems

MUSTA: A multi-stage numerical flux

Compressible two-phase flows: Two-pressure models and numerical methods

MUSTA schemes for multi-dimensional hyperbolic systems: analysis and improvements

MUSTA schemes for systems of conservation laws

Conservative hyperbolic model for compressible two-phase flow with different phase pressures and temperatures

A Riemann solver and upwind methods for a two-phase flow model in non-conservative form

Riemann solvers with evolved initial conditions

Derivative Riemann solvers for systems of conservation laws and ADER methods

Exact Riemann problem solutions and upwind fluxes for nonlinear elasticity

Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry

Multidimensional wave-wave regular interactions and genuine nonlinearity: some remarks

ADER schemes for the shallow water equations in channel with irregular bottom elevation

Alternative solvers for the derivative Riemann problem for hyperbolic balance laws

Injectivity radius of Lorentzian manifolds

Entropy solutions of the Eular equations for isothermal relativistic fluids

Explicit finite volume schemes of arbitrary high order of accuracy for hyperbolic systems with stiff source terms

ADER finite volume schemes for nonlinear diffusion-reaction equations

Nondegeneracy, from the prospect of wave-wave regular interactions of a gasdynamic type: some remarks

A unified framework for the construction of one-step finite-volume and discontinuous Galerkin schemes on unstructured meshes

FORCE schemes on unstructured meshes I: conservative hyperbolic systems

Martin's "differential" approach: some classifying remarks

Well-balanced high-order centred schemes for non-conservative hyperbolic systems. Applications to shallow water equations with fixed and mobile bed.

A global multi-scale mathematical model for the human circulation with emphasis on the venous system

Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes

Enhanced global mathematical model for studying cerebral venous blood flow

On Riemann solutions to weakly hyperbolic systems part 1. Modelling subcritical flows in arteries

On Riemann solutions to weakly hyperbolic systems part 2. Modelling subcritical flows in arteries

Workshops

Mathematical aspects of the dynamics of phase transitions

Mathematical theory of hyperbolic systems of conservation laws

Multiphase fluid flows and multi-dimensional hyperbolic problems

Recent activity on numerical relativity Hewlett Packard day

Hyperbolic models in astrophysics and cosmology

Seminars

Organisers

Speakers

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