eBook

**Numerical Methods for Hyperbolic Equations** is a collection of 49 articles presented at the International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications (Santiago de Compostela, Spain, 4-8 July 2011). The conference was organized to honour Professor Eleuterio Toro in the month of his 65th birthday. The topics covered include: • Recent advances in the numerical computation of environmental conservation laws with source terms • Multiphase flow and porous media • Numerical methods in astrophysics • Seismology and geophysics modelling • High order methods for hyperbolic conservation laws • Numerical methods for reactive flows • Finite volume and discontinous Galerkin schemes for stiff source term problems • Methods and models for biomedical problems • Numerical methods for reactive flows

The research interest of Eleuterio Toro, born in Chile on 16th July 1946, is reflected in **Numerical Methods for Hyperbolic Equations**, and focuses on: numerical methods for partial differential equations, with particular emphasis on methods for hyperbolic equations; design and application of new algorithms; hyperbolic partial differential equations as mathematical models of various types of processes; mathematical modelling and simulation of physico/chemical processes that include wave propagation phenomena; modelling of multiphase flows; application of models and methods to real problems. Eleuterio Toro received several honours and distinctions, including the honorary title OBE from Queen Elizabeth II (Buckingham Palace, London 2000); Distinguished Citizen of the City of Carahue (Chile, 2001); Life Fellow, Claire Hall, University of Cambridge (UK, 2003); Fellow of the Indian Society for Shock Wave Research (Bangalore, 2005); Doctor Honoris Causa (Universidad de Santiago de Chile, 2008); William Penney Fellow, University of Cambridge (UK, 2010); Doctor Honoris Causa (Universidad de la Frontera, Chile, 2012). Professor Toro is author of two books, editor of two books and author of more than 260 research works. In the last ten years he has been invited and keynote speaker in more than 100 scientific events. Professor Toro has held many visiting appointments round the world, which include several European countries, Japan, China and USA.

Preface

P.D. Lax

Foreword

E.F. Toro

Scientific committee

Sponsors

Thanks!

*I Invited lectures*

Santiago and the Jacobean pilgrimage at the height of the Middle Ages: Mentality and culture

F. Singul

Recent developments on the Lagrangian and remapping methods for compressible fluid flows

J. Cheng & C.-W. Shu

Coupling of nonlinear hyperbolic systems: A journey from mathematical to numerical issues

F. Coquel

Stochastic convergence and the software tool W*

R. Kaufman, T. Kaman, Y. Yu & J. Glimm

Numerical relativistic magnetohydrodynamics in dynamical spacetimes

J.Mª. Ibáñez

Initiation of reactive blast waves by external energy sources

A. Liñán, V. Kurdyumov & A.L. Sánchez

Numerical performance of discontinuous and stabilized continuous Galerkin methods for convection–diffusion problems

P.F. Antonietti & A. Quarteroni

The Riemann problem in computational science

E.F. Toro

*II Recent advances in the numerical computation of environmental conservation laws with source terms*

Finite volume discretisation of depth averaged scalar transport equations coupled to shallow water models

L. Cea & M.E. Vázquez-Cendón

Modeling of shallow curved flows with 3D unsteady RANS

B. Fraga, E. Peña & L. Cea

A finite volume/duality method for Bingham viscoplastic flow

J.M. Gallardo, E.D. Fernández-Nieto & P. Vigneaux

Accounting for building effects in shallow waters: Porosity approach, resolved approach and Manning coefficient approach. Comparison and experimental validation

M. Garrido, L. Cea, J. Puertas & M.E. Vázquez-Cendón

A numerical approximation for a climatological model with dynamic and diffusive boundary condition

A. Hidalgo & L. Tello

A large time step upwind scheme for the shallow water equations with source terms

M. Morales-Hernandez, J. Murillo, P. García-Navarro & J. Burguete

Augmented Roe’s approaches for Riemann problems including source terms: Definition of stability region with application to the shallow water equations with rigid and deformable bed

J. Murillo & P. García-Navarro

*III Multiphase flow and porous media*

Dynamics of submerged gravitational granular flows

A. Armanini, M. Dumbser, E. Nucci & M. Larcher

Three-phase Eulerian mixture formulation for the collapse of dense-suspension columns in ambient fluid

P. Bohorquez

Numerical simulation of three-dimensional transient variably saturated flow

D. Caviedes-Voullième, P. García-Navarro & J. Murillo

Modelling microbial chemo-tactic waves in saturated porous media using AMR

S.A.E.G. Falle, N.F. Dudley-Ward & M.S. Olson

Mathematical modeling of heat transfer during quenching process

D.N. Passarella, F. Varas & E.B. Martín

Conservative formulation for compressible fluid flow through elastic porous media

E. Romenski

On the coupling of compressible and incompressible fluids

V. Schleper

*IV Numerical methods in astrophysics*

Partially implicit high order Runge-Kutta methods for wave-like equations in spherical-type coordinates

I. Cordero-Carrión

Approximate Harten-Lax-van Leer Riemann solvers for relativistic magnetohydrodynamics

A. Mignone, G. Bodo & M. Ugliano

MUSTA schemes in magnetohydrodynamics and neutrino transfer: Application to core-collapse supernovae and gamma-ray bursts

M. Obergaulinger & M.Á. Aloy

*V Seismology and geophysics modelling*

IFCP Riemann solver: Application to tsunami modelling using GPUs

M.J. Castro, M. de la Asunción, J. Macías, C. Parés, E.D. Fernández-Nieto, J.M. González-Vida & T. Morales

Dispersive waves generated by an underwater landslide

D. Dutykh, D. Mitsotakis, S. Beisel & N. Shokina

Finite volume schemes for balance laws on time-dependent surfaces

J. Giesselmann & M. Wiebe

On multilayer shallow water systems

T.C. Rebollo, E.D. Fernández-Nieto & E.H. Koné

*VI High order methods for hyperbolic conservation laws*

Approximate solutions of generalized Riemann problems: The Toro-Titarev solver and the LeFloch-Raviart expansion

C.R. Goetz & A. Iske

CFL-Number-dependent TVD-Limiters

F. Kemm

Arbitrary high order schemes for transport problems

B. Latorre & P. García-Navarro

Efficient numerical solution of the model kinetic equations

V.A. Titarev

High order approximations for hyperbolic conservation laws with random initial data

S.A. Tokareva, S. Mishra & C. Schwab

*VII Finite volume and discontinous Galerkin schemes for stiff source term problems*

Some comments on the numerical approximation of hyperbolic nonconservative systems

M.L. Muñoz-Ruiz & C. Parés

An explicit discontinuous Galerkin scheme based on a Runge-Kutta predictor with application to magnetohydrodynamics

C. Altmann, G. Gassner & C.-D. Munz

*VIII Methods and models for biomedical problems*

Simulation of an epidemic model with nonlinear cross-diffusion

S. Berres & R. Ruiz-Baier

A simple model of filtration and macromolecule transport through microvascular walls

L. Facchini, A. Bellin & E.F. Toro

Some issues in modelling venous haemodynamics

L. Müller, G. Montecinos & E.F. Toro

Efficient algorithms for the solution of fluid-structure interaction problems in haemodynamic applications

M. Pozzoli, C. Vergara & F. Nobile

*IX Numerical methods for reactive flows*

On the use of moving least squares for pressure discretization in low mach number flows

X. Nogueira, I. Colominas, S. Khelladi, F. Bakir & J.-C. Chassaing

Numerical simulation of a pulverized coal jet

A. Bermúdez, J.L. Ferrín, A. Liñán & L. Saavedra

A framework for flux-vector splitting schemes

M.E. Vázquez-Cendón & E.F. Toro

*X Poster*

Extension of fourth-order non-oscillatory central schemes to sediment transport equations

A. Balaguer-Beser, M.T. Capilla & Ll. Gascón

First approach to the application of operational 4DVAR data assimilation to the regional ocean model system

M. Cobas-García, A. Gómez-Tato, C. Cotelo-Queijo, M.E. Vázquez-Cendón, P. Carracedo-García, P. Costa, B. Gómez-Hombre, J. Triñanes-Fernández & M. Ruiz-Villarreal

Changes in buoyancy-driven instabilities using a reaction-diffusion system

D.M. Escala, J. Guiu-Souto, J. Carballido-Landeira, A. Pérez-Muñuzuri & M.E. Vázquez-Cendón

A mean gradient method to solve shallow flows

J. Fe, F. Navarrina & L. Cueto-Felgueroso

Upwind schemes for non-homogeneous hyperbolic conservation laws with stationary solutions

Ll. Gascón, A. Balaguer-Beser & M.T. Capilla

Viscous fingering instabilities in reactive miscible media

J. Guiu-Souto, D.M. Escala, J. Carballido-Landeira, A. Pérez-Muñuzuri & E. Martín-Ortega

Author index