Publications by Eleuterio F. TORO (Updated: 15/10/2015)

Transcription

1 Publications by Eleuterio F. TORO (Updated: 15/10/2015) 2015 References [1] Eleuterio F. Toro, Cristóbal Castro and Bok Jick Lee. A novel numerical flux for the 3D Euler equations with general equation of state. Journal of Computational Physics. Vol. 303, pages 80-94, [2] Eleuterio F. Toro. Brain Venous Haemodynamics, Neurological Diseases and Mathematical Modelling. A Review. Applied Mathematics and Computation. Available online 10 August doi: /j.amc [3] Eleuterio F. Toro, Lucas O. Müller, Mariapaola Cristini, Erica Menegatti and Paolo Zamboni. Impact of Jugular Vein Valve Function on Cerebral Venous Haemodynamics. Current Neurovascular Research. Vol. 12, No. 4, pages , DOI: / [4] Eleuterio F. Toro and Gino I. Montecinos. Implicit, semi-analytical solution of the generalized Riemann problem for stiff hyperbolic balance laws. Journal of Computational Physics. Available online 28 September [5] L. O. Müller, E. F. Toro, E. M. Haacke and D. Utriainen. Impact of CCSVI on cerebral haemodynamics: a mathematical study. Phlebology Jun 2. pii: [Epub ahead of print]. [6] Jun-Bo Cheng, Eleuterio F. Toro, Song Jiang, Ming Yu. A second-order cell-centered Lagrangian scheme for one-dimensional elastic-plastic problems Computers and Fluids. Vol. 122, pp , [7] Dinshaw S. Balsara, Gino Montecinos, and Eleuterio F. Toro. Exploring Various Flux Vector Splittings for the Magnetohydrodynamic System. Journal of Computational Physics. Submitted [8] Paolo Zamboni, Mirko Tessari, Mariapaola Cristini, Andrea Ciorba, Lucas Omar Müller, Maria Elena Vannini, Erica Menegatti, Manuela Mazzoli, Stefano Pelucchi, Antonio Pastore, Eleuterio F. Toro. Jugular valve function and petrosal sinuses pressure. A computational model applied to sudden sensorineural hearing loss. BMC Neuroscience. Submitted [9] Francesco Sisini, Eleuterio Toro, Mauro Gambaccini and Paolo Zamboni. The oscillating component of the internal jugular vein flow: the overlooked element of the cerebral circulation. Behavioural Neurology. Special Issue on: Blood and Fluid Circulation of the Brain: The Neurovascular Component of Neurodegeneration. Submitted [10] Eleuterio F. Toro and Gino I. Montecinos. Advection-diffusion-reaction equations: hyperbolisation and high-order ADER discretizations. SIAM Journal of Scientific Computing. Vol. 36, No. 5, pp. A2423-A2457,

2 [11] Gino I. Montecinos, Lucas O. Müller and Eleuterio F. Toro. Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes. Journal of Computational Physics. Volume 266, Pages , 1 June, [12] Lucas O. Müller and Eleuterio F. Toro. Enhanced global mathematical model for studying cerebral venous blood flow. Journal of Biomechanics. Volume 47, Issue 13, 17 October 2014, Pages Also published as Pre-print. Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK. [13] Lucas O. Müller and Eleuterio F. Toro. A global multi-scale model for the human circulation with emphasis on the venous system. International Journal for Numerical Methods in Biomedical Engineering. Volume 30, Issue 7, pages , July [14] Laura Facchini, Alberto Bellin and Eleuterio F. Toro. A model for filtration and macromolecule transport across capillary walls. Microvascular Research. Vol. 94, pp [15] Alfonso Caiazzo, Gino I. Montecinos, Lucas O. Müller, E. Mark Haacke and Eleuterio F. Toro. Computational Haemodynamics in Stenotic Internal Jugular Veins. Journal of Mathematical Biology. Vol. 7, No 4, pp , doi: /s Also published on line as pre-print: WIAS Institute, Berlin, Germany. [16] Arturo Hidalgo, Lourdes Tello and Eleuterio F. Toro. Numerical and analytical study of an atherosclerosis inflammatory disease model. Journal of Mathematical Biology. Vol. 68, Pages , DOI /s [17] Cristobal E. Castro and Eleuterio F. Toro. Roe-type Riemann solver for general hyperbolic systems. International Journal for Numerical Methods in Fluids. Article first published online: 1 April DOI: /fld [18] Gino I. Montecinos and Eleuterio F. Toro. Reformulations for general advection-diffusionreaction equations and locally implicit ADER schemes. Journal of Computational Physics. Volume 275, 15 October, Pages , [19] Han E, Warneche G, Toro E F and Siviglia A. On Riemann solutions to weakly hyperbolic systems: Part 1. Modelling subcritical flows in arteries. SIAM Journal of Mathematical Analysis (Submitted). Also published as Pre-print. Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK. NPA-NI [20] Han E, Warneche G, Toro E F and Siviglia A. On Riemann solutions to weakly hyperbolic systems: Part 2. Modelling supercritical flows in arteries. SIAM Journal of Mathematical Analysis. (Submitted). Also published as Pre-print. Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK. NPA-NI [21] Lucas O. Müller and Eleuterio F. Toro. Well-balanced high-order solver for blood flow in networks of vessels with variable properties. International Journal for Numerical Methods in Biomedical Engineering. Vol. 29, pages , DOI: /cnm

3 [22] Lucas O. Müller, Carlos Parés, Eleuterio F. Toro. Well-balanced high-order numerical schemes for one-dimensional blood flow in vessels with varying mechanical properties. Journal of Computational Physics. Volume 242, pages 53-85, [23] E F Toro and A Siviglia. Flow in collapsible tubes with discontinuous mechanical properties: mathematical model and exact solutions. Communications in Computational Physics. Vol. 13, Number 2, pp , Feb [24] Bok Jik Lee, Eleuterio F. Toro, Cristobal E. Castro and Nikos Nikiforakis. Adaptive Oshertype scheme for the Euler equations with highly nonlinear equations of state. Journal of Computational Physics. Vol. 246, Pages , August [25] Jun-Bo Cheng, Eleuterio F. Toro, Song Jiang and Wei-Jun Tang. A sub-cell WENO reconstruction method for spatial derivatives in the ADER scheme. Journal of Computational Physics. Volume 251, Pages 53-80, 15 October [26] Annunziato Siviglia, Guglielmo Stecca, Davide Vanzo, Guido Zolezzi, Eleuterio F. Toro and Marco Tubino. Numerical modelling of two-dimensional morphodynamics with applications to river bars and bifurcations. Advances in Water Resources. Volume 52, Pages , [27] Riadh Ata, Sara Pavan, Sofiane Khelladi and Eleuterio F. Toro. A Weighted Average Flux (WAF) scheme applied to shallow water equations for real-life applications. Advances in Water Resources. Volume 62, Pages , [28] E F Toro. The Riemann problem in computational science. Numerical Methods for Hyperbolic Equations: Theory and Applications. An international conference to honour Professor E. F. Toro. M. E. Vázquez-Cendón, A. Hidalgo, P. García-Navarro and L. Cea (editors). Pages CRC Press, Taylor-Francis Group, ISBN , [29] L Facchini, A Bellin and E F Toro. A simple model of filtration and macromolecule transport through microvascular walls. Numerical Methods for Hyperbolic Equations: Theory and Applications. An international conference to honour Professor E. F. Toro. M. E. Vázquez-Cendón, A. Hidalgo, P. García-Navarro and L. Cea (editors). Pages CRC Press, Taylor-Francis Group, ISBN , [30] L O Müller, G I Montecinos and E F Toro. Some issues in modelling venous haemodynamics. Numerical Methods for Hyperbolic Equations: Theory and Applications. An international conference to honour Professor E. F. Toro. M. E. Vázquez-Cendón, A. Hidalgo, P. García-Navarro and L. Cea (editors). Pages CRC Press, Taylor-Francis Group, ISBN , [31] M E Vázquez-Cendón and E F Toro. A framework for flux-vector splitting schemes. Numerical Methods for Hyperbolic Equations: Theory and Applications. An international conference to honour Professor E. F. Toro. M. E. Vázquez-Cendón, A. Hidalgo, P. García-Navarro and L. Cea (editors). Pages CRC Press, Taylor-Francis Group, ISBN , [32] G Montecinos and E F Toro. Solver for the Generalized Riemann Problem for Balance Laws with Stiff Source Terms: the Scalar Case. Hyperbolic Problems. Theory, Numerics and Applications. Tatsien Li and Song Jian (Editors). Vol. 2, Pages Higher Education Press

4 [33] G Stecca, E F Toro and A Siviglia A finite volume upwind-biased centred scheme for hyperbolic systems of conservation laws. Applications to shallow water equations. Communications in Computational Physics. Vol. 12, No. 4, pp ; doi: /cicp a October [34] E F Toro and M E Vázquez-Cendón. Flux splitting schemes for the Euler equations. Computers and Fluids. Vol. 70, Pages 1-12, [35] G I Montecinos, C E Castro, M Dumbser and E F Toro. Comparison of solvers for the generalized Riemann problem for hyperbolic systems with source terms. Journal of Computational Physics. Vol. 231, pp , DOI: [36] C E Castro, E F Toro and M Kaeser. ADER scheme on unstructured meshes for shallow water: simulation of tsunami waves. Geophysics Journal International. Vol. 189, pages , doi: /j X x [37] C E Zambra, M Dumbser, E F Toro and N O Moraga. A novel numerical method of high order accuracy for flow in unsatured porous media. International Journal for Numerical Methods in Engineering. Vol. 89, No 2, pp , [38] V Casulli, M Dumbser and E F Toro. Semi-implicit numerical modelling of axially symmetric flows in compliant arterial systems. International Journal for Numerical Methods in Biomedical Engineering. Volume 28, Issue 2, pages , DOI: /cnm [39] E F Toro. High-order accuracy: monotonicity and non-linear methods. Lecture Notes on Numerical Methods for Hyperbolic Equations: Short Course Book. Elena Vázquez-Cendón (Editor). Pages CRC Press, Taylor and Francis Group, [40] E F Toro and A Siviglia. Simplified blood flow model with discontinuous vessel properties: analysis and exact solutions. Modelling Physiological Flows Series: Modelling, Simulation and Applications. Editors: D. Ambrosi, A. Quarteroni and G. Rozza. Springer-Verlag, 2011, ISBN [41] Alberto Canestrelli and Eleuterio F. Toro. Restoration of the contact surface in FORCEtype centred schemes I: homogeneous two-dimensional shallow water equations. Advances in Water Resources. Volume 47, Pages 88-99, [42] Alberto Canestrelli and Eleuterio F. Toro. Restoration of the contact surface in FORCEtype centred schemes II: non conservative one- and two-layer two-dimensional shallow water equations. Advances in Water Resources. Volume 47, Pages 76-87, [43] Carlos E. Zambra, Michael Dumbser, Eleuterio F. Toro, Nelson Moraga. Finite Volume Schemes of High Order of Accuracy in Time and Space for Flows in Unsaturated Porous Media. International Journal for Numerical Methods in Engineering. Volume 89, Issue 2, pages , [44] B Tian, E F Toro and C E Castro. A path-conservative method for a five-equation model of two-phase flow with an HLLC-type Riemann solver. Computers and Fluids, Vol. 46, pp ,

5 [45] Michael Dumbser and Eleuterio Toro. A simple extension of the Osher Riemann solver to general non-conservative hyperbolic systems. Journal of Scientific Computing. Volume 48, Pages 70-88, [46] Michael Dumbser and Eleuterio Toro. On universal Osher-type schemes for general nonlinear hyperbolic conservation laws. Communications in Computational Physics. Vol. 10, pp , [47] E F Toro and M Dumbser. Reformulated Osher-type Riemann solver. Computational Fluid Dynamics Springer-Verlag, Alexander Kuzmin (editor), 2011, pp [48] S A Tokareva and E F Toro. HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow. Computational Fluid Dynamics Springer-Verlag, Alexander Kuzmin (editor), 2011, pp [49] G Stecca, E F Toro and A Siviglia Upwind-biased FORCE schemes on unstructured meshes with applications to free-surface shallow flows. In Proceedings of the First European IAHR Congress, Edinburgh, UK, May [50] E F Toro. Riemann solvers in aerospace engineering. In Encyclopedia of Aerospace Engineering. R Blockey and W Shyy (Editors). John Wiley and Sons Ltd, Chichester, UK, pp , [51] E F Toro and M Dumbser. ADER schemes for time-dependent PDEs: review and applications to astrophysics. Keynote invited paper. Numerical Modelling of Space Plasma Flows. ASTRONUM N V Pogorelov, E Audit and G P Zank (editors). Astronomical Society of the Pacific Conference Series, Vol. 429, pages , [52] S A Tokareva and E F Toro. HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow. Journal of Computational Physics. Vol. 229, pages , [53] Guglielmo Stecca, Annunziato Siviglia and Eleuterio Toro. Upwind-biased FORCE schemes with applications to free-surface shallow flows. Journal of Computational Physics. Vol. 229, pages , [54] Eugene Romenski, Dimitris Drikakis and Eleuterio Toro. Conservative models and numerical methods for compressible two-phase flow. Journal of Scientific Computing. Vol. 42, pages 68-95, DOI /s y. [55] Giovanna Grosso, Matteo Antuono and Eleuterio Toro. The Riemann problem for the dispersive non-linear shallow water equations. Communications in Computational Physics. Vol. 7, No. 1, pp , doi: /cicp [56] A M Canestrelli, M Dumbser, A Siviglia and E F Toro. Well-balanced high-order centred schemes on unstructured meshes for multi-dimensional non-conservative hyperbolic systems. Advances in Water Resources. Vol. 33, No. 3, pages [57] Michael Dumbser, Manuel Castro, Carlos Parés, Eleuterio Toro and Arturo Hidalgo. FORCE schemes on unstructured meshes II: non-conservative hyperbolic systems. Computer Methods in Applied Mechanics and Engineering. Vol. 199, Issue 9-12, pages , [58] A Ferrari, L Fraccarollo, M Dumbser, E F Toro and A Armanini. Three-dimensional flow evolution after a dam break. Journal of Fluid Mechanics. Vol. 663, pp ,

6 [59] A Ferrari, M Dumbser, E F Toro and A Armanini. A new 3D parallel SPH scheme for freesurface flows. In book High Performance Computing on Vector Systems. Springer- Verlag, pages , [60] Eleuterio Toro. Riemann solvers and numerical methods for fluid dynamics. A practical introduction. Third edition. Springer-Verlag, Berlin Heidelberg, BOOK (724 pages). ISBN , [61] E F Toro, A Hidalgo and M Dumbser. FORCE schemes on unstructured meshes I: conservative hyperbolic systems. Journal of Computational Physics. Vol. 228, pages , [62] Eleuterio Toro and Arturo Hidalgo. ADER finite volume schemes for non-linear reactiondiffusion equations. Applied Numerical Mathematics. Vol. 59, pages , [63] C E Castro, M Kaeser and E F Toro. Space-time adaptive numerical methods for geophysical applications. Phil. Trans. Royal Soc. London A. Vol. 367, pages , doi: /rsta [64] Alberto Canestrelli, Annunziato Siviglia, Michael Dumbser and Eleuterio Toro. Well-balanced high-order centred schemes for non-conservative hyperbolic systems. Applications to shallow water equations with fixed and mobile bed. Advances in Water Resources. Vol. 32, pages , [65] A Siviglia and E F Toro. The WAF method and splitting procedures for simulating hydro and thermal peaking waves in open channel flows. Journal of Hydraulic Engineering. Vol. 135, No 8, pages , [66] A Ferrari, M Dumbser, E F Toro and A Armanini. A new 3D parallel SPH scheme for free-surface flows. Computers and Fluids. Vol. 38, pages , [67] M Dumbser, M Castro, C Parés and E F Toro. ADER schemes on ustructured meshes for nonconservative hyperbolic systems: applications to geophysical flows. Computers and Fluids. Vol. 38, Number 9, pages , [68] M Castro, A Pardo, C Parés and E F Toro. On some fast well-balanced first order solvers for nonconservative systems. Mathematics of Computation. Vol. 79, pages , [69] A Canestrelli, A Siviglia, M Dumbser and E F Toro. Well-balanced high-order centred schemes for non-conservative hyperbolic systems. Applications to shallow water equations with fixed and mobile bed. Isaac Newton Institute for Mathematical Sciences Preprint Series NI09023-NPA. University of Cambridge, UK. Available in pdf format at: [70] C E Castro and E F Toro. Solvers for the high-order Riemann problem for hyperbolic balance laws. Journal of Computational Physics. Vol. 227, pages , [71] M Dumbser, C Enaux and E F Toro. Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws. Journal of Computational Physics. Vol. 227, pages ,

7 [72] M Dumbser, D Balsara, E F Toro and C D Munz.A unified framework for the construction of one-step finite-volume and discontinuous Galerkin schemes on unstructured meshes. Journal of Computational Physics. Vol. 227, pages , [73] G Vignoli, V A Titarev and E F Toro. ADER schemes for the shallow water equations in channel with irregular bottom elevation. Journal of Computational Physics. Vol. 227, pages , [74] R Bernetti, V A Titarev and E F Toro. Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry. Journal of Computational Physics. Vol. 227, pages , [75] V A Titarev, E Romenski and E F Toro. MUSTA-type upwind fluxes for non-linear elasticity. International Journal for Numerical Methods in Engineering. Vol. 73, pages , [76] A Ferrari, M Dumbser, E F Toro and A Armanini. A new stable SPH scheme in Lagrangian coordinates. Communications in Computational Physics. Vol. 4, No 2, pages , [77] E F Toro. Computational methods for hyperbolic equations. Invited contribution. In Jets from Young Stars: Numerical MHD and Instabilities. Springer Lecture Notes in Physics. Vol S Massaglia, G Bodo, A Mignone and P Rossi (editors) [78] E F Toro and C E Castro. The derivative Riemann problem for the Baer-Nunziato equations. In Hyperbolic Problems: Theory, Numerics and Applications. Vol. 1, pages , Sylvie Benzoni-Gavage and Denis Serre (editors). Springer, [79] G Russo, V A Titarev and E F Toro. ADER-Runge-Kutta schemes for conservation laws in one space dimension. In Hyperbolic Problems: Theory, Numerics and Applications. Vol. 1, pages , Sylvie Benzoni-Gavage and Denis Serre (editors). Springer, [80] E F Toro, A Hidalgo and M Dumbser. FORCE schemes on unstructured meshes I: conservative hyperbolic systems. Isaac Newton Institute for Mathematical Sciences Preprint Series NI09005-NPA. University of Cambridge, UK. Available in pdf format at: [81] Manuel Castro, Carlos Parés, Eleuterio Toro, Michael Dumbser and Arturo Hidalgo. FORCE schemes on unstructured meshes II: non-conservative hyperbolic systems. Isaac Newton Institute for Mathematical Sciences Preprint Series NI09017-MPA. University of Cambridge, UK. Available in pdf format at: [82] M J Castro, C Parés, A Pardo and E F Toro. Well-balanced high-order MUSTA schemes for non-conservative hyperbolic systems. Numerical Mathematics and Advanced Applications, Springer, pages , [83] E F Toro and P Garcia-Navarro. Godunov-type methods for free-surface shallow flows: a review. Journal of Hydraulic Research. Vol. 45, pages , [84] M Dumbser, M Kaeser, V A Titarev and E F Toro. Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for non-linear hyperbolic systems. Journal of Computational Physics. Vol. 221, pages ,

8 [85] M Dumbser, M Kaeser and E F Toro. An arbitrary high order discontinuous Galerkin method for elastic waves on unstructured meshes V: local time stepping and p-adaptivity. Geophysical Journal International. Vol. 171, pages , [86] V A Titarev and E F Toro. Analysis of ADER and ADER-WAF schemes. IMA Journal of Numerical Analysis. Vol. 27, pages , [87] D Zeidan, A Slaouti, E Romenski and E F Toro. Numerical solution for hyperbolic conservative two-phase flow equations. International Journal of Computational Methods. Vol. 4, No. 2, pages , [88] D Zeidan, E Romenski, A Slaouti and E. F. Toro. Numerical study of wave propagation in compressible two-phase flow. International Journal for Numerical Methods in Fluids. Vol. 54, pages , [89] E Romensky, A D Resnyanski and E F Toro. Conservative hyperbolic formulation for compressible two-phase flow with different phase pressures and temperatures. Quarterly of Applied Mathematics. Vol. 6, pages , [90] E F Toro, C E Castro and M Dumbser. ADER high-order schemes for evolutionary PDEs: a brief review. Keynote invited paper. In Proceedings of Japanese Conference on Computational Fluid Dynamics. Tokyo, Japan, June Aiso H (editor). [91] E F Toro, M Dumbser, V A Titarev and M Kaeser. The derivative Riemann problem: the basis for high order ADER schemes. In Proceedings of ECCOMAS CFD 2006 Conference. Egmond aan Zee, The Netherlands. September 5-8, P Wesseling, E Onate and J Periaux (editors) [92] G Vignoli, E F Toro and V A Titarev. ADER schemes for the shallow water equations in channels with irregular bottom elevation. In Proceedings of ECCOMAS CFD 2006 Conference. Egmond aan Zee, The Netherlands. September 5-8, P Wesseling, E Onate and J Periaux (editors) [93] V A Titarev, E Romenski and E F Toro. Development and application of generalized MUSTA schemes. In Proceedings of ECCOMAS CFD 2006 Conference. Egmond aan Zee, The Netherlands. September 5-8, P Wesseling, E Onate and J Periaux (editors) [94] V A Titarev and E F Toro. ADER schemes for hyperbolic conservation laws with reactive terms. In Proceedings of ECCOMAS CFD 2006 Conference. Egmond aan Zee, The Netherlands. September 5-8, P Wesseling, E Onate and J Periaux (editors) [95] C E Castro and E F Toro. New numerical approaches to multiphase flow modelling. In Advancements in Energetic Materials and Chemical Propulsion. 6-ISICP. Redding, Connecticut, USA. K K Kuo and J D Rivera (editors). ISBN/ISSN: , 2007 [96] C E Castro and E F Toro. ADER DG and FV schemes for shallow water flows. In Proceedings 14th European Conference on Mathematics for Industry. ECMI, Madrid, Spain, July, [97] A Ferrari, M Dumbser, E F Toro and A Armanini. A new stable and consistent version of the SPH method in Lagrangian coordinates. In Proceedings of SPHERID: 2nd International Workshop. Vol. 1, pages Caica Ediciones, ISBN: ,

9 [98] E F Toro and A Hidalgo. ADER finite volume schemes for non-linear diffusion-reaction equations. Isaac Newton Institute for Mathematical Sciences Preprint Series NI07011-NPA. University of Cambridge, UK. Available in pdf format at: [99] M Dumbser, D Balsara, C D Munz and E F Toro. A unified framework for the construction of one-step finite-volume and discontinuous Galerkin schemes on unstructured meshes. Isaac Newton Institute for Mathematical Sciences Preprint Series NI07084-NPA. University of Cambridge, UK. Available in pdf format at: [100] M Dumbser, C Enaux and E F Toro. Explicit finite volume schemes of arbitrary high order of accuracy for hyperbolic systems with stiff source terms. Isaac Newton Institute for Mathematical Sciences Preprint Series NI07007-NPA. University of Cambridge, UK. Available in pdf format at: [101] E F Toro and V A Titarev. Derivative Riemann solvers for systems of conservation laws and ADER methods. Journal of Computational Physics. Vol. 212, pages , [102] E F Toro. Riemann solvers with evolved initial conditions. International Journal for Numerical Methods in Fluids. Vol. 52, pages , [103] E F Toro. A multi-stage numerical flux. Applied Numerical Mathematics. Vol. 56, pages , [104] E F Toro and V A Titarev. MUSTA fluxes for systems of conservation laws. Journal of Computational Physics. Vol. 216, pages , [105] E Romenski, V A Titarev and E F Toro. Perfectly matched layers with high rate damping for hyperbolic systems. International Journal of Computational Fluid Dynamics. Vol. 15, pages , [106] C E Castro and E F Toro. A Riemann solver and upwind methods for a two-phase flow model in non-conservative form. International Journal for Numerical Methods in Fluids. Vol. 60, pages , [107] E F Toro, M Kaeser, M Dumbser and C E Castro. ADER shock-capturing schemes and geophysical applications. Invited inaugural lecture of the 25th International Symposium on Shock Waves, Bangalore, India, July, In Shock Waves: Proceedings of the 25th International Symposium on Shock Waves-ISSW25, July 17-22, 2005, Bangalore, India. G Jagadeesh, E Arunan and K P J Reddy (editors). Universities Press (India). Distributed by Orient Longman. ISBN: , [108] R Bernetti, V A Titarev and E F Toro. Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry. Isaac Newton Institute for Mathematical Sciences Preprint Series NI06020-NPA. University of Cambridge, UK. Available in pdf format at: [109] G Vignoli, V A Titarev and E F Toro. ADER schemes for the shallow water equations in channel with irregular bottom elevation. Isaac Newton Institute for Mathematical Sciences Preprint Series NI06051-NPA. University of Cambridge, UK. Available in pdf format at: 9

10 [110] C E Castro, E F Toro. Alternative solvers for the derivative Riemann problem for hyperbolic balance laws. Isaac Newton Institute for Mathematical Sciences Preprint Series NI06053-NPA. University of Cambridge, UK. Available in pdf format at: [111] E F Toro and V A Titarev.ADER schemes for scalar hyperbolic conservation laws with source terms in three space dimensions. Journal of Computational Physics. Vol. 202, pages , [112] V A Titarev and E F Toro. ADER schemes for three-dimensional non-linear hyperbolic systems. Journal of Computational Physics. Vol. 204, pages , [113] V A Titarev and E F Toro. ENO and WENO schemes based on upwind and centred TVD fluxes. Computers and Fluids. Vol. 3, pages , [114] V A Titarev and E F Toro. MUSTA schemes for multi-dimensional hyperbolic systems: analysis and improvements. International Journal for Numerical Methods in Fluids. Vol. 49, pages , [115] H. Städtke, G. Franchello, B. Worth, U. Graf, P. Romstedt, A. Kumbaro, J. García-Cascales, H. Paillere, H. Deconinck, M. Ricchiuto, B. Smith, F. De Cachard, E. F. Toro, E. Romenski, S. Mimouni Advanced three-dimensional two-phase flow simulation tools for application to reactor safety (ASTAR). Nuclear Engineering Design. Vol. 235, pages , [116] E F Toro and V A Titarev. TVD fluxes for the high-order ADER schemes. Journal of Scientific Computing. Vol. 24, pages , [117] E F Toro. Conventional and derivative Riemann solvers. In Finite Volumes for Complex Applications IV. Problems and Perspectives. Benkhaldoun, Ouazar and Raghay (editors). Pages Hermes Science P. London, Great Britain. [118] E F Toro, V A Titarev and M Dumbser. Recent developments on high-order numerical methods for the shallow water equations. Pages , Catellon, Spain. J Castello and V Martinez (editors), [119] E F Toro Riemann solvers with evolved initial conditions. Isaac Newton Institute for Mathematical Sciences Preprint Series NI05003-NPA. University of Cambridge, UK. Available in pdf format at: [120] E F Toro, V A Titarev. Derivative Riemann solvers for systems of conservation laws and ADER methods. Isaac Newton Institute for Mathematical Sciences Preprint Series NI05004-NPA. University of Cambridge, UK. Available in pdf format at: [121] C E Castro and E F Toro. A Riemann solver and upwind methods for a two-phase flow model in non-conservative form. Isaac Newton Institute for Mathematical Sciences Preprint Series NI05001-NPA. University of Cambridge, UK. Available in pdf format at: [122] C Woodley, D Finbow, V A Titarev and E F Toro. Two-Dimensional modelling of mortar internal ballistics. Proceedings of the 22nd International Symposium on Ballistics. Pages Vancouver, Canada, 14-18th November William Flis and Brian Scott (editors). DEStech Publications, Inc. 10

11 [123] C Woodley, S J Billett, C Lowe and E F Toro. The FHIBS Internal Ballistics Code. Proceedings of the 22nd International Symposium on Ballistics. Pages Vancouver, Canada, 14-18th November William Flis and Brian Scott (editors). DEStech Publications, Inc [124] G Q Chen and E F Toro. Centred schemes for non-linear hyperbolic equations. Journal of Hyperbolic Equations. Vol. 1, pages , [125] V A Titarev and E F Toro. Finite volume WENO schemes for three-dimensional conservation laws. Journal of Computational Physics. Vol. 201, pages , [126] E Romenski and E F Toro. Hyperbolicity and one-dimensional waves in compressible twophase flow models. Shock Waves. Vol. 13, pages , [127] E Romenski and E F Toro. Compressible two-phase flows: two-pressure models and numerical methods. Computational Fluid Dynamics Journal. Vol. 13, pages , [128] E F Toro. Conservative hyperbolic model for two-phase flow and one-dimensional waves. In Proceedings of the 10th International Conference on Hyperbolic Problems: Theory, Numerics, Applications. Osaka, Japan, [129] E F Toro. MUSTA: A multi-stage numerical flux. Isaac Newton Institute for Mathematical Sciences Preprint Series NI04008-NPA. University of Cambridge, UK. Available in pdf format at: [130] E Romenski, E Resnyanski and E F Toro. Conservative hyperbolic model for compressible twophase flow with different phase pressures and temperatures, Isaac Newton Institute for Mathematical Sciences Preprint Series NI04034-NPA. University of Cambridge, UK. Available in pdf format at: [131] V A Titarev and E F Toro. MUSTA schemes for multi-dimensional hyperbolic systems: analysis and improvements. Isaac Newton Institute for Mathematical Sciences Preprint Series NI04032-NPA. University of Cambridge, UK. Available in pdf format at: [132] V A Titarev and E F Toro. ADER schemes for shallow water equations with pollutant transport. In Proceedings of the XXIX Convegno di Idraulica e Costruzioni Idrauliche. Trento, Italy, 7-10 September, Vol. 1, pages , [133] E F Toro and A Siviglia. PRICE: primitive centred schemes for hyperbolic systems. International Journal for Numerical Methods in Fluids. Vol. 42, pages , [134] M J Ivings, E F Toro and D M Webber. Numerical schemes for 2D shallow layer equations including dry fronts. International Journal of Computational Fluid Dynamics. Vol. 12, No 1, pages 41-52, [135] V A Titarev and E F Toro. High order ADER schemes for scalar advection-diffusion-reaction equations. International Journal of Computational Fluid Dynamics. Vol. 12, No 1, pages 1-6,

12 [136] Y Takakura and E F Toro. Arbitrarily accurate non-oscillatory schemes for non-linear scalar conservation laws with source terms II. In Proceedings of the 2nd International Conference on Computational Fluid Dynamics. Springer-Verlag. S Armfield, P Morgan and K Srinivas (editors), pages , [137] G Q Chen and E F Toro. Centred schemes for non-linear hyperbolic equations. Isaac Newton Institute for Mathematical Sciences Preprint Series NI NPA. University of Cambridge, UK. In pdf format available in: [138] E F Toro and V A Titarev. TVD fluxes for the high-order ADER schemes. Isaac Newton Institute for Mathematical Sciences Preprint Series NI03011-NPA. University of Cambridge, UK. In pdf format available at: [139] E F Toro. Multi-stage predictor-corrector fluxes for hyperbolic equations. Isaac Newton Institute for Mathematical Sciences Preprint Series NI NPA. University of Cambridge, UK. Also available in pdf format at: [140] E I Romenski and E F Toro. Shock waves in compressible two-phase flows. Isaac Newton Institute for Mathematical Sciences Preprint Series NI03026-NPA. University of Cambridge, UK. In pdf format available at: [141] E I Romenski, D Zeidan, A Slaouti and E F Toro. Hyperbolic conservative model for compressible two-phase flow. Isaac Newton Institute for Mathematical Sciences Preprint Series NI03022-NPA. University of Cambridge, UK. Available in pdf format at: [142] V A Titarev and E F Toro. ENO and WENO schemes based on upwind and centred TVD fluxes. Isaac Newton Institute for Mathematical Sciences Preprint Series NI03052-NPA. University of Cambridge, UK. In pdf format available at: [143] V A Titarev and E F Toro. Finite volume WENO schemes for three-dimensional conservation laws. Isaac Newton Institute for Mathematical Sciences Preprint Series NI03057-NPA. University of Cambridge, UK. Available in pdf format at: [144] V A Titarev and E F Toro. ADER schemes for scalar hyperbolic conservation laws in three space dimensions. Isaac Newton Institute for Mathematical Sciences Preprint Series NI03063-NPA. University of Cambridge, UK. Available in pdf format at: [145] R Bernetti, E F Toro and M Brocchini. An operator-splitting method for long waves. In Proceedings of Long Waves Symposium. Tessaloniki, Greece. Vol. 1, pages 49-56, [146] F De Cachard, H Deconinck, G Franchello, U Graf, A Kumbaro, S Mimouni, H Paillere, E Romenski, P Romstedt, JM Rovarche, B Smith, H Staedtke, EF Toro, B Worth. The ASTAR Project-Status and Perspective. In Proc. 10th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-10), pp 5-9,

13 [147] E F Toro and V A Titarev. Solution of the generalised Riemann problem for advectionreaction equations. Proceedings of the Royal Society of London. Series A. Vol. 458, pages , [148] V A Titarev and E F Toro. ADER: arbitrary high order Godunov approach. Journal of Scientific Computing. Vol. 17, pages , [149] T Schwartzkopff, C D Munz and E F Toro. ADER: High-order approach for linear hyperbolic systems in 2D. Journal of Scientific Computing. Vol. 17, pages , [150] Y Takakura and E F Toro. Arbitrarily accurate non-oscillatory schemes for a non-linear conservation law. International Journal of Computational Fluid Dynamics. Vol. 11, No 1, pages 7-18, [151] E F Toro. Anomalies of conservative methods: analysis, numerical evidence and possible cures. International Journal of Computational Fluid Dynamics. Vol. 11, pages , [152] M E Vázquez-Cendón and E F Toro. Exact solution of some hyperbolic systems with sources terms. Proceedings of the Royal Society of London. Series A. Vol. 459, pages , [153] D Zeidan, E F Toro and A Slaouti. Numerical simulation of compressible two-phase flow model based on the Riemann problem. In Proceedings of the 2nd Annual European Multiphase Systems Institute Meeting and the 40th European Two-Phase Flow Group Meeting. Stockholm. June 10-13, [154] D Zeidan, E F Toro and A Slaouti. On the Riemann problem for a hyperbolic two-phase flow model. In Proceedings ACOMEN Conference. Belgium. May 28-31, [155] E F Toro. Shock-capturing methods for free-surface shallow flows. Wiley and Sons Ltd. (UK). Chichester, New York. First Edition (book, 309 pages). ISBN: [156] T Schwartzkopff, C S Munz, E F Toro and R C Millington. ADER-2D: a high-order approach for linear hyperbolic systems in 2D. In Proceedings of ECCOMAS Computational Fluid Dynamics Conference. Swansea, Wales 4-7 September, [157] T Schwartzkopff, C D Munz, E F Toro and R C Millington. The ADER approach in 2D. In Discrete Modelling and Discrete Algorithms in Continuum Mechanics. Berlin, Germany. T Sonar (editor). Vol. 1, pages , [158] B Zanutigh, A Lamberti and E F Toro. Exact solution of the Riemann problem for a powerlaw channel section. In Proceedings of ECCOMAS Computational Fluid Dynamics Conference. Swansea, UK, September 4-7, [159] B Zanutigh, A Lamberti and E F Toro. Weighted average flux method including source terms for a power-law channel. In Proceedings of ECCOMAS Computational Fluid Dynamics Conference. Swansea, UK, September 4-7, [160] E F Toro and V A Titarev. Very-high order Godunov-type schemes for non-linear scalar conservation laws. In Proceedings of ECCOMAS Computational Fluid Dynamics Conference. Swansea, UK, September 4-7,

14 [161] E F Toro and R C Millington. The ADER approach to linear advection. In Proceedings of ECCOMAS Computational Fluid Dynamics Conference. Swansea, UK, September 4-7, [162] E F Toro and V A Titarev. The ADER approach for nonlinear advection-diffusion-reaction equations. In Proceedings of 8th National Conference on Computational Fluid Dynamics. Keynote Lecture. In E-Land and Taiwan, August 18-20, [163] E F Toro, R C Millington and L A M Nejad. Towards very high-order Godunov schemes. In Godunov Methods: Theory and Applications. Edited Review. E F Toro (Editor). Kluwer Academic/Plenum Publishers. Conference in Honour of S K Godunov. Vol. 1, pages New York, Boston and London, [164] E F Toro and M E Vázquez-Cendón. Model hyperbolic systems with source terms: exact and numerical solutions. In Godunov Methods: Theory and Applications. Edited Review. E F Toro (Editor). Kluwer Academic/Plenum Publishers. Conference in Honour of S K Godunov. Vol. 1, pages New York, Boston and London, [165] W Hu and E F Toro. Centred unsplit finite volume schemes for hyperbolic conservation laws. In Godunov Methods: Theory and Applications. Edited Review. E F Toro (Editor). Kluwer Academic/Plenum Publishers. Conference in Honour of S K Godunov. Vol. 1, pages New York, Boston and London, [166] E F Toro. (editor) Godunov Methods: Theory and Applications. Book (1077 pages) containing 97 refereed articles from conference in honour of S K Godunov, University of Oxford, UK, October Kluwer Academic/Plenum Publishers. New York, Boston and London [167] E F Toro and S J Billett. Centred TVD schemes for hyperbolic conservation laws. IMA Journal of Numerical Analysis. Vol. 20, pages 47-79, [168] E F Toro. The Lax-Wendroff method. In Encyclopaedia of Mathematics. Invited Article, Supplement II. pages , [169] E F Toro. NUMERICA: a library of source codes for teaching, research and applications. HYPER-WAT. Methods for the shallow water equations. Numeritek Limited UK. ISBN: Software [170] E F Toro. Riemann solvers and numerical methods for fluid dynamics: A practical introduction. Second edition. Springer-Verlag. Berlin Heidelberg Book (624 pages). ISBN: , [171] E F Toro, M Olim and K Takayama. Unusual increase in tsunami wave amplitude at the Oshukiri island: Mach reflection of shallow water waves. In Proceedings of 22th International Symposium on Shock Waves. G J Ball, R Hillier and G T Roberts (editors). Published by the University of Southampton, UK. Vol. 2, pages , [172] E F Toro. NUMERICA: A Library of Source Codes for Teaching, Research and Applications. HYPER-EUL. Methods for the Euler equations. Numeritek Limited UK. ISBN Software

15 [173] E F Toro. NUMERICA: A Library of Source Codes for Teaching, Research and Applications. HYPER-LIN. Methods for model hyperbolic equations. Numeritek Limited UK. ISBN Software [174] M J Ivings, D M Causon and E F Toro. On Riemann solvers for compressible liquids. International Journal for Numerical Methods in Fluids. Vol. 28, pages , [175] S J Billett and E F Toro. Unsplit WAF-type schemes for three-dimensional hyperbolic conservation laws. In Numerical Methods for Wave Propagation. Kluwer Academic Publishers. E F Toro and J F Clarke (editors). Pages , [176] E F Toro. Primitive, conservative and adaptive schemes for hyperbolic conservation laws. In Numerical Methods for Wave Propagation. Kluwer Academic Publishers. E F Toro and J F Clarke (editors). Pages , [177] E F Toro. Anomalies of conservative methods: the shear wave problem. In Proceedings International Conference on Numerical Methods for Fluid Dynamics VI. M J Baines (editor). Pages , [178] E F Toro, R C Millington and L A M Nejad. Primitive upwind numerical methods for hyperbolic partial differential equations. In Sixteenth International Conference on Numerical Methods for Fluid Dynamics. Lecture Notes in Physics. C H Bruneau (editor). Springer-Verlag, [179] E F Toro and J F Clarke. Numerical methods for wave propagation. Book containing 14 refereed research articles (385 pages). Kluwer Academic Publishers. London, [180] E F Toro. Riemann solvers and numerical methods for fluid dynamics: A practical introduction. First edition. Springer-Verlag. Berlin Heidelberg New York Book (592 pages). ISBN: [181] S J Billett and E F Toro. On the accuracy and stability of explicit schemes for multidimensional linear homogeneous advection equations. Journal of Computational Physics. Vol. 131, pages , [182] S J Billett and E F Toro. On WAF-type schemes for multidimensional hyperbolic conservation laws. Journal of Computational Physics. Vol. 130, pages 1-24, [183] E F Toro and S J Billett. A unified Riemann-problem based extension of the Warming-Beam and Lax-Wendroff schemes. IMA Journal of Numerical Analysis. Vol. 17, pages , [184] E P Boden and E F Toro. A combined CHIMERA-AMR technique for computing hyperbolic PDEs. In Proceedings of the Fifth Annual Conference of the CFD Society of Canada. Pages , [185] E P Boden and E F Toro. Centred TVD schemes for hyperbolic conservation laws. Technical Report. MMU Department of Mathematics and Physics Manchester Metropolitan University, UK [186] E F Toro. On two Glimm-related schemes for hyperbolic conservation laws. In Proceedings of the Fifth Annual Conference of the CFD Society of Canada. Pages ,

16 [187] E F Toro. Exact and approximate Riemann solvers for the artificial compressibility equations. Technical report. MMU Department of Mathematics and Physics Manchester Metropolitan University. UK [188] J Shi and E F Toro. Fully-discrete high-order shock-capturing numerical schemes. International Journal for Numerical Methods in Fluids. Vol. 23, pages , [189] J Shi and E F Toro. Fully discrete high resolution schemes for hyperbolic conservation laws. International Journal for Numerical Methods in Fluids. Vol. 23, pages , [190] E F Toro, S J Billett and E P Boden. Advanced modelling techniques for propulsion systems. In Proceedings of Conference on Energetic Materials and Propulsion Technology. Salisbury, Australia. April 18-19, [191] E F Toro. On Glimm-related schemes for conservation laws. Technical Report. Department of Mathematics and Physics. Manchester Metropolitan University, UK [192] S J Billett and E F Toro. Implementing a three-dimensional finite volume WAF-type scheme for the Euler equations. In Proceedings of ECCOMAS. Vol. 96, pages Paris, September 9-13, [193] M J Ivings, D M Causon and E F Toro. Riemann solvers for compressible water. In Proceedings of ECCOMAS. Vol. 96, pages Paris, September 9-13, [194] L Fraccarollo and E F Toro. Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problems. Journal of Hydraulic Research. Vol. 33, pages , [195] E F Toro. Direct Riemann solvers for the time dependent Euler equations. Shock Waves. Vol. 5, pages 75-80, [196] W Speares and E F Toro. An adaptive gridding approach to the computation of reactive twophase flows in two dimensions. In Proceedings of 19th International Symposium on Shock Waves. Brun and Dumitrescu (editors). Springer, Vol. 3, pages , [197] S J Billett and E F Toro. TVD limiter functions for multidimensional schemes. In Proceedings of 6th International Symposium on Computational Fluid Dynamics. Lake Tahoe, Nevada, USA. September 4-8, [198] P Batten, C Lambert, R Saunders, D M Causon and E F Toro. A temporal refinement algorithm for unstructured mesh methods. In Proceedings of ICFD Conference on Numerical Methods for Fluid Dynamics. Oxford University, April 3-6, [199] N Nikiforakis and E F Toro. Evaluation of the WAF method for kinematic and dynamic atmospheric modelling problems. In Proceedings of ICFD Conference on Numerical Methods for Fluid Dynamics. Oxford University, April 3-6, [200] J Shi and E F Toro. A new approach for steady incompressible flows. In Proceedings of 9th International Conference on Numerical Methods in Laminar and Turbulent Flow. Atlanta, USA. July 10-14,

17 [201] E F Toro. Some IVPs for which conservative methods fail miserably. In Proceedings of 6th International Symposium on Computational Fluid Dynamics. Lake Tahoe, Nevada, USA. September 4-8, [202] E F Toro. On adaptive primitive-conservative schemes for conservation laws. In Proceedings of 6th International Symposium on Computational Fluid Dynamics. Lake Tahoe, Nevada, USA. September 4-8, [203] S J Billett and E F Toro. Numerical methods for overlapping grids and moving boundaries. In Proceedings of 6th International Symposium on Computational Fluid Dynamics. Lake Tahoe, Nevada, USA. September 4-8, [204] E F Toro, W Heilig and M Jochims. A numerical and experimental study of blast wave phenomena in channels. In Proceedings of 19th International Symposium on Shock Waves. Brun and Dumitrescu (editors). Vol. 4, pages Springer, [205] E F Toro. Multi-dimensional WAF-type schemes for conservation laws. In Proceedings of 1st Asian Computational Fluid Dynamics Conference. Vol. 1, pages Hong Kong, January 16-19, [206] C Lowe, J F Clarke and E F Toro. Numerical methods for propellant systems. In Proceedings of 1st Asian Computational Fluid Dynamics Conference. Vol. 2, pages Hong Kong, January 16-19, [207] J Shi and E F Toro. A family of fully discrete high-order TVD methods for hyperbolic conservation laws. In Proceedings of 1st Asian Computational Fluid Dynamics Conference. Vol. 3, pages Hong Kong, January 16-19, [208] E F Toro. MUSCL-type primitive variable schemes. Technical Report. Department of Mathematics and Physics. Manchester Metropolitan University. Manchester, UK [209] E F Toro, M Spruce and W Speares. Restoration of the contact surface in the Harten-Lax-van Leer Riemann solver. Shock Waves. Vol. 4, pages 25-34, [210] A Chakraborty and E F Toro. Development of an approximate Riemann solver for the steady supersonic Euler equations. The Aeronautical Journal. Vol. 98, pages , [211] L. Fraccarollo and E F Toro. Experimental and numerical analysis for two-dimensional dambreak type-problems. Technical report IDR 2. Dipartimento di Ingegneria Civile ed Ambientale. Universita degli Studi di Trento. Trento, Italia [212] K Takayama, Y Miura, M Olim, T Saito and E F Toro. Mach reflection of water waves in conjunction with tsunami at the Okushiri Island. In Proceedings of Japanese Symposium on Shock Waves. (In Japanese), pages January 20-22, [213] E F Toro. Defects of conservative approaches and adaptive primitive-conservative schemes for computing solutions to hyperbolic conservation laws. Technical report. Department of Mathematics and Physics. Manchester Metropolitan University. Manchester, UK. December,

18 [214] C C Chou and E F Toro. A linearised Riemann solver for the steady supersonic Euler equations. International Journal for Numerical Methods in Fluids. Vol. 16, pages , [215] J F Clarke, S Karni, J J Quirk, L G Simmons, P L Roe and E F Toro. Numerical computation of two-dimensional, unsteady detonation waves in high energy solids. Journal of Computational Physics. Vol. 106, pages , [216] L Fraccarollo and E F Toro. A shock-capturing computational method for two-dimensional dam break type problems. In Proceedings of the 5th International Symposium on Computational Fluid Dynamics. Published by the Japan Society of Computational Fluid Dynamics. Daiguji (Editor). Pages , [217] E F Toro and S J Billett. A unified Riemann-problem based extension of the Warming-Beam and Lax-Wendroff schemes. In Proceedings of the 5th International Symposium on Computational Fluid Dynamics. Published by the Japan Society of Computational Fluid Dynamics. Daiguji (Editor). Pages , [218] E F Toro and S J Billett. A unified extension of the Warming-Beam and Lax-Wendroff schemes. Technical report CoA Department of Aerospace Science, College of Aeronautics, Cranfield Institute of Technology. UK. February, [219] E F Toro. Riemann solvers: Linearisations and adaptation. In Numerical Methods for Fluid Dynamics IV. Oxford University Press. M J Baines and K W Morton (Editors). Pages , [220] E F Toro. Multi-dimensional WAF-type schemes for model conservation laws. Technical report CoA Department of Aerospace Science, College of Aeronautics, Cranfield Institute of Technology. UK [221] J Shi and E F Toro. Fully discrete arbitrary-order schemes for a model hyperbolic conservation law. Technical report CoA Department of Aerospace Science, College of Aeronautics, Cranfield Institute of Technology. UK. August, [222] J Shi and E F Toro. Fully discrete high-order TVD schemes for a scalar hyperbolic conservation law. Technical report CoA Department of Aerospace Science, College of Aeronautics, Cranfield Institute of Technology. UK. August, [223] E F Toro. Riemann problems and the WAF method for solving the two dimensional shallow water equations. Philosophical Transactions of the Royal Society of London Series A: Physical Sciences and Engineering. Vol. 338, pages 43-68, [224] E F Toro. The Weighted Average Flux method applied to the Euler equations. Philosophical Transactions of the Royal Society of London Series A: Physical Sciences and Engineering. Vol. 341, pages , [225] E F Toro and R E Brown. The WAF method and splitting procedures for viscous, shocked flows. In Proceedings of the 18th International Symposium on Shock Waves. Tohoku University, Sendai, Japan. Springer-Verlag. K Takayama (Editor). Vol. 2, pages ,