Edit Profile (opens in new tab) Toro, Eleuterio F. Compute Distance To: Compute Author ID: toro.eleuterio-f Published as: Toro, E. F.; Toro, Eleuterio F.; Toro, Eleuterio Documents Indexed: 144 Publications since 1981, including 4 Books 3 Contributions as Editor · 1 Further Contribution Biographic References: 2 Publications Co-Authors: 91 Co-Authors with 117 Joint Publications 1,234 Co-Co-Authors all top 5 Co-Authors 26 single-authored 17 Titarev, Vladimir A. 16 Dumbser, Michael 11 Montecinos, Gino I. 10 Castro, Cristóbal E. 7 Romenskii, Evgenii I. 7 Vázquez-Cendón, María Elena 6 Müller, Lucas O. 6 O’Carroll, M. J. 6 Siviglia, Annunziato 6 Tokareva, Svetlana A. 5 Hidalgo, Arturo 5 Parés Madroñal, Carlos 4 Billett, S. J. 4 Castro, Manuel J. 4 Jiang, Song 3 Armanini, Aronne 3 Busto, Saray 3 Causon, D. M. 3 Cheng, Junbo 3 Contarino, Christian 3 Ferrari, Angela 3 Munz, Claus-Dieter 2 Balsara, Dinshaw S. 2 Clarke, John F. 2 Ferrín, Jose Luis 2 Ivings, M. J. 2 Jia, Yueling 2 Käser, Martin 2 Lee, Bok Jik 2 Millington, R. C. 2 Nikiforakis, Nikolaos 2 Pardo, Alberto 2 Schwartzkopff, Thomas 2 Slaouti, A. S. 2 Speares, W. 2 Stecca, Guglielmo 2 Tang, Weijun 2 Tian, Baolin 2 Yu, Ming 2 Zeidan, Dia 1 Antuono, Matteo 1 Bellamoli, Francesca 1 Bermúdez, Alfredo 1 Bernetti, R. 1 Bertazzi, Laura 1 Berthon, Christophe 1 Billet, S. J. 1 Bonmassari, R. 1 Borsche, Raul 1 Caiazzo, Alfonso 1 Casulli, Vincenzo 1 Chen, Gui-Qiang G. 1 Chiapolino, Alexandre 1 Chou, Cheng-Chiang 1 Del Grosso, Alessia 1 Demattè, R. 1 Demidenko, Gennadiĭ Vladimirovich 1 Drikakis, Dimitris 1 Enaux, Cedric 1 Farina, Angiolo 1 Fraccarollo, Luigi 1 Fusi, Lorenzo 1 Ghitti, Beatrice 1 Grosso, Giovanna 1 Haacke, E. Mark 1 Kall, Jochen 1 Karni, Smadar 1 Le, Minh Hoang 1 Lecaros, Rodrigo 1 López-Ríos, Juan C. 1 Mikelić, Andro 1 Moraga, Nelson O. 1 Nejad, Lida A. M. 1 Ortega, Jaime H. 1 Petrella, M. 1 Quirk, James J. 1 Resnyansky, A. D. 1 Roe, Philip L. 1 Rosso, Fabio 1 Russo, Giovanni 1 Saavedra, Laura 1 Saccomandi, Giuseppe 1 Saggiorato, B. 1 Saunders, Robert M. 1 Saurel, Richard 1 Scoz, Alessia 1 Sequeira, Adélia 1 Simmonds, L. G. 1 Spilimbergo, Alessandra 1 Spiller, C. 1 Spruce, M. 1 Strocchi, M. 1 Takakura, Yoko 1 Tello, Lourdes 1 Vanzo, Davide 1 Vignoli, Giulio 1 Zambra, C. E. all top 5 Serials 35 Journal of Computational Physics 16 International Journal for Numerical Methods in Fluids 9 Communications in Computational Physics 8 Computers and Fluids 5 Applied Mathematics and Computation 5 Journal of Scientific Computing 3 IMA Journal of Numerical Analysis 3 Shock Waves 2 Journal of Mathematical Biology 2 International Journal for Numerical Methods in Engineering 2 Applied Numerical Mathematics 2 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 2 Philosophical Transactions of the Royal Society of London. Series A 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Engineering Mathematics 1 Journal of Fluid Mechanics 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Mathematics of Computation 1 Quarterly of Applied Mathematics 1 Applied Mathematics Letters 1 Applied Mathematical Modelling 1 SIAM Journal on Scientific Computing 1 International Journal of Numerical Methods for Heat & Fluid Flow 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 International Journal of Computational Methods 1 Journal of Hyperbolic Differential Equations 1 Fluid Mechanics and its Applications 1 Lecture Notes in Mathematics 1 International Journal for Numerical Methods in Biomedical Engineering 1 Communications on Applied Mathematics and Computation all top 5 Fields 110 Fluid mechanics (76-XX) 72 Numerical analysis (65-XX) 63 Partial differential equations (35-XX) 13 Biology and other natural sciences (92-XX) 9 Mechanics of deformable solids (74-XX) 4 General and overarching topics; collections (00-XX) 3 Geophysics (86-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 120 Publications have been cited 5,163 times in 2,616 Documents Cited by ▼ Year ▼ Riemann solvers and numerical methods for fluid dynamics. A practical introduction. 3rd ed. Zbl 1227.76006Toro, Eleuterio F. 618 2009 Riemann solvers and numerical methods for fluid dynamics. A practical introduction. 2nd ed. Zbl 0923.76004Toro, Eleuterio F. 455 1999 Restoration of the contact surface in the HLL-Riemann solver. Zbl 0811.76053Toro, E. F.; Spruce, M.; Speares, W. 428 1994 Riemann solvers and numerical methods for fluid dynamics. A practical introduction. Zbl 0888.76001Toro, Eleuterio F. 322 1997 Shock-capturing methods for free-surface shallow flows. Zbl 0996.76003Toro, Eleuterio F. 250 2001 A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes. Zbl 1147.65075Dumbser, Michael; Balsara, Dinshaw S.; Toro, Eleuterio F.; Munz, Claus-Dieter 234 2008 ADER: Arbitrary high-order Godunov approach. Zbl 1024.76028Titarev, V. A.; Toro, E. F. 155 2002 ADER schemes for three-dimensional non-linear hyperbolic systems. Zbl 1060.65641Titarev, V. A.; Toro, E. F. 144 2005 Finite-volume WENO schemes for three-dimensional conservation laws. Zbl 1059.65078Titarev, V. A.; Toro, E. F. 134 2004 Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems. Zbl 1124.65074Dumbser, Michael; Käser, Martin; Titarev, Vladimir A.; Toro, Eleuterio F. 134 2007 Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws. Zbl 1142.65070Dumbser, Michael; Enaux, Cedric; Toro, Eleuterio F. 127 2008 Solution of the generalized Riemann problem for advection-reaction equations. Zbl 1019.35061Toro, E. F.; Titarev, V. A. 109 2002 Towards very high order Godunov schemes. Zbl 0989.65094Toro, E. F.; Millington, R. C.; Nejad, L. A. M. 96 2001 A simple extension of the Osher Riemann solver to non-conservative hyperbolic systems. Zbl 1220.65110Dumbser, Michael; Toro, Eleuterio F. 94 2011 ADER schemes on unstructured meshes for nonconservative hyperbolic systems: applications to geophysical flows. Zbl 1177.76222Dumbser, Michael; Castro, Manuel; Parés, Carlos; Toro, Eleuterio F. 92 2009 Derivative Riemann solvers for systems of conservation laws and ader methods. Zbl 1087.65590Toro, E. F.; Titarev, V. A. 83 2006 A new 3D parallel SPH scheme for free surface flows. Zbl 1242.76270Ferrari, Angela; Dumbser, Michael; Toro, Eleuterio F.; Armanini, Aronne 79 2009 HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow. Zbl 1391.76440Tokareva, S. A.; Toro, E. F. 72 2010 On universal Osher-type schemes for general nonlinear hyperbolic conservation laws. Zbl 1373.76125Dumbser, Michael; Toro, Eleuterio F. 70 2011 FORCE schemes on unstructured meshes. II: Non-conservative hyperbolic systems. Zbl 1227.76043Dumbser, Michael; Hidalgo, Arturo; Castro, Manuel; Parés, Carlos; Toro, Eleuterio F. 64 2010 Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry. Zbl 1132.76027Bernetti, R.; Titarev, V. A.; Toro, E. F. 59 2008 ADER: A high-order approach for linear hyperbolic systems in 2D. Zbl 1022.76034Schwartzkopff, T.; Munz, C. D.; Toro, E. F. 56 2002 Flux splitting schemes for the Euler equations. Zbl 1365.76243Toro, E. F.; Vázquez-Cendón, M. E. 54 2012 ADER schemes for scalar non-linear hyperbolic conservation laws with source terms in three-space dimensions. Zbl 1061.65103Toro, E. F.; Titarev, V. A. 48 2005 Centred TVD schemes for hyperbolic conservation laws. Zbl 0943.65100Toro, E. F.; Billet, S. J. 48 2000 Solvers for the high-order Riemann problem for hyperbolic balance laws. Zbl 1148.65066Castro, C. E.; Toro, E. F. 46 2008 Riemann problems and the WAF method for solving the two-dimensional shallow water equations. Zbl 0747.76027Toro, E. F. 45 1992 FORCE schemes on unstructured meshes. I: Conservative hyperbolic systems. Zbl 1168.65377Toro, Eleuterio F.; Hidalgo, Arturo; Dumbser, Michael 41 2008 On WAF-type schemes for multidimensional hyperbolic conservation laws. Zbl 0873.65088Billett, S. J.; Toro, E. F. 38 1997 A weighted average flux method for hyperbolic conservation laws. Zbl 0674.76060Toro, E. F. 36 1989 On some fast well-balanced first order solvers for nonconservative systems. Zbl 1369.65107Castro, Manuel J.; Pardo, Alberto; Parés, Carlos; Toro, E. F. 34 2010 Well-balanced high-order numerical schemes for one-dimensional blood flow in vessels with varying mechanical properties. Zbl 1323.92066Müller, Lucas O.; Parés, Carlos; Toro, Eleuterio F. 34 2013 TVD fluxes for the high-order ADER schemes. Zbl 1096.76029Toro, E. F.; Titarev, V. A. 32 2005 Conservative hyperbolic formulation for compressible two-phase flow with different phase pressures and temperatures. Zbl 1145.35430Romenski, E.; Resnyansky, A. D.; Toro, E. F. 29 2007 WENO schemes based on upwind and centred TVD fluxes. Zbl 1134.65361Titarev, V. A.; Toro, E. F. 29 2005 Comparison of solvers for the generalized Riemann problem for hyperbolic systems with source terms. Zbl 1284.35268Montecinos, G.; Castro, C. E.; Dumbser, M.; Toro, E. F. 27 2012 Advection-diffusion-reaction equations: hyperbolization and high-order ADER discretizations. Zbl 1307.65117Toro, Eleuterio F.; Montecinos, Gino I. 26 2014 On Riemann solvers for compressible liquids. Zbl 0918.76047Ivings, M. J.; Causon, D. M.; Toro, E. F. 26 1998 Flow in collapsible tubes with discontinuous mechanical properties: mathematical model and exact solutions. Zbl 1373.76362Toro, Eleuterio F.; Siviglia, Annunziato 25 2013 MUSTA-type upwind fluxes for nonlinear elasticity. Zbl 1159.74046Titarev, V. A.; Romenski, E.; Toro, E. F. 25 2008 A path-conservative method for a five-equation model of two-phase flow with an HLLC-type Riemann solver. Zbl 1433.76166Tian, Baolin; Toro, E. F.; Castro, C. E. 24 2011 A fast Riemann solver with constant covolume applied to the random choice method. Zbl 0673.76090Toro, E. F. 23 1989 MUSTA fluxes for systems of conservation laws. Zbl 1097.65091Toro, E. F.; Titarev, V. A. 23 2006 Numerical study of wave propagation in compressible two-phase flow. Zbl 1241.76338Zeidan, D.; Romenski, E.; Slaouti, A.; Toro, E. F. 23 2007 Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes. Zbl 1323.92065Montecinos, Gino I.; Müller, Lucas O.; Toro, Eleuterio F. 22 2014 Reformulations for general advection-diffusion-reaction equations and locally implicit ADER schemes. Zbl 1349.65378Montecinos, Gino I.; Toro, Eleuterio F. 22 2014 ADER finite volume schemes for nonlinear reaction-diffusion equations. Zbl 1155.65065Toro, Eleuterio F.; Hidalgo, Arturo 21 2009 Conservative models and numerical methods for compressible two-phase flow. Zbl 1203.76095Romenski, Evgeniy; Drikakis, Dimitris; Toro, Eleuterio 20 2010 A Riemann solver and upwind methods for a two-phase flow model in non-conservative form. Zbl 1086.76046Castro, C. E.; Toro, E. F. 20 2006 ADER schemes for the shallow water equations in channel with irregular bottom elevation. Zbl 1132.76035Vignoli, G.; Titarev, V. A.; Toro, E. F. 19 2008 Numerical computation of two-dimensional unsteady detonation waves in high energy solids. Zbl 0770.76040Clarke, J. F.; Karni, S.; Quirk, J. J.; Roe, P. L.; Simmonds, L. G.; Toro, E. F. 18 1993 Semi-implicit numerical modeling of axially symmetric flows in compliant arterial systems. Zbl 1242.92019Casulli, Vincenzo; Dumbser, Michael; Toro, Eleuterio F. 17 2012 The weighted average flux method applied to the Euler equations. Zbl 0767.76043Toro, E. F. 16 1992 A sub-cell WENO reconstruction method for spatial derivatives in the ADER scheme. Zbl 1349.65279Cheng, Jun Bo; Toro, Eleuterio F.; Jiang, Song; Tang, Weijun 16 2013 A linearized Riemann solver for the time-dependent Euler equations of gas dynamics. Zbl 0825.76702Toro, E. F. 15 1991 Brain venous haemodynamics, neurological diseases and mathematical modelling. A review. Zbl 1410.76487Toro, Eleuterio F. 15 2016 A novel numerical flux for the 3D Euler equations with general equation of state. Zbl 1349.76398Toro, Eleuterio F.; Castro, Cristóbal E.; Lee, Bok Jik 15 2015 Primitive, conservative and adaptive schemes for hyperbolic conservation laws. Zbl 0958.76062Toro, E. F. 14 1998 PRICE: Primitive centred schemes for hyperbolic systems. Zbl 1078.76566Toro, E. F.; Siviglia, A. 14 2003 Numerical solution for hyperbolic conservative two-phase flow equations. Zbl 1198.76078Zeidan, D.; Slaouti, A.; Romenski, E.; Toro, E. F. 14 2007 Three-dimensional flow evolution after a dam break. Zbl 1205.76228Ferrari, A.; Fraccarollo, L.; Dumbser, M.; Toro, E. F.; Armanini, A. 14 2010 Design and analysis of ADER-type schemes for model advection-diffusion-reaction equations. Zbl 1422.65203Busto, S.; Toro, E. F.; Vázquez-Cendón, M. E. 14 2016 Space-time adaptive numerical methods for geophysical applications. Zbl 1192.86006Castro, C. E.; Käser, M.; Toro, E. F. 13 2009 Adaptive Osher-type scheme for the Euler equations with highly nonlinear equations of state. Zbl 1349.76354Lee, Bok Jik; Toro, Eleuterio F.; Castro, Cristóbal E.; Nikiforakis, Nikolaos 12 2013 Analysis of ADER and ADER-WAF schemes. Zbl 1119.65083Titarev, V. A.; Toro, E. F. 12 2007 A projection hybrid high order finite volume/finite element method for incompressible turbulent flows. Zbl 1380.76052Busto, S.; Ferrín, J. L.; Toro, E. F.; Vázquez-Cendón, M. E. 11 2018 A high-order cell-centered Lagrangian scheme for one-dimensional elastic-plastic problems. Zbl 1390.76558Cheng, Jun-Bo; Toro, Eleuterio F.; Jiang, Song; Yu, Ming; Tang, Weijun 11 2015 Hyperbolicity and one-dimensional waves in compressible two-phase flow models. Zbl 1136.76702Romenski, E.; Toro, E. F. 10 2004 Centered difference schemes for nonlinear hyperbolic equations. Zbl 1063.65076Chen, Gui-Qiang; Toro, Eleuterio F. 9 2004 Riemann solvers: Linearizations and adaption. Zbl 0801.76062Toro, E. F. 9 1993 MUSTA: a multi-stage numerical flux. Zbl 1101.65088Toro, E. F. 9 2006 Numerical and analytical study of an atherosclerosis inflammatory disease model. Zbl 1293.35343Hidalgo, A.; Tello, L.; Toro, E. F. 8 2014 Implicit, semi-analytical solution of the generalized Riemann problem for stiff hyperbolic balance laws. Zbl 1349.76399Toro, Eleuterio F.; Montecinos, Gino I. 8 2015 Junction-generalized Riemann problem for stiff hyperbolic balance laws in networks: an implicit solver and ADER schemes. Zbl 1349.76318Contarino, Christian; Toro, Eleuterio F.; Montecinos, Gino I.; Borsche, Raul; Kall, Jochen 8 2016 A new stable version of the SPH method in Lagrangian coordinates. Zbl 1364.76175Ferrari, A.; Dumbser, M.; Toro, E. F.; Armanini, A. 7 2008 Exploring various flux vector splittings for the magnetohydrodynamic system. Zbl 1349.76885Balsara, Dinshaw S.; Montecinos, Gino I.; Toro, Eleuterio F. 7 2016 A novel numerical method of high-order accuracy for flow in unsaturated porous media. Zbl 1242.76188Zambra, C. E.; Dumbser, M.; Toro, E. F.; Moraga, N. O. 6 2012 Upwind-biased FORCE schemes with applications to free-surface shallow flows. Zbl 1426.35192Stecca, Guglielmo; Siviglia, Annunziato; Toro, Eleuterio F. 6 2010 Direct Riemann solvers for the time-dependent Euler equations. Zbl 0837.76051Toro, E. F. 6 1995 Computational haemodynamics in stenotic internal jugular veins. Zbl 1350.92012Caiazzo, Alfonso; Montecinos, Gino; Müller, Lucas O.; Haacke, E. Mark; Toro, Eleuterio F. 5 2015 The ADER approach in 2D for a system of linear hyperbolic PDEs. Zbl 1028.76030Schwartzkopff, T.; Munz, C. D.; Toro, E. F.; Millington, R. C. 5 2001 MUSTA schemes for multi-dimensional hyperbolic systems: analysis and improvements. Zbl 1073.65553Titarev, V. A.; Toro, E. F. 5 2005 A second-order cell-centered Lagrangian method for two-dimensional elastic-plastic flows. Zbl 07414382Cheng, Jun-Bo; Jia, Yueling; Jiang, Song; Toro, Eleuterio F.; Yu, Ming 5 2017 On the exact solution of the Riemann problem for blood flow in human veins, including collapse. Zbl 1411.76182Spiller, C.; Toro, E. F.; Vázquez-Cendón, M. E.; Contarino, C. 4 2017 Riemann solvers with evolved initial conditions. Zbl 1108.65091Toro, E. F. 4 2006 Pollutant transport by shallow water equations on unstructured meshes: hyperbolization of the model and numerical solution via a novel flux splitting scheme. Zbl 1349.76401Vanzo, Davide; Siviglia, Annunziato; Toro, Eleuterio F. 4 2016 Solver for the generalized Riemann problem for balance laws with stiff source terms: the scalar case. Zbl 1306.65251Montecinos, Gino; Toro, Eleuterio 4 2012 Bounds for wave speeds in the Riemann problem: direct theoretical estimates. Zbl 07336663Toro, E. F.; Müller, L. O.; Siviglia, A. 4 2020 A flux splitting method for the Baer-Nunziato equations of compressible two-phase flow. Zbl 1415.76480Tokareva, S. A.; Toro, E. F. 3 2016 Viscous flux limiters. Zbl 0761.76063Toro, E. F. 3 1992 Unsplit WAF-type schemes for three-dimensional hyperbolic conservation laws. Zbl 0947.76060Billett, S. J.; Toro, E. F. 3 1998 Model hyperbolic systems with source terms: Exact and numerical solutions. Zbl 0989.65095Toro, E. F.; Vazquez-Cendon, M. E. 3 2001 A unified Riemann-problem-based extension of the Warming-Beam and Lax-Wendroff schemes. Zbl 0872.65082Toro, E. F.; Billett, S. J. 3 1997 Fully discrete high-order shock-capturing numerical schemes. Zbl 0864.76060Shi, J.; Toro, E. F. 3 1996 A numerical method for junctions in networks of shallow-water channels. Zbl 1427.76156Bellamoli, Francesca; Müller, Lucas O.; Toro, Eleuterio F. 2 2018 Lectures on hyperbolic equations and their numerical approximation. Zbl 1448.35002Toro, Eleuterio F. 2 2018 A global mathematical model for the simulation of stenoses and bypass placement in the human arterial system. Zbl 1411.76183Strocchi, M.; Contarino, C.; Zhang, Q.; Bonmassari, R.; Toro, E. F. 2 2017 A linearized Riemann solver for the steady supersonic Euler equations. Zbl 0767.76044Toro, Eleuterio F.; Chou, Cheng-Chiang 2 1993 Low-dissipation centred schemes for hyperbolic equations in conservative and non-conservative form. Zbl 1437.65119Toro, E. F.; Saggiorato, B.; Tokareva, S.; Hidalgo, A. 2 2020 An ADER-type scheme for a class of equations arising from the water-wave theory. Zbl 1390.76494Montecinos, G. I.; López-Rios, J. C.; Lecaros, R.; Ortega, J. H.; Toro, E. F. 2 2016 Bounds for wave speeds in the Riemann problem: direct theoretical estimates. Zbl 07336663Toro, E. F.; Müller, L. O.; Siviglia, A. 4 2020 Low-dissipation centred schemes for hyperbolic equations in conservative and non-conservative form. Zbl 1437.65119Toro, E. F.; Saggiorato, B.; Tokareva, S.; Hidalgo, A. 2 2020 Uncertainty quantification methodology for hyperbolic systems with application to blood flow in arteries. Zbl 1452.76130Petrella, M.; Tokareva, S.; Toro, E. F. 1 2019 A projection hybrid high order finite volume/finite element method for incompressible turbulent flows. Zbl 1380.76052Busto, S.; Ferrín, J. L.; Toro, E. F.; Vázquez-Cendón, M. E. 11 2018 A numerical method for junctions in networks of shallow-water channels. Zbl 1427.76156Bellamoli, Francesca; Müller, Lucas O.; Toro, Eleuterio F. 2 2018 Lectures on hyperbolic equations and their numerical approximation. Zbl 1448.35002Toro, Eleuterio F. 2 2018 A second-order cell-centered Lagrangian method for two-dimensional elastic-plastic flows. Zbl 07414382Cheng, Jun-Bo; Jia, Yueling; Jiang, Song; Toro, Eleuterio F.; Yu, Ming 5 2017 On the exact solution of the Riemann problem for blood flow in human veins, including collapse. Zbl 1411.76182Spiller, C.; Toro, E. F.; Vázquez-Cendón, M. E.; Contarino, C. 4 2017 A global mathematical model for the simulation of stenoses and bypass placement in the human arterial system. Zbl 1411.76183Strocchi, M.; Contarino, C.; Zhang, Q.; Bonmassari, R.; Toro, E. F. 2 2017 A flux splitting method for the Baer-Nunziato equations of compressible two-phase flow. Zbl 1366.76063Tokareva, Svetlana; Toro, Eleuterio 1 2017 Brain venous haemodynamics, neurological diseases and mathematical modelling. A review. Zbl 1410.76487Toro, Eleuterio F. 15 2016 Design and analysis of ADER-type schemes for model advection-diffusion-reaction equations. Zbl 1422.65203Busto, S.; Toro, E. F.; Vázquez-Cendón, M. E. 14 2016 Junction-generalized Riemann problem for stiff hyperbolic balance laws in networks: an implicit solver and ADER schemes. Zbl 1349.76318Contarino, Christian; Toro, Eleuterio F.; Montecinos, Gino I.; Borsche, Raul; Kall, Jochen 8 2016 Exploring various flux vector splittings for the magnetohydrodynamic system. Zbl 1349.76885Balsara, Dinshaw S.; Montecinos, Gino I.; Toro, Eleuterio F. 7 2016 Pollutant transport by shallow water equations on unstructured meshes: hyperbolization of the model and numerical solution via a novel flux splitting scheme. Zbl 1349.76401Vanzo, Davide; Siviglia, Annunziato; Toro, Eleuterio F. 4 2016 A flux splitting method for the Baer-Nunziato equations of compressible two-phase flow. Zbl 1415.76480Tokareva, S. A.; Toro, E. F. 3 2016 An ADER-type scheme for a class of equations arising from the water-wave theory. Zbl 1390.76494Montecinos, G. I.; López-Rios, J. C.; Lecaros, R.; Ortega, J. H.; Toro, E. F. 2 2016 A novel numerical flux for the 3D Euler equations with general equation of state. Zbl 1349.76398Toro, Eleuterio F.; Castro, Cristóbal E.; Lee, Bok Jik 15 2015 A high-order cell-centered Lagrangian scheme for one-dimensional elastic-plastic problems. Zbl 1390.76558Cheng, Jun-Bo; Toro, Eleuterio F.; Jiang, Song; Yu, Ming; Tang, Weijun 11 2015 Implicit, semi-analytical solution of the generalized Riemann problem for stiff hyperbolic balance laws. Zbl 1349.76399Toro, Eleuterio F.; Montecinos, Gino I. 8 2015 Computational haemodynamics in stenotic internal jugular veins. Zbl 1350.92012Caiazzo, Alfonso; Montecinos, Gino; Müller, Lucas O.; Haacke, E. Mark; Toro, Eleuterio F. 5 2015 Advection-diffusion-reaction equations: hyperbolization and high-order ADER discretizations. Zbl 1307.65117Toro, Eleuterio F.; Montecinos, Gino I. 26 2014 Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes. Zbl 1323.92065Montecinos, Gino I.; Müller, Lucas O.; Toro, Eleuterio F. 22 2014 Reformulations for general advection-diffusion-reaction equations and locally implicit ADER schemes. Zbl 1349.65378Montecinos, Gino I.; Toro, Eleuterio F. 22 2014 Numerical and analytical study of an atherosclerosis inflammatory disease model. Zbl 1293.35343Hidalgo, A.; Tello, L.; Toro, E. F. 8 2014 Roe-type Riemann solvers for general hyperbolic systems. Zbl 1455.65144Castro, Cristóbal E.; Toro, Eleuterio F. 1 2014 Well-balanced high-order numerical schemes for one-dimensional blood flow in vessels with varying mechanical properties. Zbl 1323.92066Müller, Lucas O.; Parés, Carlos; Toro, Eleuterio F. 34 2013 Flow in collapsible tubes with discontinuous mechanical properties: mathematical model and exact solutions. Zbl 1373.76362Toro, Eleuterio F.; Siviglia, Annunziato 25 2013 A sub-cell WENO reconstruction method for spatial derivatives in the ADER scheme. Zbl 1349.65279Cheng, Jun Bo; Toro, Eleuterio F.; Jiang, Song; Tang, Weijun 16 2013 Adaptive Osher-type scheme for the Euler equations with highly nonlinear equations of state. Zbl 1349.76354Lee, Bok Jik; Toro, Eleuterio F.; Castro, Cristóbal E.; Nikiforakis, Nikolaos 12 2013 Flux splitting schemes for the Euler equations. Zbl 1365.76243Toro, E. F.; Vázquez-Cendón, M. E. 54 2012 Comparison of solvers for the generalized Riemann problem for hyperbolic systems with source terms. Zbl 1284.35268Montecinos, G.; Castro, C. E.; Dumbser, M.; Toro, E. F. 27 2012 Semi-implicit numerical modeling of axially symmetric flows in compliant arterial systems. Zbl 1242.92019Casulli, Vincenzo; Dumbser, Michael; Toro, Eleuterio F. 17 2012 A novel numerical method of high-order accuracy for flow in unsaturated porous media. Zbl 1242.76188Zambra, C. E.; Dumbser, M.; Toro, E. F.; Moraga, N. O. 6 2012 Solver for the generalized Riemann problem for balance laws with stiff source terms: the scalar case. Zbl 1306.65251Montecinos, Gino; Toro, Eleuterio 4 2012 A finite volume upwind-biased centred scheme for hyperbolic systems of conservation laws: application to shallow water equations. Zbl 1373.76146Stecca, Guglielmo; Siviglia, Annunziato; Toro, Eleuterio F. 2 2012 A simple extension of the Osher Riemann solver to non-conservative hyperbolic systems. Zbl 1220.65110Dumbser, Michael; Toro, Eleuterio F. 94 2011 On universal Osher-type schemes for general nonlinear hyperbolic conservation laws. Zbl 1373.76125Dumbser, Michael; Toro, Eleuterio F. 70 2011 A path-conservative method for a five-equation model of two-phase flow with an HLLC-type Riemann solver. Zbl 1433.76166Tian, Baolin; Toro, E. F.; Castro, C. E. 24 2011 High-order accuracy: monotonicity and non-linear methods. Zbl 1260.65079Toro, E. F. 1 2011 HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow. Zbl 1391.76440Tokareva, S. A.; Toro, E. F. 72 2010 FORCE schemes on unstructured meshes. II: Non-conservative hyperbolic systems. Zbl 1227.76043Dumbser, Michael; Hidalgo, Arturo; Castro, Manuel; Parés, Carlos; Toro, Eleuterio F. 64 2010 On some fast well-balanced first order solvers for nonconservative systems. Zbl 1369.65107Castro, Manuel J.; Pardo, Alberto; Parés, Carlos; Toro, E. F. 34 2010 Conservative models and numerical methods for compressible two-phase flow. Zbl 1203.76095Romenski, Evgeniy; Drikakis, Dimitris; Toro, Eleuterio 20 2010 Three-dimensional flow evolution after a dam break. Zbl 1205.76228Ferrari, A.; Fraccarollo, L.; Dumbser, M.; Toro, E. F.; Armanini, A. 14 2010 Upwind-biased FORCE schemes with applications to free-surface shallow flows. Zbl 1426.35192Stecca, Guglielmo; Siviglia, Annunziato; Toro, Eleuterio F. 6 2010 The Riemann problem for the dispersive nonlinear shallow water equations. Zbl 1364.35268Grosso, Giovanna; Antuono, Matteo; Toro, Eleuterio 1 2010 Riemann solvers and numerical methods for fluid dynamics. A practical introduction. 3rd ed. Zbl 1227.76006Toro, Eleuterio F. 618 2009 ADER schemes on unstructured meshes for nonconservative hyperbolic systems: applications to geophysical flows. Zbl 1177.76222Dumbser, Michael; Castro, Manuel; Parés, Carlos; Toro, Eleuterio F. 92 2009 A new 3D parallel SPH scheme for free surface flows. Zbl 1242.76270Ferrari, Angela; Dumbser, Michael; Toro, Eleuterio F.; Armanini, Aronne 79 2009 ADER finite volume schemes for nonlinear reaction-diffusion equations. Zbl 1155.65065Toro, Eleuterio F.; Hidalgo, Arturo 21 2009 Space-time adaptive numerical methods for geophysical applications. Zbl 1192.86006Castro, C. E.; Käser, M.; Toro, E. F. 13 2009 A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes. Zbl 1147.65075Dumbser, Michael; Balsara, Dinshaw S.; Toro, Eleuterio F.; Munz, Claus-Dieter 234 2008 Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws. Zbl 1142.65070Dumbser, Michael; Enaux, Cedric; Toro, Eleuterio F. 127 2008 Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry. Zbl 1132.76027Bernetti, R.; Titarev, V. A.; Toro, E. F. 59 2008 Solvers for the high-order Riemann problem for hyperbolic balance laws. Zbl 1148.65066Castro, C. E.; Toro, E. F. 46 2008 FORCE schemes on unstructured meshes. I: Conservative hyperbolic systems. Zbl 1168.65377Toro, Eleuterio F.; Hidalgo, Arturo; Dumbser, Michael 41 2008 MUSTA-type upwind fluxes for nonlinear elasticity. Zbl 1159.74046Titarev, V. A.; Romenski, E.; Toro, E. F. 25 2008 ADER schemes for the shallow water equations in channel with irregular bottom elevation. Zbl 1132.76035Vignoli, G.; Titarev, V. A.; Toro, E. F. 19 2008 A new stable version of the SPH method in Lagrangian coordinates. Zbl 1364.76175Ferrari, A.; Dumbser, M.; Toro, E. F.; Armanini, A. 7 2008 The derivative Riemann problem for the Baer-Nunziato equations. Zbl 1372.35184Toro, E. F.; Castro, C. E. 1 2008 ADER DG and FV schemes for shallow water flows. Zbl 1308.76181Castro, Cristóbal E.; Toro, Eleuterio F. 1 2008 Well-balanced high-order MUSTA schemes for non-conservative hyperbolic systems. Zbl 1188.65114Castro, M. J.; Parés, C.; Pardo, A.; Toro, E. F. 1 2008 Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems. Zbl 1124.65074Dumbser, Michael; Käser, Martin; Titarev, Vladimir A.; Toro, Eleuterio F. 134 2007 Conservative hyperbolic formulation for compressible two-phase flow with different phase pressures and temperatures. Zbl 1145.35430Romenski, E.; Resnyansky, A. D.; Toro, E. F. 29 2007 Numerical study of wave propagation in compressible two-phase flow. Zbl 1241.76338Zeidan, D.; Romenski, E.; Slaouti, A.; Toro, E. F. 23 2007 Numerical solution for hyperbolic conservative two-phase flow equations. Zbl 1198.76078Zeidan, D.; Slaouti, A.; Romenski, E.; Toro, E. F. 14 2007 Analysis of ADER and ADER-WAF schemes. Zbl 1119.65083Titarev, V. A.; Toro, E. F. 12 2007 Derivative Riemann solvers for systems of conservation laws and ader methods. Zbl 1087.65590Toro, E. F.; Titarev, V. A. 83 2006 MUSTA fluxes for systems of conservation laws. Zbl 1097.65091Toro, E. F.; Titarev, V. A. 23 2006 A Riemann solver and upwind methods for a two-phase flow model in non-conservative form. Zbl 1086.76046Castro, C. E.; Toro, E. F. 20 2006 MUSTA: a multi-stage numerical flux. Zbl 1101.65088Toro, E. F. 9 2006 Riemann solvers with evolved initial conditions. Zbl 1108.65091Toro, E. F. 4 2006 ADER schemes for three-dimensional non-linear hyperbolic systems. Zbl 1060.65641Titarev, V. A.; Toro, E. F. 144 2005 ADER schemes for scalar non-linear hyperbolic conservation laws with source terms in three-space dimensions. Zbl 1061.65103Toro, E. F.; Titarev, V. A. 48 2005 TVD fluxes for the high-order ADER schemes. Zbl 1096.76029Toro, E. F.; Titarev, V. A. 32 2005 WENO schemes based on upwind and centred TVD fluxes. Zbl 1134.65361Titarev, V. A.; Toro, E. F. 29 2005 MUSTA schemes for multi-dimensional hyperbolic systems: analysis and improvements. Zbl 1073.65553Titarev, V. A.; Toro, E. F. 5 2005 Finite-volume WENO schemes for three-dimensional conservation laws. Zbl 1059.65078Titarev, V. A.; Toro, E. F. 134 2004 Hyperbolicity and one-dimensional waves in compressible two-phase flow models. Zbl 1136.76702Romenski, E.; Toro, E. F. 10 2004 Centered difference schemes for nonlinear hyperbolic equations. Zbl 1063.65076Chen, Gui-Qiang; Toro, Eleuterio F. 9 2004 PRICE: Primitive centred schemes for hyperbolic systems. Zbl 1078.76566Toro, E. F.; Siviglia, A. 14 2003 Arbitrarily accurate non-oscillatory schemes for nonlinear scalar conservation laws with source terms. II. Zbl 1157.76365Takakura, Yoko; Toro, Eleuterio F. 1 2003 Exact solution of some hyperbolic systems with source terms. Zbl 1047.35029Vázquez-Cendón, M. E.; Toro, E. F. 1 2003 ADER: Arbitrary high-order Godunov approach. Zbl 1024.76028Titarev, V. A.; Toro, E. F. 155 2002 Solution of the generalized Riemann problem for advection-reaction equations. Zbl 1019.35061Toro, E. F.; Titarev, V. A. 109 2002 ADER: A high-order approach for linear hyperbolic systems in 2D. Zbl 1022.76034Schwartzkopff, T.; Munz, C. D.; Toro, E. F. 56 2002 Shock-capturing methods for free-surface shallow flows. Zbl 0996.76003Toro, Eleuterio F. 250 2001 Towards very high order Godunov schemes. Zbl 0989.65094Toro, E. F.; Millington, R. C.; Nejad, L. A. M. 96 2001 The ADER approach in 2D for a system of linear hyperbolic PDEs. Zbl 1028.76030Schwartzkopff, T.; Munz, C. D.; Toro, E. F.; Millington, R. C. 5 2001 Model hyperbolic systems with source terms: Exact and numerical solutions. Zbl 0989.65095Toro, E. F.; Vazquez-Cendon, M. E. 3 2001 Godunov methods. Theory and applications. International conference, Oxford, GB, October 1999. Zbl 0978.00036 1 2001 Centered unsplit finite volume schemes for multi-dimensional hyperbolic conservation laws. Zbl 0990.65095Toro, E. F.; Hu, W. 1 2001 Centred TVD schemes for hyperbolic conservation laws. Zbl 0943.65100Toro, E. F.; Billet, S. J. 48 2000 Riemann solvers and numerical methods for fluid dynamics. A practical introduction. 2nd ed. Zbl 0923.76004Toro, Eleuterio F. 455 1999 On Riemann solvers for compressible liquids. Zbl 0918.76047Ivings, M. J.; Causon, D. M.; Toro, E. F. 26 1998 Primitive, conservative and adaptive schemes for hyperbolic conservation laws. Zbl 0958.76062Toro, E. F. 14 1998 Unsplit WAF-type schemes for three-dimensional hyperbolic conservation laws. Zbl 0947.76060Billett, S. J.; Toro, E. F. 3 1998 Riemann solvers and numerical methods for fluid dynamics. A practical introduction. Zbl 0888.76001Toro, Eleuterio F. 322 1997 On WAF-type schemes for multidimensional hyperbolic conservation laws. Zbl 0873.65088Billett, S. J.; Toro, E. F. 38 1997 ...and 20 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,546 Authors 116 Dumbser, Michael 79 Toro, Eleuterio F. 35 Balsara, Dinshaw S. 33 Munz, Claus-Dieter 31 Castro, Manuel J. 30 Parés Madroñal, Carlos 28 Boscheri, Walter 27 Xu, Kun 26 Qiu, Jianxian 26 Shu, Chi-Wang 26 Titarev, Vladimir A. 24 Liu, Tiegang 23 Adams, Nikolaus A. 23 Luo, Hong 22 Vázquez-Cendón, María Elena 21 Drikakis, Dimitris 21 Loubère, Raphaël 20 Li, Jiequan 20 Saurel, Richard 19 Berthon, Christophe 19 Garcia-Navarro, Pilar 19 Hérard, Jean-Marc 19 Murillo, Javier 18 Clain, Stéphane Louis 18 Fernández-Nieto, Enrique Domingo 18 Gassner, Gregor J. 17 Montecinos, Gino I. 17 Xiao, Feng 16 Zhu, Jun 15 Liang, Qiuhua 15 Romenskii, Evgenii I. 15 Yan, Chao 15 Zeidan, Dia 14 Abgrall, Rémi 14 Borsche, Raul 14 Chandrashekar, Praveen 14 Gavrilyuk, Sergey L. 14 Tavelli, Maurizio 13 Guermond, Jean-Luc 13 Jiang, Song 13 Kurganov, Alexander 13 Mai Duc Thanh 13 Popov, Boyan 12 Borthwick, Alistair G. 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Raja 10 Capdeville, Guy 10 Daude, Frédéric 10 Deng, Xi 10 Deng, Xiaogang 10 Nishikawa, Hiroaki 10 Peshkov, Ilya M. 10 Rogers, Benedict D. 10 Seaïd, Mohammed 10 Semplice, Matteo 10 Shen, Zhijun 10 Tang, Huazhong 10 Tsoutsanis, Panagiotis 10 Zhang, Fan 9 Antuono, Matteo 9 Cheng, Jian 9 Galon, Pascal 9 Hurisse, Olivier 9 Kopriva, David Alan 9 Li, Gang 9 Li, Ruo 9 Lukáčová-Medvid’ová, Mária 9 Morales de Luna, Tomás 9 Shu, Chang 9 Shyue, Keh-Ming 9 Utyuzhnikov, Sergey V. 9 Warnecke, Gerald G. 9 Zanotti, Olindo 8 Caleffi, Valerio 8 Castro, Cristóbal E. 8 Colominas, Ignasi 8 Hantke, Maren 8 Helluy, Philippe 8 Jiang, Zhenhua 8 Kitamura, Keiichi 8 LeVeque, Randall J. 8 Müller, Lucas O. 8 Müller, Siegfried 8 Nikiforakis, Nikos 8 Nourgaliev, Robert R. ...and 3,446 more Authors all top 5 Cited in 192 Serials 785 Journal of Computational Physics 384 Computers and Fluids 137 Journal of Scientific Computing 99 Computer Methods in Applied Mechanics and Engineering 92 International Journal for Numerical Methods in Fluids 77 Applied Mathematics and Computation 54 Computers & Mathematics with Applications 48 Journal of Fluid Mechanics 47 Applied Numerical Mathematics 47 Communications in Computational Physics 46 SIAM Journal on Scientific Computing 36 Applied Mathematical Modelling 33 International Journal of Computational Fluid Dynamics 26 Journal of Computational and Applied Mathematics 23 Computational Mathematics and Mathematical Physics 22 Shock Waves 21 International Journal for Numerical Methods in Engineering 21 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 20 Computer Physics Communications 15 Advances in Applied Mathematics and Mechanics 14 Mathematics of Computation 14 M\(^3\)AS. 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Technical Sciences 2 Meccanica 2 Studies in Applied Mathematics 2 Applied Mathematics Letters 2 SIAM Journal on Applied Mathematics 2 Computing and Visualization in Science ...and 92 more Serials all top 5 Cited in 40 Fields 2,059 Fluid mechanics (76-XX) 1,491 Numerical analysis (65-XX) 744 Partial differential equations (35-XX) 150 Mechanics of deformable solids (74-XX) 136 Geophysics (86-XX) 77 Classical thermodynamics, heat transfer (80-XX) 67 Statistical mechanics, structure of matter (82-XX) 64 Biology and other natural sciences (92-XX) 30 Astronomy and astrophysics (85-XX) 29 Operations research, mathematical programming (90-XX) 25 Optics, electromagnetic theory (78-XX) 13 Computer science (68-XX) 10 Probability theory and stochastic processes (60-XX) 9 Relativity and gravitational theory (83-XX) 8 Approximations and expansions (41-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 7 Dynamical systems and ergodic theory (37-XX) 6 Ordinary differential equations (34-XX) 5 Systems theory; control (93-XX) 4 General and overarching topics; collections (00-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Mechanics of particles and systems (70-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Integral equations (45-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Geometry (51-XX) 1 Quantum theory (81-XX) Citations by Year