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In-cell discontinuous reconstruction path-conservative methods for non conservative hyperbolic systems - Second-order extension
Ernesto Pimentel-García, Manuel J. Castro, Christophe Chalons, Tomás Morales de Luna and Carlos Parés Journal of Computational Physics 459 111152 (2022) https://doi.org/10.1016/j.jcp.2022.111152
On Thermodynamically Compatible Finite Volume Methods and Path-Conservative ADER Discontinuous Galerkin Schemes for Turbulent Shallow Water Flows
On High Order ADER Discontinuous Galerkin Schemes for First Order Hyperbolic Reformulations of Nonlinear Dispersive Systems
Saray Busto, Michael Dumbser, Cipriano Escalante, Nicolas Favrie and Sergey Gavrilyuk Journal of Scientific Computing 87(2) (2021) https://doi.org/10.1007/s10915-021-01429-8
Multidimensional approximate Riemann solvers for hyperbolic nonconservative systems. Applications to shallow water systems
Kleiton A. Schneider, José M. Gallardo, Dinshaw S. Balsara, Boniface Nkonga and Carlos Parés Journal of Computational Physics 444 110547 (2021) https://doi.org/10.1016/j.jcp.2021.110547
Numerical solutions of hyperbolic systems of conservation laws combining unsteady friction and viscoelastic pipes
NUMERICAL SIMULATIONS FOR NON CONSERVATIVE HYPERBOLIC SYSTEM. APPLICATION TO TRANSIENT TWO-PHASE FLOW WITH CAVITATION PHENOMENON
Abdelmjid Qadi El Idrissi, Boujemâa Achchab and Abdellatif Agouzal Mathematical Modelling and Analysis 24(2) 218 (2019) https://doi.org/10.3846/mma.2019.015
Towards a new friction model for shallow water equations through an interactive viscous layer
François James, Pierre-Yves Lagrée, Minh H. Le and Mathilde Legrand ESAIM: Mathematical Modelling and Numerical Analysis 53(1) 269 (2019) https://doi.org/10.1051/m2an/2018076
Fluctuation splitting Riemann solver for a non-conservative modeling of shear shallow water flow
Interdisciplinary Perspective of Surface Water Flow Numerical Analysis
Masaomi KIMURA, Tomohiro TANAKA, Issaku AZECHI, et al. Journal of Japan Society of Hydrology and Water Resources 30(5) 307 (2017) https://doi.org/10.3178/jjshwr.30.307
Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues
M.J. Castro, T. Morales de Luna and C. Parés Handbook of Numerical Analysis, Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues 18 131 (2017) https://doi.org/10.1016/bs.hna.2016.10.002
Efficient conservative ADER schemes based on WENO reconstruction and space-time predictor in primitive variables
Solving Two-Mode Shallow Water Equations Using Finite Volume Methods
Manuel Jesús Castro Diaz, Yuanzhen Cheng, Alina Chertock and Alexander Kurganov Communications in Computational Physics 16(5) 1323 (2014) https://doi.org/10.4208/cicp.180513.230514a
Numerical investigation of a modified family of centered schemes applied to multiphase equations with nonconservative sources
A Roe scheme for a compressible six‐equation two‐fluid model
Alexandre Morin, Tore Flåtten and Svend Tollak Munkejord International Journal for Numerical Methods in Fluids 72(4) 478 (2013) https://doi.org/10.1002/fld.3752
High-order unstructured Lagrangian one-step WENO finite volume schemes for non-conservative hyperbolic systems: Applications to compressible multi-phase flows
Entropy Conservative and Entropy Stable Schemes for Nonconservative Hyperbolic Systems
Manuel J. Castro, Ulrik S. Fjordholm, Siddhartha Mishra and Carlos Parés SIAM Journal on Numerical Analysis 51(3) 1371 (2013) https://doi.org/10.1137/110845379
Central Schemes for Nonconservative Hyperbolic Systems
M. J. Castro, Carlos Parés, Gabriella Puppo and Giovanni Russo SIAM Journal on Scientific Computing 34(5) B523 (2012) https://doi.org/10.1137/110828873
A path-conservative method for a five-equation model of two-phase flow with an HLLC-type Riemann solver
Numerical solution of the discontinuous-bottom Shallow-water Equations with hydrostatic pressure distribution at the step
Luca Cozzolino, Renata Della Morte, Carmine Covelli, Giuseppe Del Giudice and Domenico Pianese Advances in Water Resources 34(11) 1413 (2011) https://doi.org/10.1016/j.advwatres.2011.07.009
FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems
Michael Dumbser, Arturo Hidalgo, Manuel Castro, Carlos Parés and Eleuterio F. Toro Computer Methods in Applied Mechanics and Engineering 199(9-12) 625 (2010) https://doi.org/10.1016/j.cma.2009.10.016
Numerical Mathematics and Advanced Applications 2009
A MUSTA Scheme for a Nonconservative Two-Fluid Model
Svend Tollak Munkejord, Steinar Evje and Tore FlÅtten SIAM Journal on Scientific Computing 31(4) 2587 (2009) https://doi.org/10.1137/080719273
High Order Extensions of Roe Schemes for Two-Dimensional Nonconservative Hyperbolic Systems
M. J. Castro, E. D. Fernández-Nieto, A. M. Ferreiro, J. A. García-Rodríguez and C. Parés Journal of Scientific Computing 39(1) 67 (2009) https://doi.org/10.1007/s10915-008-9250-4
ADER schemes on unstructured meshes for nonconservative hyperbolic systems: Applications to geophysical flows
Well-Balanced High Order Extensions of Godunov's Method for Semilinear Balance Laws
Manuel Castro, José M. Gallardo, Juan A. López-GarcÍa and Carlos Parés SIAM Journal on Numerical Analysis 46(2) 1012 (2008) https://doi.org/10.1137/060674879
Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes
Manuel J. Castro, Philippe G. LeFloch, María Luz Muñoz-Ruiz and Carlos Parés Journal of Computational Physics 227(17) 8107 (2008) https://doi.org/10.1016/j.jcp.2008.05.012
WELL-BALANCED NUMERICAL SCHEMES BASED ON A GENERALIZED HYDROSTATIC RECONSTRUCTION TECHNIQUE
MANUEL J. CASTRO, ALBERTO PARDO MILANÉS and CARLOS PARÉS Mathematical Models and Methods in Applied Sciences 17(12) 2055 (2007) https://doi.org/10.1142/S021820250700256X