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Numerical Approximation of Hyperbolic Systems of Conservation Laws
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A well‐balanced positivity‐preserving central‐upwind scheme for one‐dimensional blood flow models
Gerardo Hernandez‐Duenas and Guillermo Ramirez‐Santiago International Journal for Numerical Methods in Fluids 93(2) 369 (2021) https://doi.org/10.1002/fld.4887
An effect non-staggered central scheme based on new hydrostatic reconstruction
Moving-Water Equilibria Preserving Partial Relaxation Scheme for the Saint-Venant System
Xin Liu, Xi Chen, Shi Jin, Alexander Kurganov, Tong Wu and Hui Yu SIAM Journal on Scientific Computing 42(4) A2206 (2020) https://doi.org/10.1137/19M1258098
A robust central scheme for the shallow water flows with an abrupt topography based on modified hydrostatic reconstructions
Well-balanced schemes for the Euler equations with gravitation: Conservative formulation using global fluxes
Alina Chertock, Shumo Cui, Alexander Kurganov, Şeyma Nur Özcan and Eitan Tadmor Journal of Computational Physics 358 36 (2018) https://doi.org/10.1016/j.jcp.2017.12.026
Dynamic simulation of a mountain disaster chain: landslides, barrier lakes, and outburst floods
Well-balanced schemes for the shallow water equations with Coriolis forces
Alina Chertock, Michael Dudzinski, Alexander Kurganov and Mária Lukáčová-Medvid’ová Numerische Mathematik 138(4) 939 (2018) https://doi.org/10.1007/s00211-017-0928-0
High order well-balanced discontinuous Galerkin methods based on hydrostatic reconstruction for shallow water equations
Theory, Numerics and Applications of Hyperbolic Problems I
Alina Chertock, Michael Herty and Şeyma Nur Özcan Springer Proceedings in Mathematics & Statistics, Theory, Numerics and Applications of Hyperbolic Problems I 236 345 (2018) https://doi.org/10.1007/978-3-319-91545-6_28
Handbook of Numerical Methods for Hyperbolic Problems - Applied and Modern Issues
Fully well-balanced, positive and simple approximate Riemann solver for shallow water equations
C. Berthon, C. Chalons, S. Cornet and G. Sperone Bulletin of the Brazilian Mathematical Society, New Series 47(1) 117 (2016) https://doi.org/10.1007/s00574-016-0126-1
A Well-Balanced Finite Volume Scheme for a Mixed Hyperbolic/Parabolic System to Model Chemotaxis
A shallow water with variable pressure model for blood flow simulation
Pierre-Yves Lagrée, José-Maria Fullana, Arthur R. Ghigo and Olivier Delestre Networks and Heterogeneous Media 11(1) 69 (2016) https://doi.org/10.3934/nhm.2016.11.69
Entropy stability and well-balancedness of space-time DG for the shallow water equations with bottom topography
Large Time Step and Asymptotic Preserving Numerical Schemes for the Gas Dynamics Equations with Source Terms
Christophe Chalons, Mathieu Girardin and Samuel Kokh SIAM Journal on Scientific Computing 35(6) A2874 (2013) https://doi.org/10.1137/130908671
A Well-Balanced Reconstruction of Wet/Dry Fronts for the Shallow Water Equations
Andreas Bollermann, Guoxian Chen, Alexander Kurganov and Sebastian Noelle Journal of Scientific Computing 56(2) 267 (2013) https://doi.org/10.1007/s10915-012-9677-5
Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws
Yunlong Chen, Alexander Kurganov, Minlan Lei and Yu Liu Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws 120 125 (2013) https://doi.org/10.1007/978-3-642-33221-0_8
A well‐balanced stable generalized Riemann problem scheme for shallow water equations using adaptive moving unstructured triangular meshes
Feng Zhou, Guoxian Chen, Sebastian Noelle and Huaicheng Guo International Journal for Numerical Methods in Fluids 73(3) 266 (2013) https://doi.org/10.1002/fld.3800
A ‘well‐balanced’ finite volume scheme for blood flow simulation
O. Delestre and P.‐Y. Lagrée International Journal for Numerical Methods in Fluids 72(2) 177 (2013) https://doi.org/10.1002/fld.3736
Efficient well-balanced hydrostatic upwind schemes for shallow-water equations
Finite Volumes for Complex Applications VI Problems & Perspectives
Christophe Berthon and Françoise Foucher Springer Proceedings in Mathematics, Finite Volumes for Complex Applications VI Problems & Perspectives 4 97 (2011) https://doi.org/10.1007/978-3-642-20671-9_11
Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
Steve Bryson, Yekaterina Epshteyn, Alexander Kurganov and Guergana Petrova ESAIM: Mathematical Modelling and Numerical Analysis 45(3) 423 (2011) https://doi.org/10.1051/m2an/2010060
A Subsonic-Well-Balanced Reconstruction Scheme for Shallow Water Flows
Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances
François Bouchut Edited Series on Advances in Nonlinear Science and Complexity, Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances 2 189 (2007) https://doi.org/10.1016/S1574-6909(06)02004-1
Upwinding of the source term at interfaces for Euler equations with high friction
The generalized Riemann problem method for the shallow water equations with bottom topography
Jiequan Li and Guoxian Chen International Journal for Numerical Methods in Engineering 65(6) 834 (2006) https://doi.org/10.1002/nme.1471
Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
Sebastian Noelle, Normann Pankratz, Gabriella Puppo and Jostein R. Natvig Journal of Computational Physics 213(2) 474 (2006) https://doi.org/10.1016/j.jcp.2005.08.019
High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms