Open Access
Issue |
ESAIM: M2AN
Volume 56, Number 4, July-August 2022
|
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Page(s) | 1115 - 1150 | |
DOI | https://doi.org/10.1051/m2an/2022032 | |
Published online | 27 June 2022 |
- R. Abgrall and S. Karni, A comment on the computation of non-conservative products. J. Comput. Phys. 229 (2010) 2759–2763. [Google Scholar]
- C. Berthon, F. Coquel, J. Hérard and M. Uhlmann, An approximate solution of the Riemann problem for a realisable second-moment turbulent closure. Shock Waves 11 (2002) 245–269. [CrossRef] [Google Scholar]
- A. Bhole, B. Nkonga, S. Gavrilyuk and K. Ivanova, Fluctuation splitting Riemann solver for a non-conservative modeling of shear shallow water flow. J. Comput. Phys. 392 (2019) 205–226. [CrossRef] [MathSciNet] [Google Scholar]
- S. Busto, M. Dumbser, S. Gavrilyuk and K. Ivanova, On thermodynamically compatible finite volume methods and path-conservative ADER discontinuous galerkin schemes for turbulent shallow water flows. J. Sci. Comput. 88 (2021) 28. [CrossRef] [Google Scholar]
- M.J. Castro, P.G. LeFloch, M.L. Muñoz-Ruiz and C. Parés, Why many theories of shock waves are necessary: convergence error in formally path-consistent schemes. J. Comput. Phys. 227 (2008) 8107–8129. [CrossRef] [MathSciNet] [Google Scholar]
- M.J. Castro, C. Parés, G. Puppo and G. Russo, Central schemes for nonconservative hyperbolic systems. SIAM J. Sci. Comput. 34 (2012) B523–B558. [CrossRef] [Google Scholar]
- M.J. Castro Díaz, A. Kurganov and T. Morales de Luna, Path-conservative central-upwind schemes for nonconservative hyperbolic systems. ESAIM: M2AN 53 (2019) 959–985. [CrossRef] [EDP Sciences] [Google Scholar]
- J. Cauret, J. Colombeau and A. Le Roux, Discontinuous generalized solutions of nonlinear nonconservative hyperbolic equations. J. Math. Anal. App. 139 (1989) 552–573. [CrossRef] [Google Scholar]
- P. Chandrashekar, B. Nkonga, A.K. Meena and A. Bhole, A path conservative finite volume method for a shear shallow water model. J. Comput. Phys. 413 (2020) 109457. [CrossRef] [MathSciNet] [Google Scholar]
- J.F. Colombeau and A.Y. Le Roux, Multiplications of distributions in elasticity and hydrodynamics. J. Math. Phys. 29 (1988) 315–319. [CrossRef] [MathSciNet] [Google Scholar]
- G. Dal Maso, P.G. Lefloch and F. Murat, Definition and weak stability of nonconservative products. J. Math. Pures Appl. 74 (1995) 483–548. [Google Scholar]
- M. Dumbser and D.S. Balsara, A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems. J. Comput. Phys. 304 (2016) 275–319. [CrossRef] [MathSciNet] [Google Scholar]
- M. Dumbser, M. Castro, C. Parés and E.F. Toro, ADER schemes on unstructured meshes for nonconservative hyperbolic systems: Applications to geophysical flows. Comput. Fluids 38 (2009) 1731–1748. [CrossRef] [MathSciNet] [Google Scholar]
- B. Einfeldt, On Godunov-type methods for gas dynamics. SIAM J. Numer. Anal. 25 (1988) 294–318. [CrossRef] [MathSciNet] [Google Scholar]
- S. Gavrilyuk, K. Ivanova and N. Favrie, Multi-dimensional shear shallow water flows: problems and solutions. J. Comput. Phys. 366 (2018) 252–280. [Google Scholar]
- S. Gavrilyuk, B. Nkonga, K.-M. Shyue and L. Truskinovsky, Stationary shock-like transition fronts in dispersive systems. Nonlinearity 33 (2020) 5477–5509. [CrossRef] [MathSciNet] [Google Scholar]
- E. Godlewski and P.-A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws. Vol. 118 of Applied Mathematical Sciences. Springer, New York, New York, NY (1996). [CrossRef] [Google Scholar]
- L. Gosse, A well-balanced scheme using non-conservative products designed for hyperbolic systems of conservation laws with source terms. Math. Models Methods Appl. Sci. 11 (2001) 339–365. [Google Scholar]
- K. Joseph and P. Sachdev, Exact solutions for some non-conservative hyperbolic systems. Int. J. Non-Linear Mech. 38 (2003) 1377–1386. [CrossRef] [Google Scholar]
- P. Lax and B. Wendroff, Systems of conservation laws. Commun. Pure Appl. Math. 13 (1960) 217–237. [CrossRef] [Google Scholar]
- C.D. Levermore, Moment closure hierarchies for kinetic theories. J. Stat. Phys. 83 (1996) 1021–1065. [Google Scholar]
- C.D. Levermore and W.J. Morokoff, The gaussian moment closure for gas dynamics. SIAM J. Appl. Math. 59 (1998) 72–96. [CrossRef] [Google Scholar]
- C. Parés, Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM J. Numer. Anal. 44 (2006) 300–321. [Google Scholar]
- C. Parés and E. Pimentel, The Riemann problem for the shallow water equations with discontinuous topography: the wet – dry case. J. Comput. Phys. 378 (2019) 344–365. [CrossRef] [MathSciNet] [Google Scholar]
- K.A. Schneider, J.M. Gallardo, D.S. Balsara, B. Nkonga and C. Parés, Multidimensional approximate Riemann solvers for hyperbolic nonconservative systems. Applications to shallow water systems. J. Comput. Phys. 444 (2021) 110547. [CrossRef] [Google Scholar]
- V.M. Teshukov, Gas-dynamic analogy for vortex free-boundary flows. J. Appl. Mech. Tech. Phys. 48 (2007) 303–309. [CrossRef] [MathSciNet] [Google Scholar]
- E.F. Toro, Shock-Capturing Methods for Free-Surface Shallow Flows. Wiley-Blackwell (2001). [Google Scholar]
- I. Toumi, A weak formulation of roe’s approximate riemann solver. J. Comput. Phys. 102 (1992) 360–373. [CrossRef] [MathSciNet] [Google Scholar]
- A.I. Volpert, The spaces BV and quasilinear equations. Math. USSR-Sbornik 2 (1967) 225–267. [CrossRef] [Google Scholar]
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