Free Access
Issue |
ESAIM: M2AN
Volume 47, Number 1, January-February 2013
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Page(s) | 1 - 32 | |
DOI | https://doi.org/10.1051/m2an/2012017 | |
Published online | 31 July 2012 |
- R. Abgrall and S. Karni, A comment on the computation of non-conservative products. J. Comput. Phys. 229 (2010) 2759–2763. [CrossRef] [MathSciNet] [Google Scholar]
- M.S. Altinaker, W.H. Graf and E. Hopfinger, Flow structure in turbidity currents. J. Hydr. Res. 34 (1996) 713–718. [CrossRef] [Google Scholar]
- F. Bouchut, Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources, in Frontiers in Mathematics. Birkhäuser Verlag, Basel (2004). [Google Scholar]
- S.F. Bradford and N.D. Katopodes, Hydrodynamics of turbid underflows. i : Formulation and numerical analysis. J. Hydr. Eng. 125 (1999) 1006–1015. [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, E.D. Fernández-Nieto, A.M. Ferreiro, J.A. García-Rodríguez and C. Parés, High order extensions of Roe schemes for two-dimensional nonconservative hyperbolic systems. J. Sci. Comput. 39 (2009) 67–114. [CrossRef] [Google Scholar]
- M. Castro Díaz, E. Fernéndez-Nieto and A. Ferreiro, Sediment transport models in shallow water equations and numerical approach by high order finite volume methods. Comput. Fluids 37 (2008) 299–316. [CrossRef] [MathSciNet] [Google Scholar]
- M.J. Castro Díaz, E.D. Fernández-Nieto, A.M. Ferreiro and C. Parés, Two-dimensional sediment transport models in shallow water equations. A second order finite volume approach on unstructured meshes. Comput. Methods Appl. Mech. Eng. 198 (2009) 2520–2538. [CrossRef] [Google Scholar]
- S. Cordier, M. Le and T. Morales de Luna, Bedload transport in shallow water models : Why splitting (may) fail, how hyperbolicity (can) help. Adv. Water Resour. 34 (2011) 980–989. [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]
- F. Exner, Über die wechselwirkung zwischen wasser und geschiebe in flüssen. Sitzungsber., Akad. Wissenschaften IIa (1925). [Google Scholar]
- E.D. Fernández-Nieto, Modelling and numerical simulation of submarine sediment shallow flows : transport and avalanches. Bol. Soc. Esp. Mat. Apl. S MA 49 (2009) 83–103. [Google Scholar]
- A.C. Fowler, N. Kopteva and C. Oakley, The formation of river channels. SIAM J. Appl. Math. 67 (2007) 1016–1040. [CrossRef] [MathSciNet] [Google Scholar]
- J. Gallardo, S. Ortega, M. de la Asunción and J. Mantas, Two-Dimensional compact third-order polynomial reconstructions. solving nonconservative hyperbolic systems using GPUs. J. Sci. Comput. 48 (2011) 141–163. [CrossRef] [Google Scholar]
- A. Grass, Sediment transport by waves and currents. SERC London Cent. Mar. Technol. Report No. FL29 (1981). [Google Scholar]
- A. Harten, P.D. Lax and B. van Leer, On upstream differencing and godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 25 (1983). [Google Scholar]
- T.Y. Hou and P.G. Le Floch, Why nonconservative schemes converge to wrong solutions : error analysis. Math. Comput. 62 (1994) 497–530. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
- S.M. Khan, J. Imran, S. Bradford and J. Syvitski, Numerical modeling of hyperpycnal plume. Mar. Geol. 222-223 (2005) 193–211. [CrossRef] [Google Scholar]
- Y. Kubo, Experimental and numerical study of topographic effects on deposition from two-dimensional, particle-driven density currents. Sediment. Geol. 164 (2004) 311–326. [CrossRef] [Google Scholar]
- Y. Kubo and T. Nakajima, Laboratory experiments and numerical simulation of sediment-wave formation by turbidity currents. Mar. Geol. 192 (2002) 105–121. [CrossRef] [Google Scholar]
- D.A. Lyn and M. Altinakar, St. Venant-Exner equations for Near-Critical and transcritical flows. J. Hydr. Eng. 128 (2002) 579–587. [CrossRef] [Google Scholar]
- E. Meyer-Peter, and R. Müller, Formulas for bed-load transport, in 2nd meeting IAHSR. Stockholm, Sweden (1948) 1–26. [Google Scholar]
- T. Morales de Luna, M.J. Castro Díaz, C. Parés Madroñal and E.D. Fernández Nieto, On a shallow water model for the simulation of turbidity currents. Commun. Comput. Phys. 6 (2009) 848–882. [CrossRef] [Google Scholar]
- T. Morales de Luna, M.J. Castro Díaz and C. Parés Madroñal, A duality method for sediment transport based on a modified Meyer-Peter & Müller model. J. Sci. Comput. 48 (2010) 258–273. [Google Scholar]
- P.H. Morris and D.J. Williams, Relative celerities of mobile bed flows with finite solids concentrations. J. Hydr. Eng. 122 (1996) 311–315. [CrossRef] [Google Scholar]
- M.L. Muñoz Ruiz and C. Parés, On the convergence and Well-Balanced property of Path-conservative numerical schemes for systems of balance laws. J. Sci. Comput. 48 (2011) 274–295. [CrossRef] [Google Scholar]
- P. Nielsen, Coastal Bottom Boundary Layers and Sediment Transport. World Scientific Pub. Co. Inc. (1992). [Google Scholar]
- C. Parés, Numerical methods for nonconservative hyperbolic systems : a theoretical framework. SIAM J. Numer. Anal. 44 (2006) 300–321 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
- C. Parés and M.L. Muñoz Ruiz, On some difficulties of the numerical approximation of nonconservative hyperbolic systems. Bol. Soc. Esp. Mat. Apl. 47 (2009) 23–52. [Google Scholar]
- G. Parker, Y. Fukushima and H.M. Pantin, Self-accelerating turbidity currents. J. Fluid Mech. 171 (1986) 145–181. [Google Scholar]
- E.F. Toro, M. Spruce and W. Speares, Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 4 (1994) 25–34. [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- E.F. Toro, Shock-capturing methods for free-surface shallow flows. John Wiley (2001). [Google Scholar]
- L. Van Rijn, Sediment transport : bed load transport. J. Hydr. Eng. 110 (1984) 1431–1456. [Google Scholar]
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