Free Access
Volume 47, Number 1, January-February 2013
Page(s) 1 - 32
Published online 31 July 2012
  1. R. Abgrall and S. Karni, A comment on the computation of non-conservative products. J. Comput. Phys. 229 (2010) 2759–2763. [CrossRef] [MathSciNet]
  2. M.S. Altinaker, W.H. Graf and E. Hopfinger, Flow structure in turbidity currents. J. Hydr. Res. 34 (1996) 713–718. [CrossRef]
  3. 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).
  4. S.F. Bradford and N.D. Katopodes, Hydrodynamics of turbid underflows. i : Formulation and numerical analysis. J. Hydr. Eng. 125 (1999) 1006–1015. [CrossRef]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. 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. [CrossRef]
  10. G. Dal Maso, P.G. Lefloch and F. Murat, Definition and weak stability of nonconservative products. J. Math. Pures Appl. 74 (1995) 483–548.
  11. F. Exner, Über die wechselwirkung zwischen wasser und geschiebe in flüssen. Sitzungsber., Akad. Wissenschaften IIa (1925).
  12. 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.
  13. A.C. Fowler, N. Kopteva and C. Oakley, The formation of river channels. SIAM J. Appl. Math. 67 (2007) 1016–1040. [CrossRef] [MathSciNet]
  14. 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]
  15. A. Grass, Sediment transport by waves and currents. SERC London Cent. Mar. Technol. Report No. FL29 (1981).
  16. A. Harten, P.D. Lax and B. van Leer, On upstream differencing and godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 25 (1983).
  17. T.Y. Hou and P.G. Le Floch, Why nonconservative schemes converge to wrong solutions : error analysis. Math. Comput. 62 (1994) 497–530. [CrossRef] [MathSciNet]
  18. S.M. Khan, J. Imran, S. Bradford and J. Syvitski, Numerical modeling of hyperpycnal plume. Mar. Geol. 222-223 (2005) 193–211. [CrossRef]
  19. 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]
  20. Y. Kubo and T. Nakajima, Laboratory experiments and numerical simulation of sediment-wave formation by turbidity currents. Mar. Geol. 192 (2002) 105–121. [CrossRef]
  21. D.A. Lyn and M. Altinakar, St. Venant-Exner equations for Near-Critical and transcritical flows. J. Hydr. Eng. 128 (2002) 579–587. [CrossRef]
  22. E. Meyer-Peter, and R. Müller, Formulas for bed-load transport, in 2nd meeting IAHSR. Stockholm, Sweden (1948) 1–26.
  23. 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]
  24. 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. [CrossRef]
  25. 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]
  26. 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]
  27. P. Nielsen, Coastal Bottom Boundary Layers and Sediment Transport. World Scientific Pub. Co. Inc. (1992).
  28. C. Parés, Numerical methods for nonconservative hyperbolic systems : a theoretical framework. SIAM J. Numer. Anal. 44 (2006) 300–321 (electronic). [CrossRef] [MathSciNet]
  29. 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.
  30. G. Parker, Y. Fukushima and H.M. Pantin, Self-accelerating turbidity currents. J. Fluid Mech. 171 (1986) 145–181. [CrossRef]
  31. 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]
  32. E.F. Toro, Shock-capturing methods for free-surface shallow flows. John Wiley (2001).
  33. L. Van Rijn, Sediment transport : bed load transport. J. Hydr. Eng. 110 (1984) 1431–1456. [CrossRef]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you