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Preface
Multilayer Saint-Venant equations over movable beds
1. | LAGA, Université Paris 13, 99 Av J.B. Clement, 93430 Villetaneuse, France, France |
2. | Laboratoire d’Hydraulique Saint-Venant, 6 Quai Watier, BP 49, 78401 Chatou, France |
3. | School of Engineering and Computing Sciences, University of Durham, South Road, Durham DH1 3LE, United Kingdom |
References:
[1] |
E. Audusse and M. O. Bristeau, A well-balanced positivity preserving second order scheme for shallow water flows on unstructured meshes, JCP, 206 (2005), 311-333.
doi: doi:10.1016/j.jcp.2004.12.016. |
[2] |
E. Audusse, F. Bouchut, M. O. Bristeau, R. Klein and B. Perthame, A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows, SIAM J. Sci. Comp., 25 (2004), 2050-2065.
doi: doi:10.1137/S1064827503431090. |
[3] |
E. Audusse, M. O. Bristeau, B. Perthame and J. Sainte-Marie, "A Multilayer Saint-Venant Model With Mass Exchange: Derivation and Numerical Validation," M2AN, 2010, in press. |
[4] |
F. Benkhaldoun, S. Sahmim and M. Seaid, A two-dimensional finite volume morphodynamic model on unstructured triangular grids, Int. J. Num. Meth. Fluids, 63 (2010), 1296-1327. in press. |
[5] |
F. Bouchut and T. Morales de Luna, An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment, M2AN, 42 (2008), 683-698. |
[6] |
F. Benkhaldoun, S. Sahmim and M. Seaid, Solution of the sediment transport equations using a finite volume method based on sign matrix, SIAM J. Sci. Comp., 31 (2009), 2866-2889.
doi: doi:10.1137/080727634. |
[7] |
A. Bermúdez, C. Rodríguez and M. A. Vilar, Solving shallow water equations by a mixed implicit finite element method, IMA J Numer Anal., 11 (1991), 79-97.
doi: doi:10.1093/imanum/11.1.79. |
[8] |
M. J. Castro, J. Macías and C. Parés, A Q-scheme for a class of coupled conservation laws with source term. Application to a two-layer 1d shallow water system, M2AN, 35 (2001), 107-127. |
[9] |
A. Crotogino and K. P. Holz, Numerical movable-bed models for practical engineering, Applied Mathematical Modelling, 8 (1984), 45-49.
doi: doi:10.1016/0307-904X(84)90176-8. |
[10] |
J. A. Dutton, "The Ceaseless Wind: An Introduction to the Theory of Atmospheric Motion," Dover Publications Inc, 1987. |
[11] |
A. J. Grass, "Sediment Transport by Waves and Currents," SERC London Cent. Mar. Technol. Report No: FL29, 1981. |
[12] |
J. Hudson and P. K. Sweby, Formations for numerically approximating hyperbolic systems governing sediment transport, J. Scientific Computing, 19 (2003), 225-252.
doi: doi:10.1023/A:1025304008907. |
[13] |
E. Meyer-Peter and R. Müller, Formulas for bed-load transport, In: Report on 2nd meeting on international association on hydraulic structures research, Stockholm., 8 (1948), 39-64. |
[14] |
E. Miglio, A. Quarteroni and F. Saleri, Finite element approximation of quasi-3D shallow water equations, Computer Methods in Applied Mechanics and Engineering, 174 (1999), 355-369.
doi: doi:10.1016/S0045-7825(98)00304-1. |
[15] |
B. Perthame, "Kinetic Formulation of Conservation Laws," Oxford University Press, 2004. |
[16] |
D. Pritchard and A. J. Hogg, On sediment transport under dam-break flow, J. Fluid Mech., 473 (2002), 265-274.
doi: doi:10.1017/S0022112002002550. |
[17] |
G. Rosatti and L. Fraccarollo, A well-balanced approach for flows over mobile-bed with high sediment-transport, J. Comput. Physics, 220 (2006), 312-338.
doi: doi:10.1016/j.jcp.2006.05.012. |
[18] |
G. K. Vallis, "Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation," Cambridge University Press, 2006.
doi: doi:10.1017/CBO9780511790447. |
show all references
References:
[1] |
E. Audusse and M. O. Bristeau, A well-balanced positivity preserving second order scheme for shallow water flows on unstructured meshes, JCP, 206 (2005), 311-333.
doi: doi:10.1016/j.jcp.2004.12.016. |
[2] |
E. Audusse, F. Bouchut, M. O. Bristeau, R. Klein and B. Perthame, A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows, SIAM J. Sci. Comp., 25 (2004), 2050-2065.
doi: doi:10.1137/S1064827503431090. |
[3] |
E. Audusse, M. O. Bristeau, B. Perthame and J. Sainte-Marie, "A Multilayer Saint-Venant Model With Mass Exchange: Derivation and Numerical Validation," M2AN, 2010, in press. |
[4] |
F. Benkhaldoun, S. Sahmim and M. Seaid, A two-dimensional finite volume morphodynamic model on unstructured triangular grids, Int. J. Num. Meth. Fluids, 63 (2010), 1296-1327. in press. |
[5] |
F. Bouchut and T. Morales de Luna, An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment, M2AN, 42 (2008), 683-698. |
[6] |
F. Benkhaldoun, S. Sahmim and M. Seaid, Solution of the sediment transport equations using a finite volume method based on sign matrix, SIAM J. Sci. Comp., 31 (2009), 2866-2889.
doi: doi:10.1137/080727634. |
[7] |
A. Bermúdez, C. Rodríguez and M. A. Vilar, Solving shallow water equations by a mixed implicit finite element method, IMA J Numer Anal., 11 (1991), 79-97.
doi: doi:10.1093/imanum/11.1.79. |
[8] |
M. J. Castro, J. Macías and C. Parés, A Q-scheme for a class of coupled conservation laws with source term. Application to a two-layer 1d shallow water system, M2AN, 35 (2001), 107-127. |
[9] |
A. Crotogino and K. P. Holz, Numerical movable-bed models for practical engineering, Applied Mathematical Modelling, 8 (1984), 45-49.
doi: doi:10.1016/0307-904X(84)90176-8. |
[10] |
J. A. Dutton, "The Ceaseless Wind: An Introduction to the Theory of Atmospheric Motion," Dover Publications Inc, 1987. |
[11] |
A. J. Grass, "Sediment Transport by Waves and Currents," SERC London Cent. Mar. Technol. Report No: FL29, 1981. |
[12] |
J. Hudson and P. K. Sweby, Formations for numerically approximating hyperbolic systems governing sediment transport, J. Scientific Computing, 19 (2003), 225-252.
doi: doi:10.1023/A:1025304008907. |
[13] |
E. Meyer-Peter and R. Müller, Formulas for bed-load transport, In: Report on 2nd meeting on international association on hydraulic structures research, Stockholm., 8 (1948), 39-64. |
[14] |
E. Miglio, A. Quarteroni and F. Saleri, Finite element approximation of quasi-3D shallow water equations, Computer Methods in Applied Mechanics and Engineering, 174 (1999), 355-369.
doi: doi:10.1016/S0045-7825(98)00304-1. |
[15] |
B. Perthame, "Kinetic Formulation of Conservation Laws," Oxford University Press, 2004. |
[16] |
D. Pritchard and A. J. Hogg, On sediment transport under dam-break flow, J. Fluid Mech., 473 (2002), 265-274.
doi: doi:10.1017/S0022112002002550. |
[17] |
G. Rosatti and L. Fraccarollo, A well-balanced approach for flows over mobile-bed with high sediment-transport, J. Comput. Physics, 220 (2006), 312-338.
doi: doi:10.1016/j.jcp.2006.05.012. |
[18] |
G. K. Vallis, "Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation," Cambridge University Press, 2006.
doi: doi:10.1017/CBO9780511790447. |
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