Lattice Boltzmann simulation of depth-averaged models in flow hydraulics

References

• Almazán, J.I., Bryden, H., Kinder, T., and Parrilla, G., 1988. Seminario sobre la oceanografía física del estrecho de Gibraltar. Madrid: SECEG; 1988.
   Google Scholar
• Bermúdez, A., and Vázquez, M.E., 1994. Upwind methods for hyperbolic conservation laws with source terms, Computers and Fluids 23 (1994), pp. 1049–1071.
   Web of Science ®Google Scholar
• Bhatnagar, P., Gross, E., and Krook, M., 1954. A model for collision process in gases, Physical Review Letters 94 (1954), pp. 511–525.
   Web of Science ®Google Scholar
• Chen, S., and Doolen, G.D., 1998. Lattice Boltzmann method for fluid flows, Annual Review of Fluid Mechanics 30 (1998), pp. 329–364.
   Web of Science ®Google Scholar
• Dawson, S.P., Chen, S., and Doolen, G.D., 1993. Lattice Boltzmann computations for reaction–diffusion equations, Journal of Chemical Physics 98 (1993), pp. 1514–1523.
   Web of Science ®Google Scholar
• Dellar, P.J., 2002. Non-hydrodynamic modes and a priori construction of shallow water lattice Boltzmann equations, Physical Review E, Statistical Nonlinear and Soft Matter Physics 65 (036309) (2002), pp. 1–12.
   Google Scholar
• Feng, S., Zhao, Y., Tsutahara, M., and Ji, Z., 2002. Lattice Boltzmann model in rotational flow field, Chinese Journal of Geophysics 45 (2002), pp. 170–175.
   Web of Science ®Google Scholar
• Gallivan, M.A., Noble, D.R., Georgiads, J.G., and Buckius, R.O., 1997. An evaluation of the bounce-back boundary condition for lattice Boltzmann simulations, International Journal for Numerical Methods in Fluids 25 (1997), pp. 249–263.
   Web of Science ®Google Scholar
• Gómez, F., 2003. The role of the exchanges through the Strait of Gibraltar on the budget of elements in western Mediterranean sea: consequences of human-induced modifications, Marine Pollution Bulletin 46 (2003), pp. 685–694.
   PubMed Web of Science ®Google Scholar
• González, M., and Sánchez-Arcilla, A., 1995. Un Modelo numérico en elementos finitos para la corriente inducida por la marea. Aplicaciones al estrecho de Gibraltar., Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 11 (1995), pp. 383–400.
   Google Scholar
• Lafuente, J.G., Almazán, J.L., Catillejo, F., Khribeche, A., and Hakimi, A., 1990. Sea level in the Strait of Gibraltar: Tides, International Hydrographic Review LXVII 1 (1990), pp. 111–130.
   Google Scholar
• LeVeque, R.J., 1998. Balancing source terms and the flux gradients in high-resolution Godunov methods: the quasi-steady wave-propagation algorithm, Journal of Computational Physics 146 (1998), pp. 346–365.
   Web of Science ®Google Scholar
• Qian, Y.H., d'Humieres, D., and Lallemand, P., 1992. Lattice BGK Models for the Navier–Stokes equation, Europhysics Letters 17 (1992), pp. 479–484.
   Google Scholar
• Salmon, R., 1999a. The lattice Boltzmann method as a basis for ocean circulation modeling, Journal of Marine Research 57 (1999a), pp. 503–535.
   Web of Science ®Google Scholar
• Salmon, R., 1999b. The lattice Boltzmann solutions of the three-dimensional planetary geostrophic equations, Journal of Marine Research 57 (1999b), pp. 847–884.
   Web of Science ®Google Scholar
• Staniforth, A., and Cóté, J., 1991. Semi-Lagrangian integration schemes for the atmospheric models: A review, Weather Review 119 (1991), pp. 2206–2223.
   Web of Science ®Google Scholar
• Tejedor, L., Izquierdo, A., Kagan, B.A., and Sein, D.V., 1999. Simulation of the semidiurnal tides in the Strait of Gibraltar, Journal of Geophysical Research 104 (1999), pp. 13541–13557.
   Web of Science ®Google Scholar
• Thömmes, G., Seaïd, M., and Banda, M.K., 2007. Lattice Boltzmann methods for shallow water flow applications, International Journal for Numerical Methods in Fluids 55 (2007), pp. 673–692.
   Web of Science ®Google Scholar
• Toro, E.F., 1992. Riemann problems and the WAF method for solving two-dimensional shallow water equations, Philosophical Transactions Royal Society of London A 338 (1992), pp. 43–68.
   Web of Science ®Google Scholar
• Vázquez-Cendón, M.E., 1999. Improved treatment of source terms in upwind schemes for shallow water equations in channels with irregular geometry, Journal of Computational Physics 148 (1999), pp. 497–526.
   Web of Science ®Google Scholar
• Vukovic, S., and Sopta, L., 2002. ENO and WENO schemes with the exact conservation property for one-dimensional shallow-water equations, Journal of Computational Physics 179 (2002), pp. 593–621.
   Web of Science ®Google Scholar
• Xu, K., 2005. A well-balanced gas-kinetic scheme for the shallow-water equations with source terms, Journal of Computational Physics 22 (2005), pp. 349–358.
   Google Scholar
• Zhong, L., Feng, S., and Gao, S., 2001. Wind-driven ocean circulation in shallow water lattice Boltzmann model, Advanced in Atmospheric Science 178 (2001), pp. 533–562.
   Google Scholar
• Zhou, J.G., 1995. Velocity-depth coupling in shallow water flows, Journal of Hydraulic Engineering ASCE (1995), pp. 10717–10724.
   Google Scholar
• Zhou, J.G., 2002. A lattice Boltzmann model for the shallow water equations, Computer Methods in Applied Mechanics and Engineering 191 (2002), pp. 3527–3539.
   Web of Science ®Google Scholar
• Zou, Q., and He, X., 2002. On pressure and velocity boundary condition for the lattice Boltzmann BGK model, Physics of Fluids 9 (2002), pp. 1591–1598.
   Web of Science ®Google Scholar