Numerical modelling of two-layer shallow water flow in microtidal salt-wedge estuaries: Finite volume solver and field validation

Arita, M., Jirka, G.H., 1987. Two-layer model of saline wedge. II: Prediction. J. Hydraul. Eng., 113, 10, 1249-1263.10.1061/(ASCE)0733-9429(1987)113:10(1249)Search in Google Scholar

Armi, L., 1986. The hydraulics of two flowing layers with different densities. J. Fluid Mech., 163, 27-58.10.1017/S0022112086002197Search in Google Scholar

Balloffet, A., Borah, D.K., 1985. Lower Mississippi Salinity Analysis. J. Hydraul. Eng., 111, 2, 300-315.10.1061/(ASCE)0733-9429(1985)111:2(300)Search in Google Scholar

Bermudez, A., Vázquez-Cendón, M., 1994. Upwind methods for hyperbolic conservation laws with source terms. Comput. Fluids, 23, 8, 1049-1071.10.1016/0045-7930(94)90004-3Search in Google Scholar

Brufau, P., 2002. A numerical model for the flooding and drying of irregular domains. Int. J. Numer. Methods Fluids, 39, 3, 247-275.10.1002/fld.285Search in Google Scholar

Castro, M.J., Macias, J., Parés, C., 2001. A Q-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1D shallow water system. ESAIM Math. Model. Numer. Anal., 35, 1, 107-127.10.1051/m2an:2001108Search in Google Scholar

Castro, M.J., Garcia-Rodriguez, J., González-Vida, J.M., Macas, J., Parés, C., Vázquez-Cendón, M., 2004. Numerical simulation of two-layer shallow water flows through channels with irregular geometry. J. Comput. Phys., 195, 1, 202-235.10.1016/j.jcp.2003.08.035Search in Google Scholar

Castro, M.J., Ferreiro Ferreiro, A., García-Rodríguez, J., González- Vida, J., Macas, J., Parés, C., Elena Vázquez-Cendón, M., 2005. The numerical treatment of wet/dry fronts in shallow flows: application to one-layer and two-layer systems. Math. Comput. Model., 42, 3-4, 419-439.10.1016/j.mcm.2004.01.016Search in Google Scholar

Castro, M.J., Gonzales-Vida, J., Pares, C., 2006. Numerical treatment of wet/dry fronts in shallow flows with a modified Roe scheme. Math. Models Methods Appl. Sci., 16, 6, 897-934.10.1142/S021820250600139XSearch in Google Scholar

Castro, M.J., García-Rodríguez, J.A., González-Vida, J.M., Macas, J., Parés, C., 2007. Improved FVM for two-layer shallow-water models: Application to the Strait of Gibraltar. Adv. Eng. Softw., 38, 6, 386-398.10.1016/j.advengsoft.2006.09.012Search in Google Scholar

Castro, M.J., Dumbser, M., Pares, C., Toro, E.F., 2009a. ADER schemes on unstructured meshes for nonconservative hyperbolic systems: applications to geophysical flows. Comp. & Fluids, 38, 1731-1748.10.1016/j.compfluid.2009.03.008Search in Google Scholar

Castro, M.J., Fernández-Nieto, E.D., Ferreiro, A.M., García- Rodríguez, J.A., Parés, C., 2009b. High order extensions of Roe schemes for two-dimensional nonconservative hyperbolic systems. Journal of Scientific Computing, 39, 1, 67-114.10.1007/s10915-008-9250-4Search in Google Scholar

Castro, M.J., Fernandez-Nieto, E.D., Gonzalez-Vida, J.M., Pares, C., 2011. Numerical treatment of the loss of hyperbolicity of the two-layer shallow-water system. J. Sci. Comput., 48, 1, 16-40.10.1007/s10915-010-9427-5Search in Google Scholar

Dazzi, R., Tomasino, M., 1974. Mathematical model of salinity intrusion in the delta of the Po River. Coast. Eng. Proc., 134, 2302-2321.10.9753/icce.v14.134Search in Google Scholar

Dermissis, V., Partheniades, E., 1985. Dominant shear stresses in arrested saline wedges. J. Waterw. Port, Coastal, Ocean Eng., 111, 4, 733-752.10.1061/(ASCE)0733-950X(1985)111:4(733)Search in Google Scholar

Farmer, D., Armi, L., 1986. Maximal two-layer exchange over a sill and through the combination of a sill and contraction with barotropic flow. J. Fluid Mech., 164, 53-76.10.1017/S002211208600246XSearch in Google Scholar

Geyer, W.R., Ralston, D.K., 2011. The dynamics of strongly stratified estuaries. In: Wolanski, E., McLusky, D. (Eds.): Treatise on Estuarine and Coastal Science, Volume 2, Elsevier, pp. 37-52.10.1016/B978-0-12-374711-2.00206-0Search in Google Scholar

Grubert, J., 1989. Interfacial mixing in stratified channel flows. J. Hydraul. Eng., 115, 7, 887-905.10.1061/(ASCE)0733-9429(1989)115:7(887)Search in Google Scholar

Hansen, D., Rattray Jr, M., 1966. New dimensions in estuary classification. Limnol. Oceanogr., 11, 3, 319-326.10.4319/lo.1966.11.3.0319Search in Google Scholar

Harten, A., 1984. On a class of high resolution total-variationstable finite-difference schemes. SIAM J. Numer. Anal., 21, 1, 1-23.10.1137/0721001Search in Google Scholar

Johnson, B., Boyd, M., Keulegan, G., 1987. A Mathematical Study of the Impact on Salinity Intrusion of Deepening the Lower Mississippi River Navigation Channel. Technical Report April, US Army Corps of Engineers, Vicksburg, Mississippi.Search in Google Scholar

Krvavica, N., Mofardin, B., Ruzic, I., Ozanic, N., 2012. Measurement and analysis of salinization at the Rječina estuary. Gradevinar, 64, 11, 923-933.10.14256/JCE.805.2012Search in Google Scholar

Liu, H., Yoshikawa, N., Miyazu, S., Watanabe, K., 2015. Influence of saltwater wedges on irrigation water near a river estuary. Paddy Water Environ., 13, 2, 179-189.10.1007/s10333-014-0419-1Search in Google Scholar

Ljubenkov, I., 2015. Hydrodynamic modeling of stratified estuary: case study of the Jadro River (Croatia). J. Hydrol. Hydromech., 63, 1, 29-37.10.1515/johh-2015-0001Search in Google Scholar

Rebollo, T.C., Dom, A., Fern, E.D., 2003. A family of stable numerical solvers for the shallow water equations with source terms. Comput. Methods Appl. Mech. Eng., 192, 1-2, 203-225.10.1016/S0045-7825(02)00551-0Search in Google Scholar

Roe, P., 1981. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys., 43, 2, 357-372.10.1016/0021-9991(81)90128-5Search in Google Scholar

Sargent, F.E., Jirka, G.H., 1987. Experiments on saline wedge. J. Hydraul. Eng., 113, 10, 1307-1323.10.1061/(ASCE)0733-9429(1987)113:10(1307)Search in Google Scholar

Schijf, J., Schönfeld, J., 1953. Theoretical considerations on the motion of salt and fresh water. In: Proc. Minnesota Int. Hydraul. Conv., ASCE, Minneapolis, Minnesota, pp. 321-333.Search in Google Scholar

Sierra, J.P., Sánchez-Arcilla, a., Figueras, P. a., González del Ro, J., Rassmussen, E.K., Mösso, C., 2004. Effects of discharge reductions on salt wedge dynamics of the Ebro River. River Res. Appl., 20, 1, 61-77.10.1002/rra.721Search in Google Scholar

Stommel, H.M., Farmer, H.G., 1952. On the nature of estuarine circulation, part 1, chap. 3 and 4. Technical report. Woods Hole Oceanographic Institution, Woods Hole, Massachusetts.Search in Google Scholar

Vázquez-Cendón, M.E., 1999. Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry. J. Comput. Phys., 148, 2, 497-526.10.1006/jcph.1998.6127Search in Google Scholar