References
- Afshar, A., Kazemi, H., & Saadatpour, M. (2011). Particle swarm optimization for automatic calibration of large scale water quality model (CE-QUAL-W2): Application to Karkheh Reservoir, Iran. Water Resources Management, 25(10), 2613–2632. https://doi.org/10.1007/s11269-011-9829-7
- Ahmed, N., & Sunada, D. K. (1969). Nonlinear flow in porous media. Journal of the Hydraulics Division, 95(6), 1847–1858. https://doi.org/10.1061/JYCEAJ.0002193
- Bari, R., & Hansen, D. (2002). Application of gradually-varied flow algorithms to simulate buried streams. Journal of Hydraulic Research, 40(6), 673–683. https://doi.org/10.1080/00221680209499914
- Bazargan, J., & Bayat, Н. (2002a). Determination of the nonlinear equation coefficients for flow through coarse Alluvium foundations. Journal of Esteghla, 21, 101–112. (In Persian language).
- Bazargan, J., & Byatt, H. (2002b). A new method to supply water from the sea through rockfill intakes. 5th International Conference on Coasts, Ports and Marine Structures (ICOPMAS) (pp. 14–17) (In Persian language).
- Bazargan, J., & Norouzi, H. (2018). Investigation the effect of using variable values for the parameters of the linear Muskingum method using the Particle Swarm Algorithm (PSO). Water Resources Management, 32(14), 4763–4777. https://doi.org/10.1007/s11269-018-2082-6
- Bazargan, J., & Shoaei, S. M. (2006). Discussion, “application of gradually varied flow algorithms to simulate buried streams”. Journal of Hydraulic Research, 44(1), 138–141. https://doi.org/10.1080/00221686.2006.9521669
- Bordier, C., & Zimmer, D. (2000). Drainage equations and non-Darcian modelling in coarse porous media or geosynthetic materials. Journal of Hydrology, 228(3–4), 174–187. S0022169400001517. https://doi.org/10.1016/S0022-1694(00)00151-7
- Burcharth, H. F., & Andersen, O. K. (1995). On the one-dimensional steady and unsteady porous flow equations. Coastal Engineering, 24(3–4), 233–257. https://doi.org/10.1016/0378-3839(94)00025-S
- Chau, K. (2005). A split-step PSO algorithm in prediction of water quality pollution. International Symposium on Neural Networks (pp. 1034–1039). Springer, Berlin, Heidelberg.
- Chau, K. W. (2007). A split-step particle swarm optimization algorithm in river stage forecasting. Journal of Hydrology, 346(3–4), 131–135. https://doi.org/10.1016/j.jhydrol.2007.09.004
- Chen, Z., Lyons, S. L., & Qin, G. (2001). Derivation of the Forchheimer law via homogenization. Transport in Porous Media, 44(2), 325–335. https://doi.org/10.1023/A:1010749114251
- Cheng, N. S., Hao, Z., & Tan, S. K. (2008). Comparison of quadratic and power law for nonlinear flow through porous media. Experimental Thermal and Fluid Science, 32(8), 1538–1547. https://doi.org/10.1016/j.expthermflusci.2008.04.007
- Chow, V. T., Maidment, D. R., & Mays, L. W. (1988). Applied hydrology. McGraw-Hill International Editions.
- Chow, V. (1959). Open channel hydraulics. Macgraw-Hill Book Company.
- Chu, H. J., & Chang, L. C. (2009). Applying particle swarm optimization to parameter estimation of the nonlinear Muskingum model. Journal of Hydrologic Engineering, 14(9), 1024–1027. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000070
- Clerc, M., & Kennedy, J. (2002). The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, 6(1), 58–73. https://doi.org/10.1109/4235.985692
- Di Nucci, C. (2018). Unsteady free surface flow in porous media: One-dimensional model equations including vertical effects and seepage face. Comptes Rendus Mécanique, 346(5), 366–383. https://doi.org/10.1016/j.crme.2018.03.003
- Engelund, F. (1953). On the laminar and turbulent flows of ground water through homogeneous sand. Akad. for de Tekniske Videnskaber.
- Ergun, S. (1952). Fluid flow through packed columns. Chemical Engineering Progress, 48, 89–94.
- Ferrick, M. G. (1985). Analysis of river wave types. Water Resources Research, 21(2), 209–220. https://doi.org/10.1029/WR021i002p00209
- Gurarslan, G., & Karahan, H. (2011). Parameter estimation technique for the nonlinear Muskingum flood routing model. 6thEWRA International Symposium-Water Engineering and Management in a Changing Environment, Catania, Italy.
- Haizhou, T., & Graf, W. H. (1993). Friction in unsteady open-channel flow over gravel beds. Journal of Hydraulic Research, 31(1), 99–110. https://doi.org/10.1080/00221689309498863
- Hall, K., Smith, G. M., & Turcke, D. J. (1994). Development of a non-linear porous media relationship for oscillatory unsteady flow. Journal of Coastal Research, 10(1), 158–169. https://www.jstor.org/stable/4298200
- Hannoura, A. A., & McCorquodale, J. A. (1985). Rubble mounds: Hydraulic conductivity equation. Journal of Waterway, Port, Costal and Ocean Engineering, ASCE, 111(5), 783–799. https://doi.org/10.1061/(ASCE)0733-950X(1985)111:5(783)
- Hansen, D., Garga, V. K., & Townsend, D. R. (1995). Selection and application of a one-dimensional non-Darcy flow equation for two-dimensional flow through rockfill embankments. Canadian Geotechnical Journal, 32(2), 223–232. https://doi.org/10.1139/t95-025
- Hassanizadeh, S. M., & Gray, W. G. (1987). High velocity flow in porous media. Transport in Porous Media, 2(6), 521–531. https://doi.org/10.1007/BF00192152
- Herrera, N. M., & Felton, G. K. (1991). Hydraulic of flow through the rock-fill Dam using sediment-free water. Transactions of the ASAE, 34(3), 0871–0875. https://doi.org/10.13031/2013.31742
- Higashino, M., & Stefan, H. G. (2011). Non-linear effects on solute transfer between flowing water and a sediment bed. Water Research, 45(18), 6074–6086. S0043135411005239. https://doi.org/10.1016/j.watres.2011.09.004
- Hosseini, S. M. (1997). Development of an unsteady non-linear model for flow through coarse porous media [PhD thesis, Dissertation]. University of Guelph.
- Hosseini, S. M. (2002). On the performance of different empirical loss equations for flow through coarse porous media (RESEARCH NOTE). International Journal of Engineering-Transactions B: Applications, 15(3), 249–254.
- Hosseini, S. M., & Joy, D. M. (2007). Development of an unsteady model for flow through coarse heterogeneous porous media applicable to valley fills. International Journal of River Basin Management, 5(4), 253–265. https://doi.org/10.1080/15715124.2007.9635325
- Irmay, S. (1958). On the theoretical derivation of Darcy and Forchheimer formulas. Eos, Transactions American Geophysical Union, 39(4), 702–707. https://doi.org/10.1029/TR039i004p00702
- Jain, S. C. (2001). Open-channel flow. John Wiley & Sons.
- Joy, D. M. (1991). Nonlinear porous media flow: Determination of parameters for a coarse granular media. In 13th Canadian Congress on Applied Mechanics. Winnipeg.
- Kadlec, R. H., & Knight, R. L. (1996). Treatment Wetlands. Lewis Publishers.
- Karahan, H. (2012). Determining rainfall-intensity-duration-frequency relationship using Particle Swarm Optimization. KSCE Journal of Civil Engineering, 16(4), 667–675. https://doi.org/10.1007/s12205-012-1076-9
- Katopodes, N. D. (1982). On zero-inertia and kinematic waves. Journal of the Hydraulics Division, 108(11), 1380–1387. https://doi.org/10.1061/JYCEAJ.0005939
- Kovács, G. (1981). Developments in water science: Seepage hydraulics (p. 730). Elsevier.
- Kumar, D. N., & Reddy, M. J. (2007). Multipurpose reservoir operation using particle swarm optimization. Journal of Water Resource Plan. Manage. ASCE, 133(3), 192–201. https://doi.org/10.1061/(ASCE)0733-9496(2007)133:3(192)
- Leps, T. M. (1973). Flow through rockfill in embankment dam engineering. R. Hirchfeld and S. Poulos (eds.). https://doi.org/10.1016/B978-0-444-41828-9.50007-7
- Lu, W. Z., Fan, H. Y., Leung, A. Y. T., & Wong, J. C. K. (2002). Analysis of pollutant levels in central Hong Kong applying neural network method with particle swarm optimization. Environmental Monitoring and Assessment, 79(3), 217–230. https://doi.org/10.1023/A:1020274409612
- McCorquodale, J. A., Hannoura, A. A. A., & Sam Nasser, M. (1978). Hydraulic conductivity of rockfill. Journal of Hydraulic Research, 16(2), 123–137. https://doi.org/10.1080/00221687809499625
- McWhorter, D. B., & Sunada, D. K. (1977). Groundwater hydrology and hydraulics (pp. 65–73). Water Resources Publication.
- Meraji, S. H. (2004). Optimum design of flood control systems by particle swarm optimization algorithm [Doctoral dissertation, MSc thesis]. Iran University of Science and Technology.
- Moghaddam, A., Behmanesh, J., & Farsijani, A. (2016). Parameters estimation for the new four-parameter nonlinear Muskingum model using the particle swarm optimization. Water Resources Management, 30(7), 2143–2160. https://doi.org/10.1007/s11269-016-1278-x
- Moramarco, T., Fan, Y., & Bras, R. L. (1999). Analytical solution for channel routing with uniform lateral inflow. Journal of Hydraulic Engineering, 125(7), 707–713. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:7(707)
- Moutsopoulos, K. N. (2007). One-dimensional unsteady inertial flow in phreatic aquifers induced by a sudden change of the boundary head. Transport in Porous Media, 70(1), 97–125. https://doi.org/10.1007/s11242-006-9086-z
- Nagesh Kumar, D., & Janga Reddy, M. (2007). Multipurpose reservoir operation using particle swarm optimization. Journal of Water Resources Planning and Management, 133(3), 192–201. https://doi.org/10.1061/(ASCE)0733-9496(2007)133:3(192)
- Norouzi, H., Bazargan, J. 2020. Flood routing by linear Muskingum method using two basic floods data using particle swarm optimization (PSO) algorithm. Water Supply.
- Polubarinova-Kočina, P. Ya. (1952). Theory of motion of ground water. Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow. 676 pp. (in Russian).
- Sadeghian, J., Khayat Kholghi, M., Horfar, A., & Bazargan, J. (2013). Comparison of binomial and power equations in radial non-Darcy flows in coarse porous media. Journal of Water Sciences Research, 5(1), 65–75.
- Salahi, M. B., Sedghi-Asl, M., & Parvizi, M. (2015). Nonlinear flow through a packed-column experiment. Journal of Hydrologic Engineering, 20, 9. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001166
- Samani, H. M., Samani, J. M., & Shaiannejad, M. (2003). Reservoir routing using steady and unsteady flow through rockfill dams. Journal of Hydraulic Engineering, 129(6), 448–454. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:6(448)
- Sedghi-Asl, M., & Ansari, I. (2016). Adoption of extended Dupuit–Forchheimer assumptions to non-Darcy flow problems. Transport in Porous Media, 113(3), 457–469. https://doi.org/10.1007/s11242-016-0703-1
- Sedghi-Asl, M., & Rahimi, H. (2011). Adoption of manning’s equation to 1D non-Darcy flow problems. Journal of Hydraulic Research, 49(6), 814–817. https://doi.org/10.1080/00221686.2011.629911
- Shi, Y., & Eberhart, R. (1998). A modified particle swarm optimizer. In 1998 IEEE international conference on evolutionary computation proceedings (pp. 69–73). IEEE world congress on computational intelligence (Cat. No. 98TH8360). IEEE. https://doi.org/10.1109/ICEC.1998.699146
- Shokri, M., Sabour, M., & Bayat, H. (2014). Concept of hydraulic porosity and experimental investigation in nonlinear flow analysis through Rubble-mound breakwaters. Journal of Hydrology, 508, 266–272. https://doi.org/10.1016/j.jhydrol.2013.11.005
- Shokri, M., Sabour, M., Bayat, H., & Sadeghian, J. (2012). Experimental investigation on nonlinear analysis of unsteady flow through coarse porous media. Journal of Water and Wastewater, 23(4), 106–115.
- Shourian, M., Mousavi, S. J., & Tahershamsi, A. (2008). Basin-wide water resources planning by integrating PSO algorithm and MODSIM. Water Resources Management, 22(10), 1347–1366. https://doi.org/10.1007/s11269-007-9229-1
- Sidiropoulou, M. G., Moutsopoulos, K. N., & Tsihrintzis, V. A. (2007). Determination of Forchheimer equation coefficients a and b. Hydrological Processes: An International Journal, 21(4), 534–554. https://doi.org/10.1002/hyp.6264
- Stephenson, D. J. (1979). Rockfill in hydraulic engineering. Elsevier Scientific Publishing Co.
- Straughan, B. (2010). Structure of the dependence of Darcy and Forchheimer coefficients on porosity. International Journal of Engineering Science, 48(11), 1610–1621. https://doi.org/10.1016/j.ijengsci.2010.04.012
- Venkataraman, P., & Rao, P. R. M. (1998). Darcian, transitional, and turbulent flow through porous media. Journal of Hydraulic Engineering, 124(8), 840–846. https://doi.org/10.1061/(ASCE)0733-9429(1998)124:8(840)
- Ward, J. C. (1964). Turbulent flow in porous media. Journal of the Hydraulics Division, 90(5), 1–12. https://doi.org/10.1061/JYCEAJ.0001096
- Zeng, Z., & Grigg, R. (2006). A criterion for non-Darcy flow in porous media. Transport in Porous Media, 63(1), 57–69. https://doi.org/10.1007/s11242-005-2720-3