J Lake Sci 2011 23 6 893-902 http //www jlakes org E-mail jlakes@niglas accn 2011 by Journal of Lake Sciences * 210008 HLLC 1998 2008 1-10 Two-dimensional numerical simulation of hydrodynamic and pollutant transport for Lake Poyang LAI Xijun JIANG Jiahu HUANG Qun & XU Ligang State Key Laboratory of Lake Science and Environment Nanjing Institute of Geography and Limnology Chinese Academy of Sciences Nanjing 210008 P R China Abstract The present study aims to develop a mathematical model for analyzing and predicting the hydrodynamic and water quality in one large lake Lake Poyang with great and rapid stage fluctuation the complex topography and geometry the complicated connectivity of narrow channels and depressions inside the lake the frequently switch between exposed grass beach and water Based on the two-dimensional shallow water equations and pollutant transport equations the coupled two-dimensional hydrodynamic and pollutant transport model is developed The unstructured finite volume method is applied to discretize the equations The normal water mass momentum and pollutant fluxes are computed by the HLLC solver The water front moving boundary is identified automatically by the judgment of the latest water stage It makes the model be capable of simulating the complex flow regime and the dynamic of pollutant transport in the lake with drying and wetting processes The hydrodynamic model is calibrated by the water regime of the year 1998 Based on the calibrated hydraulic parameters the hydrodynamic and water quality COD Mn and ammonia from January to October in 2008 are simulated by the proposed model The time series data of measured water stage COD Mn and ammonia and remotely water extent of CBERS data are both used to validate the results of computation in time and space The results indicate that the model has the capability to model the flows dynamic and the pollutant transport in this kind of lake Keywords Hydrodynamics water quality mathematical model unstructured grids Lake Poyang 1 Princeton ocean 2 - model 3 * KZCX1 - YW - 08-01 50709034 2011-01 - 07 2011-05 - 05 1977 E-mail xjlai@ niglas ac cn
894 J Lake Sci 2011 23 6 20 4-8 1 16 2 10 4 km 2 8 91-14 04 m 21 69 m 2933 km 2 5 1 m 21 d 1 Fig 1 The water system of Lake Poyang and main monitoring stations for water quality WASP 9-11 12-15
895 1 1 1 U = U t h hu F hv x = hφ + F U = S 1 hu hu 2 huv huφ + gh2 2 F y = hv huv hv 2 hvφ + gh2 2 0 gh S 0x - S fx + 2 ε ρ hu + c ρ a w ω 2 sin α + fvh ρ 2 S = gh S 0y - S fy + 2 ε ρ hv + c ρ a w ω 2 cos α - fuh ρ 2 x ( D φxh φ x ) + y ( D φyh φ y ) - K φhφ + Sφ h u v x y φ COD Mn F x x F y y S S 0x = - z b x x S 0y = - z b y y S fx = ρn 2 h - 4 3 u 槡 u 2 + v 2 x S fy = ρn 2 h - 4 3 v 槡 u 2 + v 2 y c w ρ a ω α y D φx D φy x y K φ φ S φ 1 2 1 2 1 V A t V UdV = - A F U nda + V SdV 2 n A F φ n U n +1 = U n - Δt T θ -1 F ΔV Σm j U A j + Δt S 3 j = 1 ΔV m A j j S j F n j = F j U n 1 2 2 3 x' - y'
896 J Lake Sci 2011 23 6 x' U t + F U = 0 4 x U x 0 = U L x < 0 { U R x > 0 5 x' n 2 U q U L U R U t = 0 t = 0 + x' = 0 F LR = F U L U R x - y HLLC 9 F LR 2 Fig 2 Cell of finite volume method F HLLC LR = { F L 0 S L F L + S L U * L - U L S L 0 S * F R + S R U * R - U R S * 0 S R F R S R 0 6 S S L S * S R Roe 16 L - U L U * L = h L 1 S S L - S * v L * φ L T U * R 1 2 3 U L U R 11 Neumann 1 2 4 L R 8 3 3a - 3d h L > ε a h R < Z bl + ε b h R > Z bl + ε h L < ε c h R < Z bl + ε d h R > Z bl + ε 3e - 3h 2 2 1
897 3 Fig 3 Possible water depth across cell interface 4 9877 9656 30 m 2000 m 1 25000 2 2 4 Fig 4 Computational grids Neumann
898 J Lake Sci 2011 23 6 2 3 1998 n n = n 0 h α n 0 1 m h α 1998 n 0 = 0 022 α = - 1 /6 5 Nash 0 94 0 97 0 91 1 00 5 1998 Fig 5 The calibration of hydrodynamic model of Lake Poyang 1998 3 3 1 2008 1-10 2008 1-10 ε 0 001 m COD Mn COD Mn 0 02 0 01 d - 1 3 2 6
899 6 Fig 6 The stage comparison between computation circle and measurements line in main stations of Lake Poyang CBERS CCD 113 km 20 m 16 01 m 7 CBERS 3 3 12 COD Mn 8 COD Mn COD Mn COD Mn COD Mn 4 6 4-6 5 mg /L 6
900 J Lake Sci 2011 23 6 7 Fig 7 Comparison of the computed left and remotely observed water extent right at different time instants COD Mn 9 4 HLLC 2008 1-10 1998 2008
901 8 COD Mn Fig 8 Comparison of computed and measured COD Mn and ammonia concentrations in the main stations of Lake Poyang
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