Phosphorus is the primary factor that limits eutrophication of surface waters in aquatic environments. Sediment particles have a strong affinity to phosphorus due to the high specific surface areas and surface active sites. In this paper, a numerical model containing hydrodynamics, sediment, and phosphorus module based on improved Langmuir equation is established, where the processes of adsorption and desorption are considered. Through the statistical analysis of the physical experiment data, the fitting formulas of two important parameters in the Langmuir equation are obtained, which are the adsorption coefficient, $k_a$, and the ratio k between the adsorption coefficient and the desorption coefficient. In order to simulate the experimental flume and get a constant and uniform water flow, a periodical numerical flume is built by adding a streamwise body force, $F_x$. The adsorbed phosphorus by sediment and the dissolved phosphorus in the water are separately added into the Advection Diffusion equation as a source term to simulate the interaction between them. The result of the numerical model turns out to be well matched with that of the physical experiment and can thus provide the basis for further analysis. With the application of the numerical model to some new and relative cases, the conclusion will be drawn through an afterwards analysis. The concentration of dissolved phosphorus proves to be unevenly distributed along the depth and the maximum value approximately appears in the 3/4 water depth because both the high velocity in the top layer and the high turbulence intensity in the bottom layer can promote sediment adsorption on phosphorus.

The simulation-optimization method, integrating the numerical model and the evolutionary algorithm, is increasingly popular for identifying the release history of groundwater contaminant sources. However, due to the usage of computationally intensive evolutionary algorithms, traditional simulation-optimization methods always require thousands of simulations to find appropriate solutions. Such methods yield a prohibitive computational burden if the simulation involved is time-consuming. To reduce general computation, this study proposes a novel simulation-optimization method for solving the inverse contaminant source identification problems, which uses surrogate models to approximate the numerical model. Unlike many existing surrogate-assisted methods using the pre-determined surrogate model, this paper presents an adaptive surrogate technique to construct the most appropriate surrogate model for the current numerical model. Two representative cases about identifying the release history of contaminant sources are used to investigate the accuracy and robustness of the proposed method. The results indicate that the proposed adaptive surrogate-assisted method effectively identifies the release history of groundwater contaminant sources with a higher degree of accuracy and shorter computation time than traditional methods.

Phosphorus is the main limiting factor in river eutrophication, whose distribution law is affected by sediment and hydrodynamics. Based on the sediment of Wujiadu Hydrological Station in the middle reaches of the Huaihe River, a physical experiment of phosphorus adsorption onto sediment in a dynamic environment was carried out in this paper to obtain two important parameters of the water quality model. By considering the effect of adsorption and desorption, diffusion, sedimentation and suspension, a numerical model of a three-dimensional periodic flume was established, verified and then applied to the generalized river according to the shape of the cross section in the Bengbu reach of the Huaihe River. The spatial-temporal distribution law of phosphorus was obtained with different single inflow factors. When DP or AP changed, the overall trend of downstream DP was consistent with that of incoming DP/AP; however, it became more complex when SS or Q changed, which aggravated the sedimentation and re-suspension process. When incoming DP changed, $D{P}_{\max }$ decreased with the distance, while when incoming AP or SS changed, $D{P}_{\max }$ increased at first and then decreased. The relationship between $\Delta D{P}_{\max }$ and $\Delta T{P}_{\mathrm{in}}$ was fitted into a straight line with a slope of 0.9951, while it was 0.2154 with the change of incoming SS. The effect of the not-constant time of the inflow on the peak concentration of phosphorus along the river was much weaker than that of the peak concentration.