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This paper makes an attempt to develop a Hausdorff fractal derivative model for describing the vertical distribution of suspended sediment in unsteady flow. The index of Hausdorff fractal derivative depends on the spatial location and the temporal moment in sediment transport. We also derive the approximate solution of the Hausdorff fractal derivative advection-dispersion equation model for the suspended sediment concentration distribution, to simulate the dynamics procedure of suspended concentration. Numerical simulation results verify that the Hausdorff fractal derivative model provides a good agreement with the experimental data, which implies that the Hausdorff fractal derivative model can serve as a candidate to describe the vertical distribution of suspended sediment concentration in unsteady flow.

Artificial bee colony (ABC) is an efficient swarm intelligence algorithm, which has shown good exploration ability. However, its exploitation capacity needs to be improved. In this paper, a novel ABC variant with recombination (called RABC) is proposed to enhance the exploitation. RABC firstly employs a new search model inspired by the updating equation of particle swarm optimization (PSO). Then, both the new search model and the original ABC model are recombined to build a hybrid search model. The effectiveness of the proposed RABC is validated on ten famous benchmark optimization problems. Experimental results show RABC can significantly improve the quality of solutions and accelerate the convergence speed.

A coupled regional and local model is required when groundwater flow and solute transport are to be simulated in local areas of interest with a finer grid while regional aquifer boundary and major stresses should be retained with a coarser grid. The coupled model should also maintain interactions between the regional and local flow systems. In the Beijing Plain (China), assessment of managed aquifer recharge (MAR), groundwater pollution caused by rivers, capture zone of well fields, and land subsidence at the cone of depression requires a coupled regional and local model. This study evaluates three methods for coupling regional and local flow models for simulating MAR in the Chaobai River catchment in the Beijing Plain. These methods are the conventional grid refinement (CGR) method, the local grid refinement (LGR) method and the unstructured grid (USG) method. The assessment included the comparison of the complexity of the coupled model construction, the goodness of fit of the computed and observed groundwater heads, the consistency of regional and local groundwater budgets, and the capture zone of a well filed influenced by the MAR site. The results indicated that the CGR method based on MODFLOW-2005 is the easiest to implement the coupled model, capable of reproducing regional and local groundwater heads and budget, and already coupled with density and viscosity dependent model codes for transport simulation. However, the CGR method inherits shortcomings of finite difference grids to create multiple local models with inefficient computing efforts. The USG method based on MODFLOW-USG has the advantage of creating multi-scale models and is flexible to simulate rivers, wells, irregular boundaries, heterogeneities and the MAR site. However, it is more difficult to construct the coupled models with the unstructured grids, therefore, a good graphic user interface is necessary for efficient model construction. The LGR method based on MODFLOW-LGR can be used to create multiple local models in uniform aquifer systems. So far, little effort has been devoted to upgrade the LGR method for complex aquifer structures and develop the coupled transport models.

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