Windowed Spatial Zooming in Finite‐Difference Ground Water Flow Models

Székely, Ferenc

doi:10.1111/j.1745-6584.1998.tb02188.x

Cited by 23 publications

(18 citation statements)

References 2 publications

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“…MODFLOW‐LGR solves these systems of equations iteratively: this ensures that the diagonal stencil of the MODFLOW coefficient matrix is preserved, so that the standard solvers of MODFLOW can be used to solve the resulting equation (Mehl and Hill 2005), and the errors observed for the TMR methods are reduced (Mehl and Hill 2002). However, the trade‐off of using the iterative method is that it can be time consuming (Mehl et al 2006) and that it requires relaxation to achieve convergence (Szekely 1998; Mehl and Hill 2002).…”

Section: The Modflow‐lgr Methodsmentioning

confidence: 99%

Evaluation of MODFLOW‐LGR in Connection with a Synthetic Regional‐Scale Model

Vilhelmsen¹,

Christensen

Mehl

2011

Groundwater

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This work studies costs and benefits of utilizing local-grid refinement (LGR) as implemented in MODFLOW-LGR to simulate groundwater flow in a buried tunnel valley interacting with a regional aquifer. Two alternative LGR methods were used: the shared-node (SN) method and the ghost-node (GN) method. To conserve flows the SN method requires correction of sources and sinks in cells at the refined/coarse-grid interface. We found that the optimal correction method is case dependent and difficult to identify in practice. However, the results showed little difference and suggest that identifying the optimal method was of minor importance in our case. The GN method does not require corrections at the models' interface, and it uses a simpler head interpolation scheme than the SN method. The simpler scheme is faster but less accurate so that more iterations may be necessary. However, the GN method solved our flow problem more efficiently than the SN method. The MODFLOW-LGR results were compared with the results obtained using a globally coarse (GC) grid. The LGR simulations required one to two orders of magnitude longer run times than the GC model. However, the improvements of the numerical resolution around the buried valley substantially increased the accuracy of simulated heads and flows compared with the GC simulation. Accuracy further increased locally around the valley flanks when improving the geological resolution using the refined grid. Finally, comparing MODFLOW-LGR simulation with a globally refined (GR) grid showed that the refinement proportion of the model should not exceed 10% to 15% in order to secure method efficiency.

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Section: The Modflow‐lgr Methodsmentioning

confidence: 99%

Evaluation of MODFLOW‐LGR in Connection with a Synthetic Regional‐Scale Model

Vilhelmsen¹,

Christensen

Mehl

2011

Groundwater

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“…Subsequently, NOD, photosynthesis, settling and re-suspension were added to the model, a breakthrough for the water quality evaluation model. In 1870s, the finite difference technology (Székely, 1998) was applied in calculations in the water quality model, to produce a high-dimension mathematical model. Along with progress of the high-dimension model, the water quality model developed from the single model to the comprehensive model boasting of higher reliability, predictability, comprehensiveness and scientificalness.…”

Section: Introductionmentioning

confidence: 99%

Research on Fast Evaluation Algorithm Based on Hopfield Neural Network

2017

Revista de la Facultad de Ingeniería

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The fast evaluation algorithm based on Hopfield neural network (HNN) was presented to solve problems of multiple influencing factors, complex evaluation mechanism, inaccurate evaluation results and slow evaluation process in water quality evaluation. In storage of evaluation criteria information, this algorithm performed orthogonal and symmetric processing of information to guarantee accurate storage of information and steady operation of the network. After storage of the evaluation criteria, the connection weights of the network were determined and the actual measured data input into the HNN model, where such data were evaluated in a fast manner. In addition, the stability of this algorithm was verified, proving that this fast learning algorithm could ensure steady operation of HNN, which converged to the minimum. The fast learning algorithm avoided modular calculations currently applied in the existing algorithms, to greatly reduce the computation. As a result, only one iterative calculation would be needed to obtain the correct water quality evaluation results, which significantly enhanced the speed of water quality evaluation. At the same time, this algorithm accurately saved the evaluation criteria to ensure correctness of the final evaluation results. Finally, this algorithm was applied in surface water environmental quality evaluation and eutrophic water quality evaluation and compared with other algorithms, leading to the conclusion that this algorithm could evaluate water quality of different kinds in a fast and accurate manner.Keywords:fast evaluation, Hopfield network, water quality. 1.INTRODUCTIONSocial and economic development, especially development of industries, has severely contaminated water bodies, and then endangered human health. Severe water pollution will hamper sustainable development of the society and economy, in which case, protection of water environment has become an urgent task. In protection and treatment of the water environment, water quality evaluation is the most basic but the foremost section. Water quality evaluation is to analyze the general conditions of the water environment quality quantitatively. Accuracy of water quality evaluation has direct influence on implementation and effect of sewage treatment. In this sense, it will be of great significance to make correct evaluation on water quality.The water environment system is a complicated, changing, and time-varying nonlinear system. Thus a proper evaluation model and method will be needed to correctly evaluate the water quality. In 1925, Streeter and Phepls (Rinaldi et al., 1979) proposed the earliest water quality model, which was a deterministic mathematical model that only considered BOD and DO and neglected the rest water quality parameters. Based on this model, new progress was made to add temperature as the state variable, so as to evaluate more complicated systems, but the number of water quality parameters considered was still too small. Subsequently, NOD, photosynthesis, settling and re-

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“…The author has developed an iterative, multi-mesh, windowed spatial zooming method (Székely, 1998) allowing for coupling four embedded or nested meshes (models). Homogeneous formation, steady state, three-dimensional (3D) flow is considered, the meshes of different lateral and vertical resolution exhibit telescopic layout and fully penetrate the formation.…”

Section: Introductionmentioning

confidence: 99%

“…The head or drawdown of child nodes located between the coinciding nodes in lateral direction can be calculated by means of interpolation. Linear interpolation can be applied for vertical interfaces (Székely, 1998). Fig.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional mesh resolution control in finite difference groundwater flow models through boxed spatial zooming

Székely¹

2008

Journal of Hydrology

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Windowed Spatial Zooming in Finite‐Difference Ground Water Flow Models

Cited by 23 publications

References 2 publications

Evaluation of MODFLOW‐LGR in Connection with a Synthetic Regional‐Scale Model

Evaluation of MODFLOW‐LGR in Connection with a Synthetic Regional‐Scale Model

Research on Fast Evaluation Algorithm Based on Hopfield Neural Network

Three-dimensional mesh resolution control in finite difference groundwater flow models through boxed spatial zooming

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