Halil Karahan

Parameter Estimation of the Nonlinear Muskingum Flood-Routing Model Using a Hybrid Harmony Search Algorithm

AbstractIn this paper, a hybrid harmony search (HS) algorithm is proposed for the parameter estimation of the nonlinear Muskingum model. The BFGS algorithm is used as local search algorithm with a low probability for accelerating the HS algorithm. In the proposed technique, an indirect penalty function approach is imposed on the model to prevent negativity of outflows and storages. The proposed algorithm finds the global or near-global minimum regardless of the initial parameter values with fast convergence. The proposed algorithm found the best solution among 12 different methods. The results demonstrate that the proposed algorithm can be applied confidently to estimate optimal parameter values of the nonlinear Muskingum model. Moreover, this hybrid methodology may be applicable to any continuous engineering optimization problems.

Implicit finite difference techniques for the advection-diffusion equation using spreadsheets

This study proposes one-dimensional advection-diffusion equation (ADE) with finite differences method (FDM) using implicit spreadsheet simulation (ADEISS). By changing only the values of temporal and spatial weighted parameters with ADEISS implementation, solutions are implicitly obtained for the BTCS, Upwind and Crank-Nicolson schemes. The ADEISS uses iterative spreadsheet solution technique. Thus, it is not required a solution of simultaneous equations for each time step using matrix algebra. Two examples which, have the numerical and analytical solutions in literature, are solved in order to test the ADEISS performance. Both examples are solved for three schemes. It has been determined that the Crank-Nicolson scheme is in good agreement with the analytical solution; however the results of the BTCS and the Upwind schemes are lower than the analytical solution. The Upwind scheme suffers from considerably numerical diffusion whereas the BTCS scheme does not produce numerical diffusion. Thus, it provided better results than Upwind scheme which are closer to analytical results depending on the selected parameters. The ADEISS implementation is a computationally convenient procedure for the three well-known methods in the literature: The BTCS, Upwind and Crank-Nicolson.

Transient groundwater modeling using spreadsheets

This study proposes a transient groundwater modeling using spreadsheet simulation (TGMSS) model for solving groundwater problems. TGMSS may be considered as a practical method and introduction to groundwater modeling that uses spreadsheets instead of conventional groundwater model codes. Irregular aquifer geometry, variable boundary conditions and sinks and/or source values, heterogeneous aquifer parameters (conductivity, storage capacities), may be evaluated in the TGMSS. Different management scenarios may be analyzed by obtaining the groundwater level of different times. Two hypothetical examples are tested with TGMSS and verified with MODFLOW. Results showed that the TGMSS and MODFLOW results were in good agreement in terms of resulting values of hydraulic heads in all cases.

A new nonlinear Muskingum flood routing model incorporating lateral flow

A new nonlinear Muskingum flood routing model taking the contribution from lateral flow into consideration was developed in the present study. The cuckoo search algorithm, a quite novel and robust algorithm, was used in the calibration and verification of the model parameters. The success and the dependability of the proposed model were tested on five different sets of synthetic and real flood data. The optimal solutions for the test cases were determined by the currently proposed model rather than by different models taken from the literature, indicating that this model could be suitable for use in flood routing problems.

Predicting Muskingum flood routing parameters using spreadsheets

In this study, two easy to use and high precision solution methods that can be used for educational and engineering purposes are proposed. The first of these methods is the “Trial–Error with Spreadsheet” procedure combining basic properties of spreadsheets and the other method is the “Nonlinear optimization with Solver” procedure that uses the nonlinear optimization code and the “Iterative calculation” which is one of the most effective properties of spreadsheets. Both of the proposed methods are tested on three samples given in literature and the comparisons of the model results, observation results, and the results of other solution techniques in literature are made.

A third-order upwind scheme for the advection-diffusion equation using spreadsheets

In this study, numerical solution of advection-diffusion equation with third-order upwind scheme by using spreadsheet simulation (ADE-TUSS) is carried out. This is a user-friendly and a flexible solution algorithm for the numerical solution of the one dimensional advection-diffusion equation (ADE). The ADE-TUSS algorithm is based on the description of ADE by using the third-order upwind scheme (TU) for advection term and second-order central finite representation. For the solution of the governing equations, spreadsheet simulation (SS) technique is used instead of conventional solution techniques. The solution of ADE can be obtained for explicit, implicit and Crank-Nicolson schemes by only changing the values of temporal weighted parameter in the ADE-TUSS algorithm. It is clear in the literature that numerical diffusion causes great deviations in the model results when the first- or second-order upwind schemes are used. In order to decrease the numerical diffusion and to obtain oscillation free results, an artificial diffusion term is usually defined or sizes of the time step and/or grid sizes are set small values. Reduce of the grid sizes and/or time step increases the computational time and generally requires writing a fairly complex code when high order schemes are used. However, numerical solution of ADE by taking into account TU scheme has been carried out by using the iterative spreadsheet solution technique in the proposed solution algorithm. In order to simulate transient solution, a simple macro that carries out time cycle is defined with the help of VBA feature of spreadsheets. One of the most important advantages of ADE-TUSS algorithm is that it does not require the matrix algebra at each time step of the transient solutions. In order to test the ADE-TUSS model, two examples having numerical and analytical solutions are solved. Results showed that use of the high-order schemes in the spreadsheet simulation is very applicable for the numerical solution of ADE. Moreover, numerical diffusion problem is drastically prevented by using the ADE-TUSS model.

Numerical Solution of Advection-Diffusion Equation Using a Sixth-Order Compact Finite Difference Method

This study aims to produce numerical solutions of one-dimensional advection-diffusion equation using a sixth-order compact difference scheme in space and a fourth-order Runge-Kutta scheme in time. The suggested scheme here has been seen to be very accurate and a relatively flexible solution approach in solving the contaminant transport equation for . For the solution of the present equation, the combined technique has been used instead of conventional solution techniques. The accuracy and validity of the numerical model are verified through the presented results and the literature. The computed results showed that the use of the current method in the simulation is very applicable for the solution of the advection-diffusion equation. The present technique is seen to be a very reliable alternative to existing techniques for these kinds of applications.

Time‐dependent groundwater modeling using spreadsheet

Time‐dependent groundwater modeling using spreadsheet simulation (TGMSS) model is developed as solution technique. It is a practical method that uses spreadsheets instead of the conventional solution methods. All of the aquifer parameters can easily be described in TGMSS model. The results of TGMSS are validated with MODFLOW. Results showed that TGMSS and MODFLOW results were in good agreement in terms of resulting values of hydraulic heads.

Solving inverse problems of groundwater-pollution-source identification using a differential evolution algorithm

In this study, an accurate model was developed for solving problems of groundwater-pollution-source identification. In the developed model, the numerical simulations of flow and pollutant transport in groundwater were carried out using MODFLOW and MT3DMS software. The optimization processes were carried out using a differential evolution algorithm. The performance of the developed model was tested on two hypothetical aquifer models using real and noisy observation data. In the first model, the release histories of the pollution sources were determined assuming that the numbers, locations and active stress periods of the sources are known. In the second model, the release histories of the pollution sources were determined assuming that there is no information on the sources. The results obtained by the developed model were found to be better than those reported in literature.RésuméDans cette étude, un modèle précis a été développé pour résoudre les problèmes d’identification de la source de pollution des eaux souterraines. Dans le modèle développé, les simulations numériques d’écoulement et de transport de polluant dans les eaux souterraines ont été réalisées en utilisant les logiciels MODFLOW et MT3DMS et les processus d’optimisation ont été conduits au moyen d’un algorithme d’évolution différentielle. La performance du modèle développé a été testée sur deux modèles d’aquifères hypothétiques en utilisant des données d’observation réelles et bruitées. Dans le premier modèle, les historiques d’émission par les sources de pollution ont été déterminés en faisant l’hypothèse selon laquelle les nombres, les localisations et les périodes d’activité des sources sont connus. Dans le second modèle, les historiques d’émission par les sources de pollution ont été déterminés en faisant l’hypothèse qu’il n’y a pas d’information sur les sources. Les résultats obtenus au moyen du modèle développé sont meilleurs que ceux rapportés dans la littérature.ResumenEn este estudio, se desarrolló un modelo exacto para la resolución de problemas de identificación de fuentes de contaminación de agua subterránea. En el modelo desarrollado, las simulaciones numéricas de flujo y de transporte de contaminantes en el agua subterránea se llevaron a cabo usando los softwares MODFLOW y MT3DMS, y el proceso de optimización fue realizado utilizando un algoritmo diferencial de evolución. El rendimiento del modelo desarrollado se probó con dos modelos de acuíferos hipotéticos usando datos observacionales reales y ruidosos. En el primer modelo, las historias de los vertidos de las fuentes de contaminación se determinaron suponiendo conocidos los números, ubicaciones y períodos activos de las fuentes. En el segundo modelo, las historias de los vertidos de las fuentes de contaminación se determinaron suponiendo que no hay ninguna información sobre las fuentes. Se encontró que los resultados obtenidos por el modelo desarrollado eran mejores que los informados en la literatura.摘要在这项研究中,建立了准确模型来解决地下水污染源识别问题。在开发的模型中,采用MODFLOW和MT3DMS软件进行了地下水水流和污染物运移的数值模拟,并且采用差分进化算法进行了最优化处理。利用真实和众多的观测数据在两个假设含水层模型上对开发模型的性能进行了测试。第一个模型中,假定污染源的数量、位置和有效压力期已知,确定了污染源的释放历史。第二个模型中,假定没有污染源的任何信息,确定了污染源的释放历史。发现,所开发的模型获取的结果比文献记载的要好。ResumoNesse estudo, um modelo acurado foi desenvolvido para solucionar problemas de identificação de fontes de poluição das águas subterrâneas. No modelo desenvolvido, as simulações numéricas de fluxo e transporte de poluentes foram conduzidas usando os softwares MODFLOW e MT3DMS, e o processo de otimização foi conduzido usando um algoritmo de evolução diferencial. O desempenho do modelo desenvolvido foi testado em dois modelos de aquíferos hipotéticos usando dados de observações reais e com ruído. No primeiro modelo, os históricos de liberação de fontes de poluição foram determinados assumindo que os números, locais e períodos de estresse ativo das fontes são conhecidos. No segundo modelo, os históricos de liberação de fontes de poluição foram determinados assumindo que não existe informação sobre as fontes. Os resultados obtidos pelo modelo desenvolvido foram considerados melhores do que aqueles referenciados na literatura.ÖzetBu çalışmada, yeraltısuyu-kirlilik-kaynağı belirlenmesi ters problemlerinin çözümü için doğruluğu yüksek bir model geliştirilmiştir. Geliştirilen modelde, yeraltısuyunda akım ve kirletici taşınımı denklemlerinin sayısal simülasyonları MODFLOW ve MT3DMS yazılımları, optimizasyon işlemleri ise diferansiyel gelişim algoritması kullanılarak gerçekleştirilmiştir. Geliştirilen modelin performansı, iki adet kurgusal akifer modeli üzerinde gerçek ve hatalı gözlem verileri kullanılarak test edilmiştir. Birinci modelde, kaynakların yerleri ve sayılarının bilindiği varsayılarak kirletici kaynakların boşalım geçmişleri elde edilmiştir. İkinci modelde ise kaynaklarla ilgili herhangi bir bilgi olmadığı varsayılarak kirletici kaynakların boşalım geçmişleri belirlenmiştir. Geliştirilen modelden elde edilen sonuçların, literatürde verilen sonuçlardan daha iyi olduğu görülmüştür.

Solution of weighted finite difference techniques with the advection–diffusion equation using spreadsheets

This study proposes one‐dimensional advection–diffusion equation (ADE) with finite differences method (FDM) using spreadsheet simulation (ADESS). By changing only the values of weighted parameter with ADESS model, solutions are obtained for the FTSC, Upwind and Lax–Wendroff schemes. Two examples which, have the numerical and analytical solutions in literature, are solved in order to test the proposed model. Both examples are solved for three schemes. It has been determined that the Lax–Wendroff scheme is in good agreement with the analytical solution; however the results of FTSC is lower than the analytical solution and the Upwind scheme is higher than the analytical solution. Moreover, it has been obtained that the model accuracy is higher than that of the other models in literature, when the results of the ADESS model are compared with the numerical solutions. Results showed that by changing the input parameters in the ADESS model, the results of the model may easily be examined graphically.