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The complicated behavior of groundwater system in an arid aquifer is generally studied by solving the governing equations using either analytical or numerical methods. In this regard, analytical methods are just for some aquifers with regular boundaries. Numerical methods used for this aim are finite difference (FDM) and finite element methods (FEM...
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Understanding groundwater responses to recharge is particularly important in alluvial aquifers which are surrounded by karstic formations in semi-arid and arid regions, such as the high Zagros region of western Iran. Evaluation of input and output time series provides comprehensive information on the hydrodynamic behavior of these aquifers. Time-se...
Citations
... The first component is groundwater flow in the aquifer. This component can be computed with the meshless local Petrov-Galerkin groundwater model developed by Mohtashami et al. (2017;2022). They applied this model to steady and unsteady real cases and found more accuracy than the other models (Mohtashami et al. 2017(Mohtashami et al. , 2022. ...
... This component can be computed with the meshless local Petrov-Galerkin groundwater model developed by Mohtashami et al. (2017;2022). They applied this model to steady and unsteady real cases and found more accuracy than the other models (Mohtashami et al. 2017(Mohtashami et al. , 2022. Meshless models, unlike mesh-based methods, due to their independence from meshing stages have more accuracy and computational cost (Liu and Gu 2005). ...
... The simulation aligned well with field data, despite the absence of measurements from a real falaj or a laboratory simulation. The groundwater model in this article, known as the meshless local Petrov-Galerkin model, is derived from the numerical model developed by Mohtashami et al. (2017Mohtashami et al. ( , 2022. The input parameters for the calculations are shown in Table 1. ...
Aflaj refers to a traditional irrigation system found in Oman, which has been used for centuries to sustainably manage groundwater resources. These resources play a vital role in meeting various consumption needs, including agriculture, domestic, and industrial. The article, for the first time, introduces the concept of “hydraulics of aflaj”, emphasizing the importance of accurate information about interaction of falaj and aquifer and also flow within their tunnels. The study utilizes the mechanisms of horizontal wells to simulate the interaction between the aquifer and the falaj tunnel, employing the meshless local Petrov–Galerkin numerical model to compute groundwater head of aquifer. The model is applied to a real test case in the Loba aquifer of Malaysia, demonstrating improved accuracy compared to previous models based on evaluation indices such as MAE, RMSE, MAPE, NSE and p-bias. The findings of the proposed model show good agreement.
... Mohtashami et al. (2017Mohtashami et al. ( , 2021 developed MLPG for groundwater simulation in both steady and unsteady states. They found their model more accurate than the finite difference method (Mohtashami et al. 2017(Mohtashami et al. , 2022a. ...
Qanat is an ancient water harvesting technology which is used for irrigation, agriculture and drinking in many countries of the world. A key element of preserving this heritage is calculating their protection area. In this study, the main aim is depiction of the hydraulic harim of qanat with the usage of the meshless numerical method. Afterward, the qanat package has been added to this model to delineate the hydraulic harim of the qanat. Two qanat systems are shown here: one in a standard aquifer and the other in a real test case, namely Haji-Abad qanat, located in the Birjand unconfined aquifer. In the real test case, the hydraulic harim of Haji-Abad qanat with 10 collection shafts is depicted in 3 time sections as well. The time sections are 3 years after extraction (2014), 6 years (2017) and 11 years (2022). The findings stated that time makes the harim area larger. In addition, the hydraulic harim is extended to areas with a higher hydraulic conductivity coefficient. Ultimately, we have delineated the hydraulic harim for 2040 and unfortunately, it is influenced by buildings. Therefore, it is necessary to find the hydraulic harim of qanats in order to protect this traditional heritage.
HIGHLIGHT
This method is applicable for all qanats with different conditions.;
... Meshfree technique gets rid of the disadvantage of meshing that exists in FDM and FEM (Mohtashami et al. 2017). Using the nodes in meshless solutions for approximation of the governing equations declines the enormous work needed to predetermine for groundwater modeling such as in meshbased methods (Mohtashami et al. 2022a). Myriad meshlessbased strategies found their place in various applications and presented great potential as a remarkable and effective numerical solution tool. ...
In this research, a simulation–optimization (S/O) model is used in order to estimate aquifer parameters on two aquifers. In this model, meshless local Petrov–Galerkin (MLPG) is used for simulation purpose and modified teaching–learning-based optimization (MTLBO) algorithm is engaged as optimization model. Linking these two powerful models generates a S/O model named MLPG-MTLBO. The proposed model is applied on two aquifers: a standard and a real field aquifer. In standard aquifer, parameters are only transmissivity coefficients in x and y direction for three zones. The acquired results by MLPG-MTLBO are really close to true values. This fact presents the power of MLPG-MTLBO inverse model. Therefore, it is applied on field aquifer. Unconfined aquifer of Birjand recognized as real case study. Parameters which are needed to be estimated are specific yields and hydraulic conductivity coefficients. These parameters are computed by MLPG-MTLBO and entered to the groundwater flow model. The achieved groundwater table compared with observation data and RMSE is calculated. RMSE value is 0.356 m; however, this error criterion for MLPG and FDM is 0.757 m and 1.197 m, respectively. This means that estimation is precise and makes the RMSE to reduce from 0.757 to 0.356 m, and also, MLPG-MTLBO is an accurate model for this aim.
... Location of Birjand unconfined aquifer in Iran(Mohtashami et al. 2022) ...
As the groundwater quantitative monitoring aimed to determine the factors affecting the aquifer behavior plays an important role in its regional management, studying the temporal and spatial groundwater level variations requires a comprehensive monitoring network. Effort has been made in this study to introduce a new linked simulation–optimization method, named MLPG-TLBO to quantitatively monitor the Birjand aquifer and determine the optimal points for piezometers. This model uses meshless local Petrov Galerkin (MLPF) method in the simulation part and teaching–learning-based optimization (TLBO) method in the optimization part. The objective function, in this study, is to minimize the difference between the groundwater level observed in piezometers and obtained computationally by the model. Since this coupled model is independent from the meshing, it eliminates the mesh-dependent shortcomings and, hence, yields more accurate results. It has been calibrated and validated in previous Birjand area studies and has led to acceptable results. By implementing the model in Birjand aquifer, the optimal positions of ten piezometers were determined mostly in areas where the density of the extraction wells was lower. Finally, the RMSE of both MLPG-TLBO and FDM was obtained to be 0.334 m and 1.483 m for 10 optimal piezometers. The RMSE value for MLPG-TLBO has shown a 0.423 m reduction compared to its previous value. This difference is quite meaningful as it shows good performance of this method in designing an optimal network for the aquifer.
The study presents the development of the Meshless Local Petrov–Galerkin (MLPG) method to model and predict contaminant transport in porous media which is known as an important issue to prevent the pollution propagation in groundwater. The research focuses on the Rafsanjan Plain in southeastern Iran as a real case study, where no studies of meshless methods have been done. Computational models were implemented using MATLAB, integrating Radial Basis Functions (RBF) as the interpolation technique. The process commenced by establishing a groundwater flow model, where hydraulic head served as the foundational parameter for determining seepage velocity under unsteady-state conditions. Subsequently, the contamination transport was simulated within the aquifer for a period of six months. Comparative analysis between observed empirical data and the modeled values in both flow dynamics and contaminant transport revealed a significant and reasonable alignment. Analysis of the parameters showed that the value of the shape parameter (\({\alpha }_{{\text{c}}})\) can have the greatest impact on achieving a more accurate value. In this research, with \({\alpha }_{{\text{c}}}\)=6 in the contamination transport model, the most reliable outputs were obtained compared to the observed values. Furthermore, the assessment of the coefficient of determination (R2 = 0.97) was conducted to evaluate the acceptability of the calibrated parameters. The high R2 value suggests a robust correlation between the observed and simulated data, indicating that the model's parameters are within an acceptable range. This finding underscores the accuracy and reliability of the developed MLPG method for analyzing contaminant transport in unconfined aquifers, particularly in the context of the Rafsanjan Plain.
Purpose
In the present work, we focus on developing an in-house parallel meshless local Petrov-Galerkin (MLPG) code for the analysis of heat conduction in two-dimensional and three-dimensional regular as well as complex geometries.
Design/methodology/approach
The parallel MLPG code has been implemented using open multi-processing (OpenMP) application programming interface (API) on the shared memory multicore CPU architecture. Numerical simulations have been performed to find the critical regions of the serial code, and an OpenMP-based parallel MLPG code is developed, considering the critical regions of the sequential code.
Findings
Based on performance parameters such as speed-up and parallel efficiency, the credibility of the parallelization procedure has been established. Maximum speed-up and parallel efficiency are 10.94 and 0.92 for regular three-dimensional geometry (343,000 nodes). Results demonstrate the suitability of parallelization for larger nodes as parallel efficiency and speed-up are more for the larger nodes.
Originality/value
Few attempts have been made in parallel implementation of the MLPG method for solving large-scale industrial problems. Although the literature suggests that message-passing interface (MPI) based parallel MLPG codes have been developed, the OpenMP model has rarely been touched. This work is an attempt at the development of OpenMP-based parallel MLPG code for the very first time.
An understanding of natural degradation of multiple reactive contaminants in the aquifers is essential before designing the monitoring or remediation programs for polluted aquifers. Since such reactive contaminants are ubiquitous, a number of research works has been performed in the past three decades for the modelling of multi-species reactive transport (MSRT) phenomenon. The widely used finite difference method (FDM) and finite element method (FEM)–based models suffer a drawback of relying on a grid/mesh, which makes the solution unstable. Addressing such difficulties, the latest research on the MSRT models is directed towards the meshless methods. In this study, the meshless local Petrov Galerkin (MLPG) method–based multi-species reactive transport model (MLPG-MSRT) is presented, with an objective to create a robust simulation tool for the prediction of fate of multiple contaminants of the first-order reaction network. The developed model is validated for reversible as well as irreversible reaction networks with the available analytical solutions. Also, the MLPG model for unconfined aquifer flow (UF) is developed, validated, and coupled with the MLPG-MSRT model. The MLPG-UF-MSRT model results are further compared with the established FDM-based MODFLOW-RT3D model solutions for a rectangular and a real field type study. The results showed that the proposed model can simulate MSRT as accurately as the FDM-based models with an additional advantage of simplicity and stability, and thus, is more efficient for complex field problems.
In this paper, two meshless methods, namely, a weak form Meshless Local Petrov Galerkin (MLPG) method, and Meshless Weak Strong (MWS) form method, obtained by combining MLPG with a strong form Radial Point Collocation Method (RPCM), are presented for simulation of advection-dispersion-reaction phenomena of the contaminants in the porous media. The first-order decay and sorption reactions are considered in this study. The Crank Nicolson scheme is applied for the time discretization. The weak form MLPG is a truly meshless and robust numerical technique, that can be applied to complex aquifer systems with derivative boundaries. However, in this method, the computational time is increased due to the integration, which is not essential for simple problems. Thus, the MLPG method is further coupled with a strong form RPCM with an aim of decreasing the background integration, by modelling only the nodes around the derivative boundaries using MLPG method and the other nodes by a direct RPCM which do not require integration. The proposed MWS model automatically converts into a complete RPCM model if there are no derivative boundaries. Thus, this model being both accurate and computationally efficient is suitable for simple and moderately complex aquifer systems and MLPG is the most stable and reliable method for modelling the most complex aquifer problems. Both the developed models are tested with available analytical solutions and applied for hypothetical case studies. The results prove the efficiency of the models and the applicability of each model is described in detail.
