Development of two-dimensional groundwater flow simulation model using meshless method based on MLS approximation function in unconfined aquifer in transient state

Abstract

In recent decades, due to reduction in precipitation, groundwater resource management has become one of the most important issues considered to prevent loss of water. Many solutions are concerned with the investigation of groundwater flow behavior. In this regard, development of meshless methods for solving the groundwater flow system equations in both complex and simple aquifers' geometry make them useful tools for such investigations. The independency of these methods to meshing and remeshing, as well as its capability in both reducing the computation requirement and presenting accurate results, make them receive more attention than other numerical methods. In this study, meshless local Petrov–Galerkin (MLPG) is used to simulate groundwater flow in Birjand unconfined aquifer located in Iran in a transient state for 1 year with a monthly time step. Moving least squares and cubic spline are employed as approximation and weight functions respectively and the simulated head from MLPG is compared to the observation results and finite difference solutions. The results clearly reveal the capability and accuracy of MLPG in groundwater simulation as the acquired root mean square error is 0.757. Also, with using this method there is no need to change the geometry of aquifer in order to construct shape function.

Application of MODFLOW with Boundary Conditions Analyses Based on Limited Available Observations: A Case Study of Birjand Plain in East Iran

“…A comprehensive study (e.g., lithology and geology studies) has been done in this research to be able to model the aquifer The aquifer geometry is determined according to the RWCSK data. A comprehensive study (e.g., lithology and geology studies) has been done in this research to be able to model the aquifer boundaries (i.e., aquifer geometry) accurately in the model [35,[56][57][58][59][60][61][62]. The bottom boundary (i.e., the bedrock in the aquifer) is also determined using the limited available geophysical study (geoelectrical soundings) carried out in Birjand Plain in 1971 ( Figure 8).…”

“…Water 2019, 11, 1904 9 of 21 boundaries (i.e., aquifer geometry) accurately in the model [35,[56][57][58][59][60][61][62]. The bottom boundary (i.e., the bedrock in the aquifer) is also determined using the limited available geophysical study (geoelectrical soundings) carried out in Birjand Plain in 1971 ( Figure 8).…”

Prediction of Groundwater Fluctuations Using Meshless Local Petrov-Galerkin Numerical Method in a Field Aquifer (Birjand Aquifer)

“…This method, which is commonly used in the fluid field, utilizes two functions: a weight function and an approximation function. The moving kriging function is used as an approximation function to compute the shape function (∅) [7,8].…”

“…The discrete form of each parameter is represented by Eq. (6)- (8) where is stiffness matrix, is Force body matrix, and U is an unknown matrix that shows groundwater level in each time period [26]. (6)…”

“…Among the meshless methods, the meshless local Petrov-Galerkin method has widely been used in the field of fluids, especially groundwater [7]. For example, Mohtashami et al 2017 [7,8] estimated groundwater head in a real unconfined aquifer both in the steady state and unsteady state using the meshless local Petrov-Galerkin method and compared the results with the results of finite difference method. The higher accuracy of the results of the meshless method shows its better performance, which can be used to predict groundwater levels more reliably and efficiently.…”