In hydrodynamics the applications range of incompressible flows is very wide. In this study, a robust, high order modeling approach is introduced, based on the MLPG meshfree method-based radial basis functions (RBF-MLPG) method, for solving the incompressible flow field. In other words a MLPG meshfree method based on an interpolation function is presented to solve the 2-D unsteady incompressible fully developed fluid flows. This meshfree method is based on the quartic (4 th order) spline. The method is then compared against the Finite Element Method on a test case of unidirectional fully developed incompressible fluid. The performance of this weight function proved that the quartic (4th order) spline gains the highest accuracy, convergence and efficiency. Finally, it can be concluded that the presented method is formidable for simulating fluid dynamics.

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The interaction between surface water and groundwater is a significant topic in groundwater-related problems. This study suggests an exact model based on Laplace transformation to calculate the groundwater flow in river-aquifer systems. Exact models play an important role in simulating the future behavior of river-aquifer systems. Therefore, investigation of the exact models for river-aquifer systems is a hot topic in the hydraulics of groundwater flow modeling. The objective of this research is to present new exact models for simulating the hydraulics of groundwater flow in river-aquifer systems with a more general function of river level variation under recharge by means of Laplace transform method. A general function is adopted to describe the river level variation, in which some situations such as linear, exponential and power of time variations in the river level can be treated as special cases. The effects of variations in aquifer parameters on groundwater hydraulic head are evaluated. It is shown that the groundwater hydraulic head grows slower in aquifers with a greater thickness or hydraulic conductivity. In addition, the effect of changes in specific storage is too little on the groundwater hydraulic head. The variations in hydraulic heads due to changes in recharge rate with different values of thickness, hydraulic conductivity, specific storage, and length are analyzed. It is observed that the groundwater hydraulic head in an aquifer with a lesser length, higher hydraulic conductivity or higher thickness is less sensitive to a change in the recharge rate than in an aquifer with a higher length, lesser hydraulic conductivity or lesser thickness. Furthermore, it is shown that the differences in hydraulic heads due to the increase in recharge rate are not significant for different values of specific storage. The results of the present new exact models are successfully verified by the results obtained from the analytical solution of Bansal and Das. Also, for more reliability, the results are compared with those results of MODFLOW. The results show that the presented new exact models are accurate, robust and efficient. One of the advantages of the solutions is to investigate the sensitivity analysis of aquifer parameters, which has been carried out in this paper. Furthermore, in the present research a more general function describing river level variation is considered, in which the linear, exponential and power of time variations are special cases.

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