Groundwater flow simulation in confined aquifers using Meshless Local Petrov-Galerkin (MLPG) method

Abstract

For the better management of available groundwater, it is essential to understand the flow behavior within the aquifer systems. The groundwater flow behavior in the complex aquifer system can be studied by solving the governing equations using either analytical or numerical methods. As the analytical solutions are available only for simple idealized cases, numerical methods such as finite difference method (FDM) and finite element method (FEM) are generally used. The Meshless method is a recently developed alternative numerical approach for the solution of existing problem. A variety of Meshless methods like point interpolation method, smooth particle hydrodynamics, Galerkin methods, etc. are under the development for the solution of many solid mechanics and fluid mechanics problems. Meshless method eliminates many of the drawbacks of grid-based methods such as difficulties in meshing and re-meshing as in FDM and FEM which require huge efforts in pre-processing and with Meshless method it translates in the lesser computational time and costs. In this paper, Meshless Local Petrov-Galerkin (MLPG) method with strong form of collocation with exponential/Gaussian radial basis function is used for solving the groundwater flow problem. A computer model in MATLAB has been developed in 1D and 2D for the solution of confined aquifer problems. The developed 1D model is verified with available analytical solution for a hypothetical problem and found to be satisfactory. Further, the 2D model is applied to two case studies and results are compared with the FEM based solutions and found to be satisfactory. The present study shows that the MLPG based Meshless method is very effective in the simulation of groundwater flow problems.

Keywords:

• Meshless Local Petrov-Galerkin (MLPG) method
• Gaussian radial basis function
• groundwater flow simulation

Acknowledgements

This article belongs to the papers presented at the Hydro-2012 conference held at IIT Bombay on 7–8 December 2012 that were short-listed by the Editor for publication in this Journal after re-review and revisions where necessary.