The method of fundamental solutions for steady-state groundwater flow problems

Abstract

The method of fundamental solutions is a meshless method. Only boundary collocation points are needed during the whole solution process. It has the merits of mathematical simplicity, ease of programming, high solution accuracy, and others. In this paper, the method of fundamental solutions is applied to simulate 2D steady-state groundwater flow problems. The principle of superposition is used during the whole solution process. Numerical results are compared with the multiquadrics method and the mixed finite element method as well as analytical solutions. It is shown that the method of fundamental solutions is promising in dealing with steady groundwater flow problems.

Keywords:

• method of fundamental solutions
• groundwater
• meshless method
• radial basis function (RBF)

Acknowledgements

We are very grateful to the three anonymous reviewers for helpful suggestions to improve academic quality and readability of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.