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

2015 ◽  
Vol 39 (2) ◽  
pp. 236-242 ◽  
Author(s):  
F.Z. Wang ◽  
K.H. Zheng
Keyword(s):  
Steady State ◽  
Groundwater Flow ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Flow Problems

scholarly journals Free surface groundwater flow solution using boundary collocation methods

2018 ◽  
Vol 196 ◽  
pp. 03026 ◽  
Author(s):  
Juraj Mužík ◽  
Roman Bulko
Keyword(s):  
Diffusion Equation ◽  
Groundwater Flow ◽  
Moving Boundary ◽  
Numerical Algorithms ◽  
Type Equation ◽  
Fundamental Solutions ◽  
Collocation Methods ◽  
Method Of Fundamental Solutions ◽  
Singular Boundary ◽  
State Diffusion

In this paper, two meshless numerical algorithms are developed for the solution of two-dimensional steady-state diffusion equation that describes the stationary groundwater flow. The proposed numerical methods, which are truly meshless, quadrature-free and boundary only, are based on the method of fundamental solutions and singular boundary method respectively. The diffusion equation is transformed into a Poisson-type equation with a known fundamental solution. Numerical examples with moving boundary are presented and compared to the solutions obtained by the finite element method.

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