The Radial Basis Functions Method for Improved Numerical Approximations of Geological Processes in Heterogeneous Systems

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Department of Mathematical Sciences


A robust, high order modeling approach is introduced, based on the finite difference-based radial basis functions method, for solving the groundwater flow equation in the presence of an active well, in the case of a confined aquifer in a complex geological environment. The two important novelties of this work are the analytical handling of the wells’ singularities and the ability to do this accurately and efficiently in a heterogeneous medium. It is argued that the most commonly used methods for this type of problem have severe weaknesses in both the treatment of the singularities associated with the well, and in representing heterogeneities which commonly occur in geological processes. The method presented here is first applied to the groundwater flow problem in a homogeneous medium for which the analytical solution is known, to show its high order algebraic convergence. The method is then compared against the United States geological survey’s MODFLOW software on a quasi-realistic benchmark test case in a heterogeneous medium. It is shown that much fewer nodes are needed by the proposed method to yield a similar accuracy.

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Mathematical Geosciences