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Application of muti-quadric interpolation in numerical simulation of 2D groundwater flow

Multi-quadric (MQ) interpolation is a numerical method to solve partial differential equations (PDEs). The purpose of this paper was to discuss the effectiveness of the method applied in groundwater flow simulation, and the influence of shape parameters, support domain, node spacing, and time steps on results. We used MQ method for the numerical solution of four cases of 2D groundwater flow in confined aquifer. Case one was a flow in a confined aquifer with constant transmissivity (T), while case two was with T varying continuously. Case three represented the flow to a fully penetrated pumping well in a confined aquifer. Case four was a transient flow in confined aquifer with constant transmissivity. The method was found to have good agreement with analytical solution of the four cases. The error was affected by the combination of shape parameters, size of support-domain, and node spacing of MQ method. Good accuracy could be obtained under comparatively big time step, when space and time discretizations were dealt with MQ method and the finite difference method, respectively.