An extended formulation of the integrated finite difference method for groundwater flow and transport

An extension to the integrated finite difference method, applied to two-dimensional problems, has been developed that permits a more accurate approximation of the governing equations for groundwater flow and mass transport in heterogeneous anisotropic media. The method adopts a linear two-dimensional interpolation over triangular elements for the numerical evaluation of gradients at any point of the spatial domain. Applications of the method are presented for various test cases. A comparison is also made between the results obtained by applying both the extended method and the finite element method to the same test problems. This comparison illustrates the utility of the extended integrated finite difference method for simulating flow in anisotropic media. The application of an automatic calibration procedure, based on Kalman filtering, to several test problems and the validation of the resulting models further confirms the advantages of the new formulation. The sources of error introduced by ignoring anisotropy in the integrated finite difference method are found to be significant in the cases presented.