A Comparison of the Effectiveness of Using the Meshless Method and the Finite Difference Method in Geostatistical Analysis of Transport Modeling

Leopold Vrankar in Goran Turk in Franc Runovc (2005) A Comparison of the Effectiveness of Using the Meshless Method and the Finite Difference Method in Geostatistical Analysis of Transport Modeling. International Journal of Computational Methods, 2 (2). str. 149-166. ISSN 0219-8762

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Disposal of radioactive waste in geological formations is a great concern with regards to nuclear safety. The general reliability and accuracy of transport modeling depends predominantly on input data such as hydraulic conductivity, water velocity, radioactive inventory, and hydrodynamic dispersion. The most important input data are obtained from field measurements, but they are not always available. One way to study the spatial variability of hydraulic conductivity is geostatistics. The numerical solution of partial differential equations (PDEs) has usually been obtained by finite difference methods (FDM), finite element methods (FEM), or finite volume methods (FVM). These methods require a mesh to support the localized approximations. The multiquadric (MQ) radial basis function method is a recent meshless collocation method with global basis functions. Solving PDEs using radial basis function (RBF) collocations is an attractive alternative to these traditional methods because no tedious mesh generation is required. We compare the meshless method, which uses radial basis functions, with the traditional finite difference scheme. In our case we determine the average and standard deviation of radionuclide concentration with regard to spatial variability of hydraulic conductivity that was modeled by a geostatistical approach.

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