NODE POSITIONING ALGORITHM
Figure 10 - Problem setup for FEM model depicting the domain mesh. For visualization purposes, only 0.11% of the nodes and 0.09% of the elements are shown.
Figure 12: Zoomed-in comparison of the CVBEM and FEM numerical outcomes. In this case, the CVBEM flowline, shown in green, accu- rately tracks the target flowline, which is shown as a black dashed line. The FEM streamline, shown in blue, is north of the target flowline.
Discussion and Conclusion
The CVBEM has been used to model groundwater contami- nant transport problems since at least as early as 1986 [19]. In this paper, we consider an important problem in ground- water transport; namely the identification of a LUST when contamination has been detected downgradient from a set of several possible sources. These types of problems are often approached using geochemical analyses. However, the out- comes of such analyses can be buttressed by computational outcomes such as those that are shown in this work. In this work we examined three Dirichlet BVPs of the Laplace type: (i) potential flow around a constrained cir- cular obstruction, (ii) potential flow around a free circular obstruction, and (iii) potential flow around a wall barrier or foundation. These demonstration problems involve the com- putational difficulty of modeling flow regimes with regions of extreme curvature. The areas of extreme curvature require extra modeling attention and computational effort in order to obtain results with satisfactory accuracy, which makes these problems interesting and relevant to the geosciences and other fields. In the example problems, we employed the symmetry of the flow situations to justify only modeling the right half of the modeling area of interest. Therefore, the computational outcomes depicted in the left half of the modeling area of inter- est were obtained by reflecting the outcomes in the right half.
Figure 11 - Depiction of the problem situation with the location of the accumulated contaminant shown as a green dot. The non-leaking candidate source points are shown as blue triangles, and the actual LUST is shown as a red triangle.
The CVBEM models used herein employ a recently-devel- oped NPA from our research group, which has been demon- strated to select highly efficient locations for computational nodes and collocation points such that the CVBEM model is capable of achieving an accurate solution while using relatively few terms in the approximation function [9]. These CVBEM models were compared with FEM models of the same problems,
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