Modeling Three-Dimensional Groundwater Flows by the Body-Fitted Coordinate (BFC) Method: II. Free and Moving Boundary Problems

This paper presents a methodology and solution procedure of the time-dependent body-fitted coordinate (BFC) method for the analysis of transient, three-dimensional groundwater flow problems characterized by free and moving boundaries. The technique consists of numerical grid generation, time-dependent body-fitted coordinate transformation, and application of the finite difference method (FDM) to the transformed partial differential equations. Based on the time-dependent BFC method, a three-dimensional finite-difference computer code, BFC3DGW, was developed and used to solve two unconfined flow problems. The code was verified by comparing numerical results with analytical solutions for a steady-state seepage problem. In order to demonstrate capability of the method in dealing with flow problems with irregular and moving boundary surfaces, an unconfined well-flow problem was solved by the developed code. Difficulties associated with the free and moving irregular boundary have been successfully overcome by employing this method.     

Application of Boundary-Fitted Coordinate Transformations to groundwater flow modeling

The Boundary-Fitted Coordinate (BFC) Transformation method is a very powerful, efficient and accurate method of modeling heat or fluid flow in two- or three-dimensional domains with complex boundary shapes and abrupt changes in internal properties. Since the late 1970's it has become the modeling method of choice among many aerodynamicists and heat-flow modelers. It is being presented here for the first time as a new approach to modeling groundwater flow, based on successful research results in two dimensions. The BFC transformation method was employed to simulate two hypothetical well-flow scenarios in isotropic and anisotropic domains, and actual groundwater flows in the area of West Lafayette, Indiana. The numerical solutions in those cases were at least as accurate as and/or consistent with those obtained by purely finite difference and finite element methods, but with the added advantage of more accurate representation and implementation of the boundary condition in the region of great sensitivity. The BFC method successfully applied to two-dimensional simulations should be easily extended to simulations of three-dimensional flow and transport and thus, this research is continuing in that direction.     

Topological variations of the PDP ligand and its prospects in molybdenum(0) dearomatization agents

The compounds fac-(κ(3)-PDP)Mo(CO)(3) {1; PDP = 2-[[2-(1-(pyridin-2-ylmethyl)pyrrolidin-2-yl)pyrrolidin-1-yl]methyl]pyridine}, [(cis-β-PDP)Mo(NO)(CO)]PF(6) ([cis-β-3]PF(6)), [(cis-α-PDP)Mo(NO)(CO)]PF(6) ([cis-α-3]PF(6)), [(cis-α-PDP)Mo(NO)Br]PF(6) ([4]PF(6)), [(trans-PDP)Cu](BF(4))(2)·CH(3)CN ([5](BF(4))(2)·CH(3)CN), and [(trans-PDP)Cu](OSO(2)CF(3))(2) ([5](OSO(2)CF(3))(2)) have been synthesized and structurally characterized by single-crystal X-ray diffraction. These are the first reported complexes of PDP on metal centers other than iron(II). The observed configurations indicate a broader range of accessible PDP topologies than has been reported. The {(cis-α-PDP)Mo(NO)}(+) fragment is found to be less π-basic than the dearomatizing {Tp(MeIm)Mo(NO)} fragment [Tp = hydridotris(1-pyrazolyl)borato; MeIm = 1-methylimidazole].     

Modeling Three-Dimensional Groundwater Flows by the Body-Fitted Coordinate (BFC) Method: I. Stationary Boundary Problems

Based on the body-fitted coordinate (BFC) method, a three-dimensional finite difference computer code, BFC3DGW, was developed to simulate groundwater flow problems. Methodology and solution procedures of the BFC method for simulating groundwater flows, particularly when the flow domain is stationary as in the case of confined aquifers, are described. The code was verified by comparing numerical results with analytical solutions for well-flow problems in an isosceles right-triangular aquifer. An example simulation is made to demonstrate capability of the code for solving flow problems in anisotropic aquifers where directions of anisotropy change continuously. The method differs from the conventional finite difference method (FDM) in the ability to use a flexible, nonorthogonal, and body-fitted grid. The main advantages of the method are the convenience of grid generation, the simplified implementation of boundary conditions, and the capability to construct a generalized computer code which can be consistently applied to problem domains of any shape.