Revisiting the stream-aquifer flow problem with a flux-based Green element model

This revisit of the stream-aquifer problem is based on a recent flux-based Green element formulation which offers more accurate solutions than previous formulations presented in Taigbenu (2003). Its accuracy also surpasses those provided by finite element and finite difference methods using grids that are coarser. As in all Green element formulations, the current formulation is predicated on the singular boundary integral theory that is implemented in an element-by-element fashion. What is new in the current formulation is that it calculates the fluxes at all nodes and not only at external nodes. While this approach exhibits much improved accuracy, its drawback lies with handling an increased number of unknowns. This drawback is, however, compensated for by the fewer elements required to achieve accuracies comparable to other conventional numerical methods. In this paper, it is demonstrated that with between 20% and 30% of elements used in finite element and finite difference models, comparable accuracy is achieved with this formulation. The main significance of the current computational technique is that it preserves the flux calculations in a manner that is consistent with the stream-aquifer interaction problem. Keywords: stream-aquifer interaction, The Green element metho

Numerics of boundary-domain integral and integro-differential equations for BVP with variable coefficient in 3D

This is the post-print version of the article. The official published version can be accessed from the links below - Copyright @ 2013 Springer-VerlagA numerical implementation of the direct boundary-domain integral and integro-differential equations, BDIDEs, for treatment of the Dirichlet problem for a scalar elliptic PDE with variable coefficient in a three-dimensional domain is discussed. The mesh-based discretisation of the BDIEs with tetrahedron domain elements in conjunction with collocation method leads to a system of linear algebraic equations (discretised BDIE). The involved fully populated matrices are approximated by means of the H-Matrix/adaptive cross approximation technique. Convergence of the method is investigated.This study is partially supported by the EPSRC grant EP/H020497/1:"Mathematical Analysis of Localised-Boundary-Domain Integral Equations for Variable-Coefficients Boundary Value Problems"

A time-dependent Green's function-based model for stream-unconfined aquifer flows

A numerical formulation that is based on the Green element method (GEM), which incorporates a time-dependent Green's function, is used to solve transient two-dimensional flows of stream-unconfined aquifer interaction. The Green's function comes from the fundamental solution to the linear diffusion differential operator in two spatial dimensions. In classical boundary element applications, this Green's function has found use primarily in linear heat transfer and flow problems; its use here for the nonlinear stream-unconfined aquifer flow problem represents the computational flexibility that is achieved with a Green element sense of implementing the singular integral theory. The nonlinear discretised element equations obtained from numerical calculations are linearised by the Picard and Newton-Raphson methods, while the global coefficient matrix, which is banded and sparse, is readily amenable to matrix solution routines. Using four numerical examples, the accuracy of the current formulation is assessed as against an earlier one that incorporates the Logarithmic fundamental solution. It is observed that comparable accuracy is achieved between both formulations, indicating that the current formulation is a viable numerical solution strategy for the stream-aquifer flow problem. Water SA Vol.29(3) 2003: 273-28

Groundwater resource evaluation of urban Bulawayo aquifer

Judicious management of a groundwater system requires an understanding of its hydrogeology and response to various recharge and pumping stresses. However, in developing countries, groundwater resource evaluations are hampered by a lack of adequate data that will allow for its complete characterisation. Under such circumstances it is not uncommon for ad hoc groundwater management measures to be embarked upon, especially during drought conditions. These were the conditions that existed during the 1991/92 drought when the CSIR Stellenbosch evaluated the groundwater resource of an urban aquifer in Bulawayo, Zimbabwe. Their recommendations revealed that about 3.5×106 m3/a could be safely abstracted from the aquifer. In this work, a more comprehensive hydrogeological investigation was carried out which included pumping tests, estimation of abstraction rates and recharge, and numerical modelling of the aquifer. The investigations indicate that the aquifer is unconfined with hydraulic conductivity and specific yield ranging from 0.1 m/d to 2.09 m/d and 0.02 to 0.11, respectively. Recharge estimates indicate an annual recharge of 105.5 mm with 38.4%, 52.1% and 9.5% accounting respectively for direct recharge, water mains and sewer leakages. Furthermore, a long-term sustainable annual abstraction of 6.1×106 m3 or 15% of current city water demand can be obtained from the aquifer. Key words: groundwater flow; pumping tests; urban groundwater; numerical modelling; groundwater resource evaluation. Water SA Vol.31(1) 2005: 23-3

Land-use impacts on the quality of groundwater in Bulawayo

The impacts of land use from commercial, industrial and domestic activities in the second largest city (Bulawayo) in Zimbabwe on groundwater quality are investigated in this paper. Thirty-two boreholes that are located in the Matsheumhlope Wellfield, a basement aquifer that underlies the city of Bulawayo, were monitored during the period between August 2000 and August 2001. The results showed that the majority of the parameters (iron, manganese, copper, nitrate, fluoride, sulphate and cyanide) at most sampling stations are within the recommended and permissible limits specified in Zimbabwe drinking water standards guidelines (SAZS 560:1997). The water can therefore be used for drinking purposes. However, levels of hardness higher than the maximum allowable according to Standard Association of Zimbabwe (SAZ) guidelines were encountered. Microbiological analysis indicates that 27% of the samples showed positive total coliform and 8% positive faecal coliform with their occurrences being randomly distributed spatially and temporally. Comparison of the water quality in the industrial and residential areas revealed statistically significant differences in water quality of the two areas. The study reveals that leaks from industrial and domestic sewers, commonly being experienced due to the age of the sewer lines, are increasingly compromising the quality of the groundwater, while unusually high levels of EC encountered at two sampling stations seem to be related to the geological formation. The results from sampling groundwater within the vicinity of the landfill site in Richmond do not present a picture that is different from the other residential areas monitored, suggesting that leachate is being contained within the landfill liner and does not, as yet, pose an environmental threat to the aquifer. Key Words: Groundwater, Water quality, Land use, Environmental impact WaterSA Vol.30(4) 2004: 453-46