A time-dependent Green’s function-based model for stream-unconfined aquifer flows
Loading...
Date
2004-07-01
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Water research commision
Abstract
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.
Description
Keywords
steam-aquifer interaction, green element method, linearisation algorithms, numerical solutions
Citation
Taigbenu, A. (2004) ‘A time-dependent green’s function-based model for stream-unconfined aquifer flows’, Water SA, 29(3). doi: 10.4314/wsa.v29i3.4926.