An improved collocation method for solving the Henry problem

An efficient model for solving density driven groundwater flow problems based on the network simulation method

“…7 compares the simulation results of the original Henry problem, which is quite similar to Croucher and O'Sullivan (1995) solution, with those of other authors (Henry, 1964;Lee and Cheng, 1974;Gotovac et al, 2003) and the semianalytical solution of Simpson and Clement (2004). Voss and Souza's (1987) results, which used the Segol boundary condition and did not assume the Boussinesq approximation, are included in the figure.…”

“…The general properties of the Henry problem are listed in Ta Pinder and Cooper (1970) Seawat (Langevin and Guo, 1999) (Segol, 1994) Sutra (Segol, 1994 Gotovac et al (2003) Seawat (Langevin and Guo, 1999) (Langevin and Guo, 1999) 1.373 --Present study appears in the outflow region for the Pinder version makes this case very interesting to study. All the simulations were carried out for a 120 · 60 (equal volume elements) grid.…”

“…More recently, Simpson and Clement (2003), who compare their results with those of Frind, provided a coupled versus uncoupled analysis, by means of a Galerkin-finite element model, to show that the saline water distribution in the Henry problem is mainly dictated by boundary-forcing and not by density-dependent effects. Gotovac et al (2003) used the streamfunction formulation and a numerical collocation method (successively dividing the domain by half in each direction toward the discharge zone for the critical parameter b = 0.035), to study the different versions of the Henry problem. Their inland distance solutions, 1.37 and 1.16, for b = 0.1 and 0.035, respectively, coincides with the estimations of Croucher and O'Sullivan.…”

“…(2) and (3) may be written in the dimensionless form (Lee and Cheng, 1974;Croucher and O'Sullivan, 1995;Holzbecher, 1998 andGotovac et al, 2003), as…”

The influence of temporal hydrological randomness on seawater intrusion in coastal aquifers

“…The CPU time on a 2.5 GHz Pentium 4 for each realization ranges from 5 to 10 min depending on the aquifer case study, which means that the maximum simulation time for a set of 100 realizations is about 16 h. This computational time may in future studies be significantly reduced by new advances in adaptive numerical methods, such as adaptive finite element (Diersch and Kolditz, 2002), finite difference (Alves et al, 2002) and collocation methods (Vasilyev and Bowman, 2000;Gotovac et al, 2003). The adaptive approach uses in cases of narrow transition zone and small dispersivities a denser discretization only around the transition zone in order to avoid classical numerical oscillations and artificial dispersion.…”