Applicability of linearized Boussinesq equation for modeling bank storage under uncertain aquifer parameters

Untitled

“…Figure 2 illustrates that case at time t * = 3 3/2 −1, such that H (t * ) is maximum. The numerical scheme shows little numerical dispersion, but the linearized solution of Govindaraju and Koelliker (1994) shows a significant discrepancy (this illustrates the value of an exact solution to check numerical results).…”

“…Also as an application of the method we plot profiles obtained by a standard numerical method (Govindaraju and Koelliker, 1994) which shows excellent accuracy except at very short time where some numerical dispersion is apparent at the wetting front. As in Hogarth et al (1997), who use the linear solution, we illustrate here the importance of exact analytical results to validate numerical scheme to solve the partial differential equation (1).…”

“…Case β > 0, Cα 2/3 = 1, the time is chosen for the maximum height at x = 0. There is minimal numerical dispersion but the linear approximation of Govindaraju and Koelliker (1994) is significantly incorrect. In that case, water flows from the channel into the aquifer.…”

Modeling stream–aquifer interactions with linear response functions

“…Stream-aquifer interactions and movement of bank storage between the aquifer and river can be simulated using analytical solutions (Cooper and Rorabaugh, 1963;Hantush, 1967;Dever and Cleary, 1979;Moench et al, 1974;Gill, 1985;Hunt, 1990;Govindaraju and Koelliker, 1994;Zlotnik and Huang, 1999;Moench and Barlow, 2000;Harada et al, 2000;Lal, 2001;Hantush et al, 2002) or by applying numerical methods (Pinder and Sauer, 1971;Zitta and Wiggert, 1971;Mariño, 1975;MorelSeytoux, 1975;Gureghian, 1978;Perkins and Koussis, 1996;Saquillace, 1996;Whiting and Pomeranets, 1997;Chen and Chen, 2003;Hilberts et al, 2004). Some of the above cited analytical solutions are actually quasi-analytical as they require either numerical inversion of the Laplace transforms or some iterative techniques (Zlotnik and Huang, 1999;Moench and Barlow, 2000;Lal, 2001).…”

Approximate analytical solutions of the Forchheimer equation

“…Barenblatt et al, 1990;Chen et al, 1995;Govindaraju and Koelliker, 1994;Hogarth et al, 1997;Parlange et al, 2000).…”