Linearised Boussinesq equation for modelling bank storage – a correction

Fully conservative coupling of HEC-RAS with MODFLOW to simulate stream–aquifer interactions in a drainage basin

“…An overview of the state-of-the-art can be found in the recent work of Sophocleous (2002). Analytical studies of the linearized 1D Boussinesq equation to describe changes in bank storage caused by temporal variations in water elevation of the adjacent channel have been pursued by Cooper and Rorabaugh (1963), Hogarth et al (1997), Moench and Barlow (2000), and Hantush, 2005), whereas its nonlinear counterpart problem has been analyzed by Serrano and Workman (1998) and Parlange et al (2000), among others. The analytical work of Theis (1947) on streamflow depletion by pumping was revisited and expanded by Hunt (1999), among many contributors to the subject.…”

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“…One solution is obtained for β = 0 and is discussed below. The other for β → ∞, β/α = 1, has also been discussed in Hogarth et al (1997) and gives h linearly dependent on x.…”

“…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). Chen et al (1995) also used Barenblatt's solution to check their numerical scheme of the ODE associated with Equation (1), that is, when there is a similarity solution.…”

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).…”