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A mass conservative method for the integration of the two dimensional groundwater (Boussinesq) equation
The Boussinesq Model
This code implements a new conservative finite-volume numerical solution for the two-dimensional groundwater flow (Boussinesq) equation, which can be used for investigations of hillslope subsurface flow processes and simulations of catchment hydrology. The Boussinesq equation, which is integrated for each grid element, can take account of the local variations of topography and soil properties within the individual elements. The numerical method allows for wetting and drying of the water table, without “ad hoc assumptions.” The stability and convergence of the method is shown to be guaranteed a priori by the properties of the solver itself, even with respect to the boundary conditions, an aspect that has been neglected in previous literature. The numeric solutions were validated against some approximate analytical solutions and compared to those of another (1-D) numerical solver of the Boussinesq equation. Further theoretical details are now available on http://onlinelibrary.wiley.com/doi/10.1002/wrcr.20072/abstract or can be asked the authors (emanuele.cordano@gmail.com) without any hesitation.
Brief Historical Introduction
The earliest drafts of code were borm from an idea of Dr. Emanuele Cordano, Prof. Riccardo Rigon and Prof. Vincenzo Casulli (University of Trento) about numerical methods for solving groundwater equation preserving the mass conservation principle and taking into account the possible variability of bedrock topograhy and soil properties within the integration cell. Some of the first 2009/2010 informal presentations introduce the physical problem and are available here.
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Code
The code is available with GPL 3.0 license (www.gnu.org) and can be downloaded via GitHUb. A Doxygen-generated documentation of the code is available on the subdirectory "doc" and on https://github.com/ecor/boussinesq/blob/master/doc/html/index.html . The source code is mostly written in C using FluidTurtle formalism (Rigon et al., 1990s).
Instructions for Usage
Here are the [git] (http://git-scm.com/) and [git-Wikipedia] (http://en.wikipedia.org/wiki/Git_(software) containing the instruction to download the code, another useful tutorial on git is here This section is UNDER CONSTRUSCTION and will be performed as soon!