In this paper, we perform a comparison of two approaches for the parallelization of an existing, free software, FullSWOF 2D (http://www. univ-orleans.fr/mapmo/soft/FullSWOF/ that solves shallow water equations for applications in hydrology) based on
a domain decomposition strategy. The first approach is based on the classical MPI library while the second approach uses Parallel Algorithmic Skeletons and more precisely a library named SkelGIS (Skeletons for Geographical Information Systems). The first results presented in this article show that the two approaches are similar in terms of performance and scalability. The two implementation strategies are however very different and we discuss the advantages of each one.
Because of their capability to preserve steady-states, well-balanced schemes for Shallow Water equations are becoming popular. Among them, the hydrostatic reconstruction proposed in Audusse et al. (2004), coupled with a positive numerical flux, allow
s to verify important mathematical and physical properties like the positivity of the water height and, thus, to avoid unstabilities when dealing with dry zones. In this note, we prove that this method exhibits an abnormal behavior for some combinations of slope, mesh size and water height.
Overland flow on agricultural fields may have some undesirable effects such as soil erosion, flood and pollutant transport. To better understand this phenomenon and limit its consequences, we developed a code using state-of-the-art numerical methods:
FullSWOF (Full Shallow Water equations for Overland Flow), an object oriented code written in C++. It has been made open-source and can be downloaded from http://www.univ-orleans.fr/mapmo/soft/FullSWOF/. The model is based on the classical system of Shallow Water (SW) (or Saint-Venant system). Numerical difficulties come from the numerous dry/wet transitions and the highly-variable topography encountered inside a field. It includes runon and rainfall inputs, infiltration (modified Green-Ampt equation), friction (Darcy-Weisbach and Manning formulas). First we present the numerical method for the resolution of the Shallow Water equations integrated in FullSWOF_2D (the two-dimension version). This method is based on hydrostatic reconstruction scheme, coupled with a semi-implicit friction term treatment. FullSWOF_2D has been previously validated using analytical solutions from the SWASHES library (Shallow Water Analytic Solutions for Hydraulic and Environmental Studies). Finally, FullSWOF_2D is run on a real topography measured on a runoff plot located in Thies (Senegal). Simulation results are compared with measured data. This experimental benchmark demonstrate the capabilities of FullSWOF to simulate adequately overland flow. FullSWOF could also be used for other environmental issues, such as river floods and dam-breaks.
