A Comparative Perspective of Numerical Methods for Shallow Water Equations for Flood Application

Floods are the most devastating natural disasters in the world. Knowledge and mastery of these phenomena is essential for scientists to guide and help decision makers. In this perspective, we are obliged to solve the Shallow Water Equations (SWE) which governs free surface flows which requires numerical approximations. The solutions obtained depend directly on the methods used. Fortunately, since the advancement of computing, researchers and engineers have continued to develop more and more efficient tools that use different methods. This study proposes to use two popular free software in order to compare the classical methods: finite differences and finite volumes. The finite difference methods consist to make a discretization using a predefined mesh (generally rectangular). The finite volume method consists of discretizing the flow domain into a multitude of control volumes (or cells), then performing mass and momentum balances on these small volumes. The results are the distribution of water depths and the flow velocity field throughout the computational domain, thus leading to knowledge of the spread and the general dynamics of the flood. The analysis is made by modeling a section of the Sambirano river, Madagascar during the flood period with a high resolution DTM (Digital Terrain Model). Studies show that the finite volume method with the use of an unstructured triangular mesh is the most suitable for modeling shallow water flows in a natural environment.