Shallow Water

• The Shallow Water equations is very commonly used for the numerical simulation of various geophysical shallow-water flows, such as rivers, lakes or coastal areas, rainfall runoff on agricultural fields or even atmosphere or avalanches when completed with appropriate source terms. Using an approach of finite volume method in FreeFem++, first on structured grid then on unstructured grid (FreeVol++), we will present several applications of the following Shallow Water equations (Saint - Venant system) in 2D with topographic source term :

Here u and v are the scalar components in the horizontal x,y directions of the depth-averaged velocity, h is the local water depth and g>0 denotes the gravity constant. U is the vector for the conservative variables, F(U) and G(U) stand for the flux functions respectively along the x and y directions and S(U) represents the bed slope source term.