For this research project, we have been doing research on the shallow water equations: a set of hyperbolic partial differential equations. These equations exist as a set of three primary equations . However, there is another version of the shallow water equations called the Saint Venant’s equations. These equations are similar to the standard shallow water equations, but these equations have been reduced to one-dimension. The primary goal of our research has been to investigate the behavior and mathematical construction of the Saint Venant’s equations and model these equations using COMSOL. Regardless of the equation type, standard or Saint Venant’s, it is useful to note that these equations are only applicable under some restrictions such as hydrostatic balance and distance from one crest to another, on any two waves, must be greater than the distance from the free surface to the sea floor (bottom topography). These restrictions, along with initial conditions, are also a target in this research, and these conditions and equations can help with flood predictions and regulations not only now, but also in the future.
Jones, Chase, "Shallow Water Equations and Floor Topography Affect on Sea Surface" (2020). Mathematics Senior Capstone Papers. 16.