Shallow water equations

The Shallow Water Equations (SWE) are a set of hyperbolic partial differential equations that describe the flow of a thin layer of fluid, such as water in rivers, lakes, and coastal areas. These equations are particularly useful in hydraulic and environmental engineering for modeling phenomena like flooding, tsunami propagation, and sediment transport. The SWE are derived under the assumption that the horizontal length scale of the fluid flow is much larger than the vertical scale of the fluid depth.