Output from a shallow water equation model of water in a bathtub. The water experiences five splashes which generate surface gravity waves that propagate away from the splash locations and reflect off the bathtub walls.
The shallow water equations are a set of hyperbolic partial differential equations that describe the flow below a pressure surface in a fluid. They are derived from depth-integrating the Navier–Stokes equations in cases where the horizontal length scale is much greater than the vertical length scale. The shallow water equations can also be simplified to the commonly used 1-D Saint Venant equation.Animation: Dan Copsey