# Shallow Water Equations

## Model Data

Physics Modes: custom equation convection and diffusion

Saint-Venant shallow water equations is a simplified model of fluid flow with a free surface. The non-conservative form of the equations read

$\left\{\begin{array}{;‘} \ \frac{\partial h}{\partial t} + (u\frac{\partial h}{\partial x} + v\frac{\partial h}{\partial y} ) + (h+H)(\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y}) = 0 \\\ \frac{\partial u}{\partial t} + (u\frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y} ) = -g\frac{\partial h}{\partial x} \\\ \frac{\partial v}{\partial t} + (u\frac{\partial v}{\partial x} + v\frac{\partial v}{\partial y} ) = -g\frac{\partial h}{\partial y} \end{array}\right.$

where h is the unknown free surface height relative to the mean level H.

This model is available as an automated tutorial by selecting Model Examples and Tutorials… > Classic PDE > Shallow Water Equations from the File menu. Or alternatively, follow the step-by-step instructions below.