> C. Ruyer-Quil
A conservative and consistent model for shallow water equations that satisfies the Galilean invariance principle
Gianluca Lavalle, Francois Charru and Jean-Paul Vila
The shallow water (or Saint-Venant) equations have been developed for shallow flows, such as thin liquid films, to avoid the use of the full Navier-Stokes equations, which turn out to be very expensive for computation.
The current work presents a conservative and consistent model of shallow water equations. It also satisfies the Galilean invariance principle, which plays an important role in aerospace applications involving rotative components. This model has been developed for a liquid film flowing down an inclined plane, driven by gravity and by a prescribed shear stress at the free surface, including possibly a moving plane.
In order to verify and validate the quality of the model, stability analysis has been provided and compared to Orr-Sommerfeld theory and other consistent shallow water models, taken from litterature (C. Ruyer-Quil and P. Manneville, Eur. Phys. J. B, 1998). Furthermore, after implementation into the ONERA code, numerical test concerning instabilities on thin liquid films have been validated by comparison with experimental data (J. Liu and J.P. Gollub, Phys.Fluids, 1994).