Kinetic entropy for the layer-averaged hydrostatic Navier-Stokes equations
Provides a stable numerical method for geophysical fluid dynamics simulations, though incremental as it extends existing techniques.
The authors developed a numerical scheme for the hydrostatic free surface Navier-Stokes equations that ensures positivity of water depth, well-balancing, and a discrete energy inequality, extending prior shallow water results.
We are interested in the numerical approximation of the hydrostatic free surface incompressible Navier-Stokes equations. By using a layer-averaged version of the equations, we are able to extend previous results obtained for shallow water system. We derive a vertically implicit / horizontally explicit finite volume kinetic scheme that ensures the positivity of the approximated water depth, the well-balancing and a fully discrete energy inequality.