A robust and stable numerical scheme for a depth-averaged Euler system
For researchers in shallow water flows, this provides a robust numerical method for a complex model, though it is an incremental improvement over existing schemes.
The paper proposes an efficient numerical scheme for a non-hydrostatic Saint-Venant type model, proving properties like positivity, well-balancing, and entropy inequality, and demonstrating stability even as water depth tends to zero.
We propose an efficient numerical scheme for the resolution of a non-hydrostatic Saint-Venant type model. The model is a shallow water type approximation of the incompressbile Euler system with free surface and slightly differs from the Green-Naghdi model. The numerical approximation relies on a kinetic interpretation of the model and a projection-correction type scheme. The hyperbolic part of the system is approximated using a kinetic based finite volume solver and the correction step implies to solve an elliptic problem involving the non-hydrostatic part of the pressure. We prove the numerical scheme satisfies properties such as positivity, well-balancing and a fully discrete entropy inequality. The numerical scheme is confronted with various time-dependent analytical solutions. Notice that the numerical procedure remains stable when the water depth tends to zero.