Extension of a Roe-type Riemann solver scheme to model non-hydrostatic pressure shallow flows

The aim of this work is, first of all, to extend a finite volume numerical scheme, previously designed for hydrostatic Shallow Water (SWE) formulation, to Non Hydrostatic Pressure (NHP) depth averaged model. The second objective is focused on exploring two available options in the context of previous work in this field: Hyperbolic-Elliptic (HE-NHP) formulations solved with a Pressure-Correction technique (PCM) and Hyperbolic Relaxation formulations (HR-NHP). Thus, besides providing an extension of a robust and well-proved Roe-type scheme developed for hydrostatic SWE to solve NHP systems, the work assesses the use of first order numerical schemes in the kind of phenomena typically solved with higher order methods. In particular, the relative performance and differences of both NHP numerical models are explored and analysed in detail. The performance of the models is compared using a steady flow test case with quasi-analytical solution and another unsteady case with experimental data, in which frequencies are analysed in experimental and computational results. The results highlight the need to understand the behaviour of a parameter-dependent model when using it as a prediction tool, and the importance of a proper discretization of non-hydrostatic source terms to ensure stability. On the other hand, it is proved that the incorporation of a non-hydrostatic model to a shallow water Roe solver provides good results.