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

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