2D non-hydrostatic pressure model integration for high-performance computing

In the context of free-surface flow simulations, Shallow Water Equations (SWE) models solved using finite volume numerical schemes are common. Certain configurations involving complex flows exhibit non-negligible vertical acceleration, so that the implementation of a non-hydrostatic formulation can enhance the capture of flow dynamics and improve simulation accuracy. Here, we explore the implementation of a 2D non-hydrostatic model in the open-source code SERGHEI from a High-Performance Computing (HPC) perspective. Two main approaches are followed based on the Depth-Integrated Incompressibility Condition (DIIC): a Hyperbolic-Elliptic (HE) model and a Hyperbolic-Relaxed (HR) model. Top-notch libraries such as Kokkos and Trilinos are used to efficiently calculate fluxes in the HR model and solve the sparse matrix system in the HE model, ensuring the performance and portability of the code. The performance-aware comparison of these two models is of great interest, due to the complexity of the problem and the bottlenecks regarding matrix inversions and Δt limitation.