# Non-Hydrostatic Pressure Shallow Flows: GPU Implementation Using Finite Volume and Finite Difference Scheme

## TL;DR

This paper presents a GPU-optimized, second-order, well-balanced hybrid finite volume-finite difference scheme for non-hydrostatic shallow flow models, demonstrating efficiency and accuracy through complex test cases.

## Contribution

It introduces a novel GPU-adapted hybrid numerical scheme for non-hydrostatic shallow flows, combining finite volume and finite difference methods with a new wave breaking handling approach.

## Key findings

- Efficient GPU implementation of the scheme.
- Accurate results on complex bathymetry test cases.
- Demonstrated robustness in wave breaking scenarios.

## Abstract

We consider the depth-integrated non-hydrostatic system derived by Yamazaki et al. An efficient formally second-order well-balanced hybrid finite volume finite difference numerical scheme is proposed. The scheme consists of a two-step algorithm based on a projection-correction type scheme initially introduced by Chorin-Temam [15]. First, the hyperbolic part of the system is discretized using a Polynomial Viscosity Matrix path-conservative finite volume method. Second, the dispersive terms are solved by means of compact finite differences. A new methodology is also presented to handle wave breaking over complex bathymetries. This adapts well to GPU-architectures and guidelines about its GPU implementation are introduced. The method has been applied to idealized and challenging experimental test cases, which shows the efficiency and accuracy of the method.