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.

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.

Full text

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