Locally Adaptive Non-Hydrostatic Shallow Water Extension for Moving Bottom-Generated Waves

TL;DR

This paper introduces an adaptive non-hydrostatic shallow water model that efficiently simulates moving bottom-generated waves by limiting complex computations to critical areas, achieving over 50% reduction in computational time without sacrificing accuracy.

Contribution

The paper presents a novel adaptive approach that localizes the non-hydrostatic extension, significantly improving computational efficiency for wave simulations involving moving bottoms.

Findings

Adaptive model reduces computational time by over 50%.

Maintains accuracy comparable to global non-hydrostatic models.

Effectively simulates complex moving bottom-generated waves.

Abstract

We propose a locally adaptive non-hydrostatic model and apply it to wave propagation generated by a moving bottom. This model is based on the non-hydrostatic extension of the shallow water equations (SWE) with a quadratic pressure relation, which is suitable for weakly dispersive waves. The approximation is mathematically equivalent to the Green-Naghdi equations. Applied globally, the extension requires solving an elliptic system of equations in the whole domain at each time step. Therefore, we develop an adaptive model that reduces the application area of the extension and by that the computational time. The elliptic problem is only solved in the area where the dispersive effect might play a crucial role. To define the non-hydrostatic area, we investigate several potential criteria based on the hydrostatic SWE solution. We validate and illustrate how our adaptive model works by first applying it to simulate a simple propagating solitary wave, where exact solutions are known. Following that, we demonstrate the accuracy and efficiency of our approach in more complicated cases involving moving bottom-generated waves, where measured laboratory data serve as reference solutions. The adaptive model yields similar accuracy as the global application of the non-hydrostatic extension while reducing the computational time by more than 50%.