Dispersive shallow water wave modelling. Part IV: Numerical simulation on a globally spherical geometry

TL;DR

This paper presents a numerical simulation method for dispersive shallow water waves on a spherical Earth, using a splitting algorithm, and applies it to idealized models and real-world tsunami events, comparing results with measurements.

Contribution

It introduces a two-step predictor-corrector numerical scheme for dispersive wave simulation on a sphere, combining elliptic and hyperbolic solvers, and demonstrates its effectiveness on real tsunami data.

Findings

The algorithm accurately models dispersive wave propagation on a sphere.

Sphericity and rotation significantly influence wave dispersion.

Simulation results align well with observed tsunami measurements.

Abstract

In the present manuscript, we consider the problem of dispersive wave simulation on a rotating globally spherical geometry. In this Part IV, we focus on numerical aspects while the model derivation was described in Part III. The algorithm we propose is based on the splitting approach. Namely, equations are decomposed on a uniformly elliptic equation for the dispersive pressure component and a hyperbolic part of shallow water equations (on a sphere) with source terms. This algorithm is implemented as a two-step predictor-corrector scheme. On every step, we solve separately elliptic and hyperbolic problems. Then, the performance of this algorithm is illustrated on model idealised situations with an even bottom, where we estimate the influence of sphericity and rotation effects on dispersive wave propagation. The dispersive effects are quantified depending on the propagation distance over the sphere and on the linear extent of generation region. Finally, the numerical method is applied to a couple of real-world events. Namely, we undertake simulations of the Bulgarian 2007 and Chilean 2010 tsunamis. Whenever the data is available, our computational results are confronted with real measurements.