A new run-up algorithm based on local high-order analytic expansions

TL;DR

This paper introduces a novel wave run-up algorithm utilizing high-order local asymptotic solutions near the shoreline, improving accuracy in modeling wave behavior in nonlinear shallow water scenarios.

Contribution

The paper presents a new run-up algorithm based on high-order local analytical expansions, enhancing shoreline motion prediction accuracy in nonlinear shallow water equations.

Findings

Algorithm accurately models shoreline motion in various wave slope cases.

Simulation results agree well with analytical and experimental data.

Method improves upon existing run-up prediction techniques.

Abstract

The practically important problem of the wave run-up is studied in this article in the framework of Nonlinear Shallow Water Equations (NSWE). The main novelty consists in the usage of high order local asymptotic analytical solutions in the vicinity of the shoreline. Namely, we use the analytical techniques introduced by S. Kovalevskaya and the analogy with the compressible gas dynamics (i.e. gas outflow problem into the vacuum). Our run-up algorithm covers all the possible cases of the wave slope on the shoreline and it incorporates the new analytical information in order to determine the shoreline motion to higher accuracy. The application of this algorithm is illustrated on several important practical examples. Finally, the simulation results are compared with the well-known analytical and experimental predictions.