Barrier Simulations and Experimental Calculations Using Cell Merging Method

TL;DR

This paper introduces a novel cell merging method for shallow water simulations with permeable boundaries, demonstrating second order convergence and realistic inundation modeling.

Contribution

The paper presents a new cell merging approach combining wave propagation and gradient reconstruction, improving scalability and accuracy in boundary simulations.

Findings

Second order convergence in model problems

Effective handling of complex boundary shapes

Realistic inundation simulation around an island

Abstract

We apply the cell merging method to a model shallow water problem with a permeable boundary. We use a cut cell approach which is more easily and systematically scalable with different shapes of boundaries. The novel cell merging method presented in this paper uses both wave propagation algorithm and gradient reconstruction for second order corrections, along with minmod and Barth-Jespersen limiters. We observe second order convergence in two model problems, one with a linear boundary and other with a composite, V-shaped boundary. We assess the effectiveness of these two boundaries by doing a realistic scenario including an island and observing inundation at the peak of the island.