Structure Preserving Model Order Reduction of Shallow Water Equations
Abstract
In this paper, we present two different approaches for constructing reduced-order models (ROMs) for the two-dimensional shallow water equation (SWE). The first one is based on the noncanonical Hamiltonian/Poisson form of the SWE. After integration in time by the fully implicit average vector field method, ROMs are constructed with proper orthogonal decomposition/discrete empirical interpolation method (POD/DEIM) that preserves the Hamiltonian structure. In the second approach, the SWE as a partial differential equation with quadratic nonlinearity is integrated in time by the linearly implicit Kahan's method and ROMs are constructed with the tensorial POD that preserves the linear-quadratic structure of the SWE. We show that in both approaches, the invariants of the SWE such as the energy, enstrophy, mass, and circulation are preserved over a long period of time, leading to stable solutions. We conclude by demonstrating the accuracy and the computational efficiency of the reduced solutions by a numerical test problem.
Keywords
Cite
@article{arxiv.1907.09406,
title = {Structure Preserving Model Order Reduction of Shallow Water Equations},
author = {Bülent Karasözen and Süleyman Yıldız and Murat Uzunca},
journal= {arXiv preprint arXiv:1907.09406},
year = {2021}
}