Structure preserving model order reduction of shallow water equations

Date

2020-07-01

Author

Karasözen, Bülent
UZUNCA, MURAT

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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(POD)/discrete empirical interpolation method 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.

Subject Keywords

Discrete empirical interpolation, Finite-difference methods, Linearly implicit methods, Preservation of invariants; proper orthogonal decomposition; Tensorial proper orthogonal decomposition

URI

https://hdl.handle.net/11511/32364

Journal

MATHEMATICAL METHODS IN THE APPLIED SCIENCES

DOI

https://doi.org/10.1002/mma.6751

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

B. Karasözen and M. UZUNCA, “Structure preserving model order reduction of shallow water equations,” MATHEMATICAL METHODS IN THE APPLIED SCIENCES, pp. 0–0, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32364.