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Öğe Structure-Preserving Reduced- Order Modeling of Non-Traditional Shallow Water Equation(Springer Science and Business Media Deutschland GmbH, 2021) Yildiz, Süleyman; Uzunca, Murat; Karasözen, BülentAn energy- preserving reduced -order model (ROM) is developed for the non-traditional shallow water equation (NTSWE) with full Coriolis force. The NTSWE in the noncanonical Hamiltonian/Poisson form is discretized in space by finite differences. The resulting system of ordinary differential equations is integrated in time by the energy preserving average vector field (AVF) method. The Poisson structure of the discretized NTSWE exhibits a skew-symmetric matrix depending on the state variables. An energy- preserving, computationally efficient reduced order model (ROM) is constructed by proper orthogonal decomposition with Galerkin projection. The nonlinearities are computed for the ROM efficiently by discrete empirical interpolation method. Preservation of the discrete energy and the discrete enstrophy are shown for the full- order model, and for the ROM which ensures the long- term stability of the solutions. The accuracy and computational efficiency of the ROMs are shown by two numerical test problems. © 2021, Springer Nature Switzerland AG.
