Structure-Preserving Reduced- Order Modeling of Non-Traditional Shallow Water Equation
[ X ]
Tarih
2021
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer Science and Business Media Deutschland GmbH
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
An 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.
Açıklama
Anahtar Kelimeler
Finite difference methods, Hamiltonian mechanics, Implicit time integrator, Model order reduction, Shallow water equation
Kaynak
International Series of Numerical Mathematics
WoS Q Değeri
Scopus Q Değeri
Q4
Cilt
171
