Structure-Preserving Reduced- Order Modeling of Non-Traditional Shallow Water Equation

An energy preserving reduced order model is developed for the nontraditional shallow water equation (NTSWE) with full Coriolis force. The NTSWE in noncanonical Hamiltonian/Poisson form discretized space by finite differences. resulting system of ordinary differential equations integrated time average vector field (AVF) method. Poisson structure exhibits a skew-symmetric matrix depending on state variables. preserving, computationally efficient reduced-order (ROM) constructed proper orthogonal decomposition Galerkin projection. nonlinearities are computed ROM efficiently discrete empirical interpolation Preservation semi-discrete and enstrophy shown model, which ensures long term stability solutions. accuracy computational efficiency ROMs two numerical test problems