论文标题
非传统浅水方程的降低结构的降低订单模型
Structure-preserving Reduced Order Modeling of non-traditional Shallow Water Equation
论文作者
论文摘要
为非传统的浅水方程（NTSWE）提供了完全的coriolis力，为保留降低的订单模型提供了降低的订单模型。非规范性汉密尔顿/泊松形式中的NTSWE在空间中被有限差异而离散。普通微分方程的最终系统通过能量保存平均矢量场（AVF）方法的时间整合。离散化的NTSWE的泊松结构取决于状态变量，表现出偏斜的矩阵。通过适当的正交分解与Galerkin投影构建的能量保存，计算有效的还原模型（ROM）是构建的。通过离散的经验插值法有效地计算了ROM的非线性。为完整阶模型显示了半差异能量和肠道的保存，以及可确保解决方案的长期稳定性的ROM。 ROM的准确性和计算效率由两个数值测试问题显示
An energy preserving reduced order model is developed for the nontraditional 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 NTSWE in discretized 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 semi-discrete energy and the 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
