An optimizing reduced order FDS for the tropical Pacific Ocean reduced gravity model
Zhendong Luo, Jing Chen, Jiang Zhu, Ruiwen Wang, I. M. Navon
Proper orthogonal decomposition (POD) and singular value decomposition (SVD) methods are used to study a finite difference discretization scheme (FDS) for the tropical Pacific Ocean reduced gravity model. Ensembles of data are compiled from transient solutions computed from the discrete equation system derived by FDS for the tropical Pacific Ocean reduced gravity model. The optimal orthogonal bases are used to reconstruct the elements of the ensemble with POD and SVD. Combining the above approach with a Galerkin projection procedure yields a new optimizing FDS model of lower dimensions and high accuracy for the tropical Pacific Ocean reduced gravity model.
An error estimate of the new reduced order optimizing FDS model is then derived. Numerical examples are presented illustrating that the error between the POD approximate solution and the full FDS solution is consistent with previously obtained theoretical results, thus validating the feasibility and efficiency of POD method.