Events
DMS Graduate Student Seminar |
| Time: Nov 20, 2019 (03:00 PM) |
| Location: Parker Hall 249 |
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Details: Speaker: Dr. Olcay Ciftci Title: A Newton - GFEM Method to Solve Reduced Dimensional Variable Density Flow and Solute Transport Equations Using POD. Abstract: Variable Density Flow and Solute Transport (VDFST) is a coupled nonlinear dynamical system that is widely used to simulate seawater intrusion and related problems. Due to the coupling process, the governing equations must be solved simultaneously. Although Finite Difference (FD) method is usually used to solve a single flow model, Galerkin Finite Element Method (GFEM) is often adopted to solve VDFST models. Proper Orthogonal Decomposition (POD), also known as Karhunen - Loeve (K - L) expansion or principle components analysis, was first introduced by Lumley (1967) to identify coherent structures in dynamical systems. In recent years, the technique has been widely used in studies and implemented effectively to a variety of fields such as control problems, inverse problems, image processing, signal analysis, pattern recognition, data compression, oceanography, and fluid mechanics. POD is an effective numerical technique to reduce the computational cost for state estimation, forward prediction and inverse modeling. The primary goal in POD is to obtain an optimal low dimensional basis for representing a set of high-dimensional experimental or simulation data. Each basis, known by several names such as POD basis, Proper Orthogonal Modes (POM), empirical Eigenfunctions or empirical orthogonal functions, is associated with a certain amount of variance or energy. In my research, GFEM-POD method was used with Newton iteration to reduce the computational time and the relative error between the results we obtain from the reduced dimensional and high dimensional models. The modified Henry problem and Elder problems were used as benchmarks to testify the capability of the model. |