Model Order Reduction of Nonlinear Parabolic PDE Systems with Moving Boundaries Using Sparse Proper Orthogonal Decomposition: Application to Hydraulic Fracturing
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Developing reduced-order models for nonlinear parabolic partial differential equation (PDE) systems with time-varying spatial domains remains a key challenge as the dominant spatial patterns of the system change with time. To address this issue, there have been several studies where the time-varying spatial domain is transformed to the time-invariant spatial domain by using an analytical expression that describes how the spatial domain changes with time. However, this information is not available in many real-world applications, and therefore, the approach is not generally applicable. This study aims to overcome this challenge by introducing sparse proper orthogonal decomposition (SPOD)-Galerkin methodology. The proposed methodology exploits the key features of ridge and lasso regularization techniques for the model order reduction of such systems. This methodology is successfully applied to a hydraulic fracturing process, and a series of simulation results indicates that it is more accurate in approximating the original nonlinear system than the standard POD-Galerkin methodology.
Subjectnonlinear model reduction
proper orthogonal decomposition
moving boundary systems
naive elastic net
Sidhu, Harwinder Singh (2018). Model Order Reduction of Nonlinear Parabolic PDE Systems with Moving Boundaries Using Sparse Proper Orthogonal Decomposition: Application to Hydraulic Fracturing. Master's thesis, Texas A & M University. Available electronically from