Sidhu, Harwinder Singh (2018-08). Model Order Reduction of Nonlinear Parabolic PDE Systems with Moving Boundaries Using Sparse Proper Orthogonal Decomposition: Application to Hydraulic Fracturing. Master's Thesis.
Thesis
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.
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.
ETD Chair
Kwon, Joseph Associate Professor and holder of the Kenneth R. Hall Career Development Professorship
