Model Order Reduction of Nonlinear Parabolic PDE Systems with Moving Boundaries Using Sparse Proper Orthogonal Decomposition: Application to Hydraulic Fracturing
Abstract
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.
Subject
nonlinear model reductionproper orthogonal decomposition
Galekin's method
moving boundary systems
hydraulic fracturing
naive elastic net
Citation
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 https : / /hdl .handle .net /1969 .1 /173981.