Model order reduction of nonlinear parabolic PDE systems with moving boundaries using sparse proper orthogonal decomposition methodology

摘要

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. Within this context, 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. To overcome this challenge, we introduce sparse proper orthogonal decomposition (SPOD)-Galerkin methodology that 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.