Sanjeeb Poudel - Dissertation Defense
"Enhancing Fluid and Thermal Simulations: Integrating Finite Element Method, Scientific Machine Learning, and Data Assimilation"
Abstract:
Computational simulations for fluid and heat dynamics are heavily constrained by three factors: spatial accuracy, temporal efficiency, and parametric uncertainty. This research presents a computational framework to address them:
- Spatial Accuracy: A pressure-robust Enriched Galerkin Finite Element Method that ensures stability and accuracy.
- Temporal Efficiency: A Scientific Machine Learning architecture that bypasses sequential time-stepping limits, significantly improving long-term neural network extrapolation.
- Parametric Uncertainty: An Ensemble Score Filter data-assimilation approach to guarantee reliable predictions in complex, high-dimensional models like two-phase porous media flows.
