This project focused on developing efficient reduced-order models for collisionless electrostatic plasma simulations governed by the Vlasov-Poisson equation. The approach decomposes the solution manifold into local regions using physical time or electric-field energy and employs a tensorial method to accelerate nonlinear computations. The resulting models accurately capture Landau damping and two-stream instability in parametric and predictive regimes, achieving approximately 90x speedup over the full-order simulations.

“Local Reduced-Order Modeling for Electrostatic Plasmas by Physics-Informed Solution Manifold Decomposition”

by P.-H. Tsai, S. W. Chung, D. Ghosh, J. Loffeld, Y. Choi, and J. L. Belof

This project focused on developing stabilized reduced-order models for the efficient simulation of turbulent flows. A new time-relaxation reduced-order model (TR-ROM) was introduced to control numerical instabilities by selectively filtering the marginally resolved scales. The approach was evaluated for turbulent channel flow at friction Reynolds numbers of 180 and 395, where it provided more accurate predictions of Reynolds stresses than standard and existing stabilized ROMs in both reproduction and predictive regimes.

“A Time-Relaxation Reduced Order Model for the Turbulent Channel Flow”

by P.-H. Tsai, P. Fischer, and T. Iliescu

This project focused on developing error-indicated parametric reduced-order models for unsteady natural convection. The approach combines POD-hGreedy sampling with stabilized ROMs to efficiently predict flow and heat-transfer quantities in challenging regimes involving bifurcations, multiple solutions, and spatio-temporal chaos.

“Parametric Model-Order-Reduction Development for Unsteady Convection”

by P.-H. Tsai and P. Fischer