Numerical Analysis and Scientific Computing Seminar | Karthik Duraisamy, Predictive Reduced Order Models for Multi-scale, Multi-physics Problems

In person (MC 5417) and online talk (for Zoom Link please contact ddelreyfernandez@uwaterloo.ca)  

Speaker

Associate Professor Karthik Duraisamy, University of Michigan Department of Aerospace Engineering

Title

Predictive Reduced Order Models for Multi-scale, Multi-physics Problems

Abstract

This talk presents advances towards the development of effective projection-based reduced order models (ROMs) for complex multi-scale multi-physics problems. As a representative application, we consider combustion dynamics in a rocket engine, which is characterized by a complex coupling between heat release, hydrodynamics and acoustics.  

- The first part of the talk is focused on improving robustness and consistency: A structure-preserving transformation of the state variables is used along with a discretely consistent least squares formulation to yield symmetrized model operators in both explicit and implicit time integration settings. The resulting reduced order model is well-conditioned and globally stable. Local stability is promoted via limiters that enforce physical realizability.  

- The second part of the talk is focused on accomplishing true predictivity: Dimension reduction approaches based on static manifolds - linear or non-linear - are not effective in predictive modeling of multi-scale problems with significant transport effects. To address this issue, we present an adaptive formulation in which the basis vectors and sampling points are adapted online using a novel non-local procedure. Opportunities for further improvement are also highlighted.  

- The last part of the talk discusses tractability :  ROMs are used to enable computations of problems for which full order models are not affordable. In particular, we develop a multi-fidelity framework in which component-level ROMs are trained on small domains, and integrated to enable full-system predictions in an affordable manner.  In essence, geometry-specific training is replaced by the response generated by perturbing the characteristics at the boundary of the truncated domain. This training method is shown to enhance predictive capabilities and robustness of the resulting ROMs, including conditions outside the training range.