Parametric model order reduction development for Navier-Stokes equations from 2D chaotic to 3D turbulent flow problems

This work presents new developments for the application of parametric model-order reduction (pMOR) for engineering thermal-fluid applications. The pMOR technique is built on a reduced order model (ROM), in which the governing thermal-fluid transport equations are approximated by a low-dimensional system of ordinary differential equations involving relatively few (N ≈ 20-200) time-dependent unknowns. Basis functions for the ROMs are derived from high-fidelity, full-order models (FOMs) typified by large-eddy simulations (LES) or direct numerical simulations (DNS) of turbulence that involve N ≈ =10^6-10^11 unknowns. The goal of pMOR is to track quantities of interest as a function of input parameters, such as Reynolds or Rayleigh number, without rerunning the FOM. This dissertation addresses several outstanding challenges in the application of pMOR to engineering problems, including: developing a time-averaged error indicator for thermal-fluids systems; improved stabilization strategies for ROM-based simulations of turbulence; and an efficient low-rank, symmetry preserving, tensor decomposition for the ROM advection operator that alleviates the leading order, O(N^3), computational complexity in time-advancement of ROMs.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2023

Author dc:creator

• Tsai, Ping-Hsuan

Contributors dc:contributor

• Fischer, Paul
• Olson, Luke
• Solomonik, Edgar
• Patera, Anthony

• Reduced Order Model
• Parametric Model Order Reduction
• Model Order Reduction
• Turbulence
• Error Indicator
• Pod
• Stabilization Method
• Regularization
• Tensor Decomposition
• Cp Decomposition

Statement dc:rights

• Copyright 2023 Ping-Hsuan Tsai

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/121993

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F121993