University of Illinois Urbana-Champaign

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

Tsai, Ping-Hsuan

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

Description

Title
Parametric model order reduction development for Navier-Stokes equations from 2D chaotic to 3D turbulent flow problems
Author(s)
Tsai, Ping-Hsuan
Issue Date
2023-11-17
Director of Research (if dissertation) or Advisor (if thesis)
Fischer, Paul
Doctoral Committee Chair(s)
Fischer, Paul
Committee Member(s)
  • Olson, Luke
  • Solomonik, Edgar
  • Patera, Anthony
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Reduced Order Model
  • Parametric Model Order Reduction
  • Model Order Reduction
  • Turbulence
  • Error Indicator
  • POD
  • Stabilization Method
  • Regularization
  • Tensor Decomposition
  • CP Decomposition
Abstract
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.
Graduation Semester
2023-12
Type of Resource
Thesis
Copyright and License Information
Copyright 2023 Ping-Hsuan Tsai

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