An augmented basis method for reduced order models of turbulent flow

Kaneko, Kento

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https://hdl.handle.net/2142/115642 Copy

Description

Title

An augmented basis method for reduced order models of turbulent flow

Author(s)

Kaneko, Kento

Issue Date

2022-04-21

Director of Research (if dissertation) or Advisor (if thesis)

Fischer, Paul

Doctoral Committee Chair(s)

Fischer, Paul

Committee Member(s)

• Pearlstein, Arne
• Matalon, Moshe
• Olson, Luke

Department of Study

Mechanical Sci & Engineering

Discipline

Theoretical & Applied Mechans

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Reduced Order Model
• Model-Order Reduction
• Turbulence

Abstract

Reduced-order models (ROMs) offer a promising approach for parametric analysis of engineering fluid dynamics applications. The standard procedure consists of using solution snapshots to produce a truncated POD basis, which is in turn used in a Galerkin projection of the governing Navier-Stokes equations (NSE). Unfortunately, the standard POD approach has well-known limitations for high Reynolds number flows that are largely attributable to the lack of fine-scale structure in the low-rank POD bases, which tend to be spatially smooth and therefore unable to generate sufficient small-scale dissipation to stabilize the solution for a small number of modes, N. Even with stabilization, the required value of N is often sufficiently large that these approaches are impaired by the O(N3) costs associated with evaluation of the third-order advection tensor at each step of the ROM time-advancement. We present a novel non-intrusive stabilization technique in the form of basis augmentation that, in many cases, reduces the total number of modes required to produce a stable and accurate ROM reconstruction for turbulent flows at modest Reynolds numbers. The approach involves augmenting the standard POD modes with divergence-free projections of subsets of POD-expanded terms originating from the advection term. Differing combinations of these basis elements are considered. Bases that include interactions with lifting function and self-interactions have proven to be quite effective for several challenging flow problems with relatively low values of Nˆ, where Nˆ is the total number of basis including the augmentation modes. We demonstrate this proposed basis set on several challenging problems and compare its stability properties with alternative stabilization approaches for POD-based ROMs.

Graduation Semester

2022-05

Type of Resource

Thesis

Copyright and License Information

Copyright 2022 Kento Kaneko

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