An augmented basis method for reduced order models of turbulent flow

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Theoretical & Applied Mechans

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Kaneko, Kento

Contributors dc:contributor

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

• Reduced Order Model
• Model-Order Reduction
• Turbulence

Statement dc:rights

• Copyright 2022 Kento Kaneko

Language dc:language

en, eng

Handle dc:identifier

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

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F115642