Commutation Error in Reduced Order Modeling

We investigate the effect of spatial filtering on the recently proposed data-driven correction reduced order model (DDC-ROM). We compare two filters: the ROM projection, which was originally used to develop the DDC-ROM, and the ROM differential filter, which uses a Helmholtz operator to attenuate the small scales in the input signal. We focus on the following questions: ``Do filtering and differentiation with respect to space variable commute, when filtering is applied to the diffusion term?'' or in other words ``Do we have commutation error (CE) in the diffusion term?" and ``If so, is the commutation error data-driven correction ROM (CE-DDC-ROM) more accurate than the original DDC-ROM?'' If the CE exists, the DDC-ROM has two different correction terms: one comes from the diffusion term and the other from the nonlinear convection term. We investigate the DDC-ROM and the CE-DDC-ROM equipped with the two ROM spatial filters in the numerical simulation of the Burgers equation with different diffusion coefficients and two different initial conditions (smooth and non-smooth).

Name thesis:degree_name

M.S.

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2018

Author dc:creator

• Koc, Birgul

Chair dc:contributor.committeechair

• Iliescu, Traian

Committee members dc:contributor.committeemember

• Borggaard, Jeffrey T.
• Gugercin, Serkan

• Reduced Order Modeling
• Data-Driven Modeling
• Filtering
• Closure Modeling
• Commutation Error

Statement dc:rights

• Creative Commons Attribution-ShareAlike 3.0 United States

Licence dc:rights.uri

• http://creativecommons.org/licenses/by-nc-sa/3.0/us/

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10919/87537

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/87537