Proper Orthogonal Decomposition Reduced Order Model for Tear Film Flows

Samir Sahyoun, Dan Wilson, Seddik M. Djouadi, Steven M. Wise, Hamid Ait Abderrahmane

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Tear film plays a key role in protecting the cornea surface against contaminations and dry eye syndrome which can lead to symptoms of discomfort, visual trouble, and tear film instability with the potential to damage the ocular surface. In this paper, coupled nonlinear partial differential equations of the fourth order proposed by Aydemir et al. to describe the evolution of tear film dynamics are considered. These equations are of Benney type and known to suffer from unbounded behavior and lack of a global attractor. The objective here is to identify a reduced order modeling framework with the potential to be used as a basis for control in future work using smart tears with a surfactant that can modify the surface tension to prevent tear film breakup. Since the dynamics are infinite dimensional and nonlinear, a reduced order model based on the proper orthogonal decomposition (POD) is developed, analyzed, and compared to the full order model. Numerical simulations illustrate that only a small number of POD modes are required to accurately capture the tear film dynamics allowing for the full partial differential model to be represented as a low-dimensional set of coupled ordinary differential equations.

Original languageBritish English
Title of host publication2021 American Control Conference, ACC 2021
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781665441971
StatePublished - 25 May 2021
Event2021 American Control Conference, ACC 2021 - Virtual, New Orleans, United States
Duration: 25 May 202128 May 2021

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Conference2021 American Control Conference, ACC 2021
Country/TerritoryUnited States
CityVirtual, New Orleans


Dive into the research topics of 'Proper Orthogonal Decomposition Reduced Order Model for Tear Film Flows'. Together they form a unique fingerprint.

Cite this