TY - GEN
T1 - Proper Orthogonal Decomposition Reduced Order Model for Tear Film Flows
AU - Sahyoun, Samir
AU - Wilson, Dan
AU - Djouadi, Seddik M.
AU - Wise, Steven M.
AU - Abderrahmane, Hamid Ait
N1 - Funding Information:
This work was supported in part by the National Science Foundation under grant No CMMI-1933583, and in part by the NSF grant No DMS-2012634.
Publisher Copyright:
© 2021 American Automatic Control Council.
PY - 2021/5/25
Y1 - 2021/5/25
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85111932219&partnerID=8YFLogxK
U2 - 10.23919/ACC50511.2021.9483018
DO - 10.23919/ACC50511.2021.9483018
M3 - Conference contribution
AN - SCOPUS:85111932219
T3 - Proceedings of the American Control Conference
SP - 2763
EP - 2768
BT - 2021 American Control Conference, ACC 2021
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2021 American Control Conference, ACC 2021
Y2 - 25 May 2021 through 28 May 2021
ER -