Mathematical and Computational Modeling of Fluid Flow with Applications in Ophthalmology and Geoscience

Wednesday, June 24, 2020 - 9:00am
Zoom presentation
Farah Abdelhafid
(MU Math)

Complex system in our life can be translated to mathematical model whose solutions can help us
to predict the behavior of the system. Disease in eye and internal erosion in the embankment dam are
examples of these complex system. The purposes of this study were (i) to simulate aqueous humor in
the anterior chamber in the human eye using mathematical modeling based on operator splitting for
the thermo-fluid-dynamical simulation and (ii) to model the motion of water and fluidized soil
particles through the embankment dam to calculate three important parameters which included
porosity, saturated and pressure of water based on the Forward Euler method. The FreeFEM
programming language software package was used to implement both problems. The simulation
results of aqueous humor indicate that the current simulations are conducted by only first-order
accurate in time. The mathematical simulations have proved that changes in posture have a nontrivial
impact on temperature and velocity profiles. Interestingly, the two vortices that describe the supine
and prone positions are not present when standing. Therefore, this study proposed a numerical
approach, which applies aqueous humor in the anterior chamber in the human eye, has the potential to
serve as a robust framework on which further physical mechanisms can be incorporated. The
simulation results of the second aim revealed that the step time dt has significant effects on the
solution of this model. Also, the study recommends considering the temperature, which should be a
focus of future simulation studies due to soil temperatures are fluctuated above and below 0 C. The
simulation results of these studies imply that developing mathematical modeling has successfully
simulated two significant problems from our life.

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Meeting ID: 952 981 1625