Regularized singularities and spectral deferred correction methods: a mathematical study of numerically modeling Stokes fluid flow

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Last Modified
  • March 21, 2019
Creator
  • Bouzarth, Elizabeth L.
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • Regularized Stokeslets and spectral deferred correction methods are used to model variations of a rigid body precessing in Stokes flow. Numerical solutions are compared to exact and asymptotic closed form solutions for a spheroid precessing about its center. This provides the opportunity to perform careful error analysis and identify different numerical errors in regard to the motion of both slender and non-slender precessing spheroids. The error has components relating to quadrature, asymptotics, regularization, and time integration. Often, the quadrature error and time integration error are small with respect to the other error contributions, all of which are discussed. The motion of both slender and non-slender spheroids is studied to find the parameter and boundary condition choices that minimize velocity error. A system of regularized image singularities is developed to create a no-slip plane that mimics the effect of a nearby wall in the experiment setup. A temporal integration strategy based on spectral deferred correction (SDC) methods using an explicit treatment with different time steps for different components of the physical system is discussed. Multi-explicit SDC (MESDC) methods provide an increase in efficiency for stiff problems by allowing non-stiff parts of the physical setup to use a larger time step requiring fewer expensive computations. The numerical methods are used to study experimental fluid dynamics phenomena relating to precessing rods that are not described by an exact closed form solution. This work has biological motivations resulting from the study of pulmonary cilia in conjunction with cystic fibrosis research as well as the motion of primary nodal cilia in developing embryos whose motion plays a critical role in developing left-right asymmetry in mammals.
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  • In Copyright
Advisor
  • Minion, Michael L.
Degree granting institution
  • University of North Carolina at Chapel Hill
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  • Open access
Date uploaded
  • October 11, 2010

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