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Title:A time-explicit immersed boundary projection method for thin elastic surfaces and stationary bodies
Author(s):Osman, Noah
Advisor(s):Goza, Andres
Department / Program:Aerospace Engineering
Discipline:Aerospace Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):immersed boundary
fluid-structure interaction
strongly coupled
non-stationary bodies
super-time stepping method
Runge–Kutta–Chebyshev method
Abstract:We present an immersed-boundary method for flows around either an arbitrary body undergoing prescribed kinematics, or a thin elastic body whose motion is fully coupled to the flow dynamics (i.e., involving fully coupled fluid-structure interaction, FSI). The key novelty here is that the proposed method uses an explicit time integration approach (via a Runge-Kutta-Chebyshev framework) for the stiff diffusive term while retaining a formal projection formulation to ensure that the no-slip boundary condition is exactly satisfied to within machine precision at each time instance. The explicit treatment of the diffusive term avoids the embedded large linear solves that plague the majority of fractional step formulations for incompressible flows, while the projection formulation avoids the use of heuristic parameters to satisfy the constraint at the immersed interface. Moreover, in the FSI setting the projection formulation results in a strongly coupled algorithm that can accurately simulate FSI dynamics involving arbitrarily large structural motions. The governing flow equations are spatially discretized using a nullspace approach that automatically enforces the incompressibility constraint, and when the immersed body is deformable the structural dynamics are spatially discretized using a finite element method. The structural model allows for geometric nonlinearity via a co-rotational formulation. We analytically demonstrate that the proposed time advancement scheme is temporally second order accurate for the primary state variables (e.g., vorticity) and first-order accurate for the surface stress. The method is verified using a suite of two-dimensional test problems: flow past both a rigid stationary cylinder at Re = 200 and past a deformable flag for various dimensionless parameters. In all cases the results are shown to be in good agreement with the literature.
Issue Date:2021-04-30
Rights Information:Copyright 2021 Noah Osman
Date Available in IDEALS:2021-09-17
Date Deposited:2021-05

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