Math @ Duke

Publications [#172887] of Elizabeth L. Bouzarth
Papers Published
 E.L. Bouzarth and M.L. Minion, A multirate time integrator for regularized Stokeslets,
Journal of Computational Physics, vol. 229 no. 11
(June, 2010),
pp. 42084224 [doi]
(last updated on 2010/03/30)
Abstract: The method of regularized Stokeslets is a numerical approach to approximating solutions of fluidâ€“structure interaction problems in the Stokes regime. Regularized Stokeslets are fundamental solutions to the Stokes equations with a regularized pointforce term that are used to represent forces generated by a rigid or elastic object interacting with the fluid. Due to the linearity of the Stokes equations, the velocity at any point in the fluid can be computed by summing the contributions of regularized Stokeslets, and the time evolution of positions can be computed using standard methods for ordinary differential equations. Rigid or elastic objects in the flow are usually treated as immersed boundaries represented by a collection of regularized Stokeslets coupled together by virtual springs which determine the forces exerted by the boundary in the fluid. For problems with boundaries modeled by springs with large spring constants, the resulting ordinary differential equations become stiff, and hence the time step for explicit time integration methods is severely constrained. Unfortunately, the use of standard implicit time integration methods for the method of regularized Stokeslets requires the solution of dense nonlinear systems of equations for many relevant problems. Here, an alternate strategy using an explicit multirate time integration scheme based on spectral deferred corrections is incorporated that in many cases can significantly decrease the computational cost of the method. The multirate methods are higherorder methods that treat different portions of the ODE explicitly with different time steps depending on the stiffness of each component. Numerical examples on two nontrivial threedimensional problems demonstrate the increased efficiency of the multiexplicit approach with no significant increase in numerical error.


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