Math @ Duke

Publications [#243700] of Anita T. Layton
Papers Published
 Layton, AT, An efficient numerical method for the twofluid Stokes equations with a moving immersed boundary,
Computer Methods in Applied Mechanics and Engineering, vol. 197 no. 2528
(2007),
pp. 21472155, ISSN 00457825 [doi]
(last updated on 2018/07/22)
Abstract: We consider the immersed boundary problem in which the boundary separates two very viscous fluids with differing viscosities. The moving elastic boundary may exert a force on the local fluid. The model solution is obtained using the immersed interface method, which computes secondorder accurate approximations by incorporating known jumps in the solution or its derivatives into a finite difference method. These jump conditions become coupled when the fluid viscosity has a jump across the boundary, and this coupling renders the application of the immersed interface method challenging. We present a method that first uses boundary integral equations to reduce the twofluid Stokes problem to the singlefluid case, and then solves the singlefluid problem using the immersed interface method. Using this method, we assess, through two numerical examples, how the fluid dynamics are affected by differing viscosities in the twofluid regions. We also propose an implicit algorithm and a fractionalstep algorithm for advancing the boundary position. Because both algorithms make use of the integral form of the solution, neither one requires the solution of a large system of coupled nonlinear equations, as is traditionally the case. Numerical results suggest that, for sufficiently stiff problems, the fractional timestepping algorithm is the most efficient, in the sense that it allows the largest timeinterval between subsequent updates of global model solutions. © 2007 Elsevier B.V. All rights reserved.


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