Math @ Duke

Publications [#243353] of J. Thomas Beale
Papers Published
 Beale, JT; Layton, AT, A velocity decomposition approach for moving interfaces in viscous fluids,
Journal of Computational Physics, vol. 228 no. 9
(2009),
pp. 33583367, ISSN 00219991 [pdf], [doi]
(last updated on 2018/06/22)
Abstract: We present a secondorder accurate method for computing the coupled motion of a viscous fluid and an elastic material interface with zero thickness. The fluid flow is described by the NavierStokes equations, with a singular force due to the stretching of the moving interface. We decompose the velocity into a "Stokes" part and a "regular" part. The first part is determined by the Stokes equations and the singular interfacial force. The Stokes solution is obtained using the immersed interface method, which gives secondorder accurate values by incorporating known jumps for the solution and its derivatives into a finite difference method. The regular part of the velocity is given by the NavierStokes equations with a body force resulting from the Stokes part. The regular velocity is obtained using a timestepping method that combines the semiLagrangian method with the backward difference formula. Because the body force is continuous, jump conditions are not necessary. For problems with stiff boundary forces, the decomposition approach can be combined with fractional timestepping, using a smaller time step to advance the interface quickly by Stokes flow, with the velocity computed using boundary integrals. The small time steps maintain numerical stability, while the overall solution is updated on a larger time step to reduce computational cost. © 2009 Elsevier Inc. All rights reserved.


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