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Mathematics > Numerical Analysis

arXiv:1405.6621 (math)
[Submitted on 26 May 2014]

Title:Adaptive Time Stepping for Vesicle Suspensions

Authors:Bryan Quaife, George Biros
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Abstract:We present an adaptive arbitrary-order accurate time-stepping numerical scheme for the flow of vesicles suspended in Stokesian fluids. Our scheme can be summarized as an approximate implicit spectral deferred correction (SDC) method. Applying a textbook fully implicit SDC scheme to vesicle flows is prohibitively expensive. For this reason we introduce several approximations. Our scheme is based on a semi-implicit linearized low-order time stepping method. (Our discretization is spectrally accurate in space.) We also use invariant properties of vesicle flows, constant area and boundary length in two dimensions, to reduce the computational cost of error estimation for adaptive time stepping. We present results in two dimensions for single-vesicle flows, constricted geometry flows, converging flows, and flows in a Couette apparatus. We experimentally demonstrate that the proposed scheme enables automatic selection of the step size and high-order accuracy.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:1405.6621 [math.NA]
  (or arXiv:1405.6621v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1405.6621

Submission history

From: Bryan Quaife [view email]
[v1] Mon, 26 May 2014 15:38:05 UTC (314 KB)
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