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A Hybrid Immersed Interface Method for Driven Stokes Flow in an Elastic Tube

Published online by Cambridge University Press:  28 May 2015

Yi Li ,
Sarah A. Williams  and
Anita T. Layton
Yi Li*
Affiliation:
Department of Mathematics, Duke University, Durham, NC 27708-0320, USA
Sarah A. Williams*
Affiliation:
Department of Mathematics, Duke University, Durham, NC 27708-0320, USA
Anita T. Layton*
Affiliation:
Department of Mathematics, Duke University, Durham, NC 27708-0320, USA
*
Corresponding author.Email address:yili@math.duke.edu
Corresponding author.Email address:williams@math.duke.edu
Corresponding author.Email address:alayton@math.duke.edu
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Abstract

We present a hybrid numerical method for simulating fluid flow through a compliant, closed tube, driven by an internal source and sink. Fluid is assumed to be highly viscous with its motion described by Stokes flow. Model geometry is assumed to be axisymmetric, and the governing equations are implemented in axisymmetric cylindrical coordinates, which capture 3D flow dynamics with only 2D computations. We solve the model equations using a hybrid approach: we decompose the pressure and velocity fields into parts due to the surface forcings and due to the source and sink, with each part handled separately by means of an appropriate method. Because the singularly-supported surface forcings yield an unsmooth solution, that part of the solution is computed using the immersed interface method. Jump conditions are derived for the axisymmetric cylindrical coordinates. The velocity due to the source and sink is calculated along the tubular surface using boundary integrals. Numerical results are presented that indicate second-order accuracy of the method.

Keywords

76M2065M0676D07Stokes flowinterface trackingimmersed interface methodsaxisymmetric cylindrical coordinatesboundary integrals
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 4 , November 2013 , pp. 600 - 616-
Copyright
Copyright © Global Science Press Limited 2013

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