Volume 6, Issue 4
A Hybrid Immersed Interface Method for Driven Stokes Flow in an Elastic Tube

Yi Li, Sarah A. Williams & Anita T. Layton

Numer. Math. Theor. Meth. Appl., 6 (2013), pp. 600-616.

Published online: 2013-06

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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

Stokes flow, interface tracking, immersed interface methods, axisymmetric cylindrical coordinates, boundary integrals.

  • AMS Subject Headings

76M20, 65M06, 76D07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-6-600, author = {}, title = {A Hybrid Immersed Interface Method for Driven Stokes Flow in an Elastic Tube}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2013}, volume = {6}, number = {4}, pages = {600--616}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2013.1219nm}, url = {http://global-sci.org/intro/article_detail/nmtma/5921.html} }
TY - JOUR T1 - A Hybrid Immersed Interface Method for Driven Stokes Flow in an Elastic Tube JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 600 EP - 616 PY - 2013 DA - 2013/06 SN - 6 DO - http://doi.org/10.4208/nmtma.2013.1219nm UR - https://global-sci.org/intro/article_detail/nmtma/5921.html KW - Stokes flow, interface tracking, immersed interface methods, axisymmetric cylindrical coordinates, boundary integrals. AB -

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.

Yi Li, Sarah A. Williams & Anita T. Layton. (2020). A Hybrid Immersed Interface Method for Driven Stokes Flow in an Elastic Tube. Numerical Mathematics: Theory, Methods and Applications. 6 (4). 600-616. doi:10.4208/nmtma.2013.1219nm
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