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Volume 22, Issue 4
A Moving-Least-Square Immersed Boundary Method for Rigid and Deformable Boundaries in Viscous Flow

Duc-Vinh Le & Boo-Cheong Khoo

DOI: 10.4208/cicp.OA-2016-0164

Commun. Comput. Phys., 22 (2017), pp. 913-934.

Published online: 2017-10

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  • Abstract

We present a moving-least-square immersed boundary method for solving viscous incompressible flow involving deformable and rigid boundaries on a uniform Cartesian grid. For rigid boundaries, no-slip conditions at the rigid interfaces are enforced using the immersed-boundary direct-forcing method. We propose a reconstruction approach that utilizes moving least squares (MLS) method to reconstruct the velocity at the forcing points in the vicinity of the rigid boundaries. For deformable boundaries, MLS method is employed to construct the interpolation and distribution operators for the immersed boundary points in the vicinity of the rigid boundaries instead of using discrete delta functions. The MLS approach allows us to avoid distributing the Lagrangian forces into the solid domains as well as to avoid using the velocity of points inside the solid domains to compute the velocity of the deformable boundaries. The present numerical technique has been validated by several examples including a Poiseuille flow in a tube, deformations of elastic capsules in shear flow and dynamics of red-blood cell in microfluidic devices.

  • Keywords

Moving least squares immersed boundary method direct-forcing method NavierStokes equations cell sorting device

  • AMS Subject Headings

65M06 76D05 74F10 92C10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-22-913, author = {}, title = {A Moving-Least-Square Immersed Boundary Method for Rigid and Deformable Boundaries in Viscous Flow}, journal = {Communications in Computational Physics}, year = {2017}, volume = {22}, number = {4}, pages = {913--934}, abstract = {

We present a moving-least-square immersed boundary method for solving viscous incompressible flow involving deformable and rigid boundaries on a uniform Cartesian grid. For rigid boundaries, no-slip conditions at the rigid interfaces are enforced using the immersed-boundary direct-forcing method. We propose a reconstruction approach that utilizes moving least squares (MLS) method to reconstruct the velocity at the forcing points in the vicinity of the rigid boundaries. For deformable boundaries, MLS method is employed to construct the interpolation and distribution operators for the immersed boundary points in the vicinity of the rigid boundaries instead of using discrete delta functions. The MLS approach allows us to avoid distributing the Lagrangian forces into the solid domains as well as to avoid using the velocity of points inside the solid domains to compute the velocity of the deformable boundaries. The present numerical technique has been validated by several examples including a Poiseuille flow in a tube, deformations of elastic capsules in shear flow and dynamics of red-blood cell in microfluidic devices.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0164}, url = {http://global-sci.org/intro/article_detail/cicp/9987.html} }
TY - JOUR T1 - A Moving-Least-Square Immersed Boundary Method for Rigid and Deformable Boundaries in Viscous Flow JO - Communications in Computational Physics VL - 4 SP - 913 EP - 934 PY - 2017 DA - 2017/10 SN - 22 DO - http://doi.org/10.4208/cicp.OA-2016-0164 UR - https://global-sci.org/intro/article_detail/cicp/9987.html KW - Moving least squares KW - immersed boundary method KW - direct-forcing method KW - NavierStokes equations KW - cell sorting device AB -

We present a moving-least-square immersed boundary method for solving viscous incompressible flow involving deformable and rigid boundaries on a uniform Cartesian grid. For rigid boundaries, no-slip conditions at the rigid interfaces are enforced using the immersed-boundary direct-forcing method. We propose a reconstruction approach that utilizes moving least squares (MLS) method to reconstruct the velocity at the forcing points in the vicinity of the rigid boundaries. For deformable boundaries, MLS method is employed to construct the interpolation and distribution operators for the immersed boundary points in the vicinity of the rigid boundaries instead of using discrete delta functions. The MLS approach allows us to avoid distributing the Lagrangian forces into the solid domains as well as to avoid using the velocity of points inside the solid domains to compute the velocity of the deformable boundaries. The present numerical technique has been validated by several examples including a Poiseuille flow in a tube, deformations of elastic capsules in shear flow and dynamics of red-blood cell in microfluidic devices.

Duc-Vinh Le & Boo-Cheong Khoo. (2020). A Moving-Least-Square Immersed Boundary Method for Rigid and Deformable Boundaries in Viscous Flow. Communications in Computational Physics. 22 (4). 913-934. doi:10.4208/cicp.OA-2016-0164
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