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A Moving-Least-Square Immersed Boundary Method for Rigid and Deformable Boundaries in Viscous Flow

Part of: Incompressible viscous fluids Partial differential equations, initial value and time-dependent initial-boundary value problems Physiological, cellular and medical topics Coupling of solid mechanics with other effects

Published online by Cambridge University Press:  28 July 2017

Duc-Vinh Le  and
Boo-Cheong Khoo
Duc-Vinh Le*
Affiliation:
Institute of High Performance Computing, A*STAR, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632
Boo-Cheong Khoo*
Affiliation:
Department of Mechanical Engineering, National University of Singapore, Kent Ridge Crescent, Singapore 119260
*
*Corresponding author. Email addresses:[email protected] (D.-V. Le), [email protected] (B.-C. Khoo)
*Corresponding author. Email addresses:[email protected] (D.-V. Le), [email protected] (B.-C. Khoo)
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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, noslip 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 squaresimmersed boundary methoddirect-forcing methodNavier-Stokes equationscell sorting device

MSC classification

Secondary: 65M06: Finite difference methods 76D05: Navier-Stokes equations 74F10: Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 92C10: Biomechanics
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 4 , October 2017 , pp. 913 - 934
Copyright
Copyright © Global-Science Press 2017 

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