DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Lubricated immersed boundary method in two dimensions

Journal Article · · Journal of Computational Physics
 [1];  [2]
  1. Harvard Univ., Cambridge, MA (United States). Paulson School of Engineering
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Mathematics Group

Many biological examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen and the intracellular trafficking of vesicles into dendritic spines, involve the near-contact of elastic structures separated by thin layers of fluid. Motivated by such problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We demonstrate 2nd-order accurate convergence for simple two-dimensional flows with known exact solutions to showcase the increased accuracy of this method compared to the standard immersed boundary method. Motivated by the phenomenon of wall-induced migration, we apply the lubricated immersed boundary method to simulate an elastic vesicle near a wall in shear flow. We also simulate the dynamics of a vesicle traveling through a narrow channel and observe the ability of the lubricated method to capture the vesicle motion on relatively coarse fluid grids.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); NSF
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1526510
Alternate ID(s):
OSTI ID: 1576609; OSTI ID: 23078188
Journal Information:
Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 356; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (36)

Dynamics of an open elastic rod with intrinsic curvature and twist in a viscous fluid journal February 2010
2–D Parachute Simulation by the Immersed Boundary Method journal January 2006
A computational fluid dynamics of `clap and fling' in the smallest insects journal January 2005
Simulation of Osmotic Swelling by the Stochastic Immersed Boundary Method journal January 2015
Hybrid finite difference/finite element immersed boundary method: Hybrid finite difference/finite element immersed boundary method journal August 2017
Penalty immersed boundary method for an elastic boundary with mass journal May 2007
Active elastohydrodynamics of vesicles in narrow blind constrictions journal November 2017
Discontinuous Shear Thickening of Frictional Hard-Sphere Suspensions journal November 2013
On the Volume Conservation of the Immersed Boundary Method journal August 2012
Lubrication corrections for lattice-Boltzmann simulations of particle suspensions journal October 2002
Multiscale computations of thin films in multiphase flows journal January 2010
Noninertial lateral migration of vesicles in bounded Poiseuille flow journal November 2008
Systematic Derivation of Jump Conditions for the Immersed Interface Method in Three-Dimensional Flow Simulation journal January 2006
A numerical study of the effects of bell pulsation dynamics and oral arms on the exchange currents generated by the upside-down jellyfish Cassiopea xamachana journal May 2011
Life at low Reynolds number journal January 1977
Fluid-mechanical interaction of flexible bacterial flagella by the immersed boundary method journal March 2012
Coupling biochemistry and hydrodynamics captures hyperactivated sperm motility in a simple flagellar model journal August 2011
Particle motions in sheared suspensions: XVIII: Wall migration (theoretical) journal March 1965
Droplet migration, deformation, and orientation in the presence of a plane wall: A numerical study compared with analytical theories journal April 1993
Forced transport of deformable containers through narrow constrictions journal September 2014
Multi-level adaptive solutions to boundary-value problems journal May 1977
On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems journal September 2005
A remark on jump conditions for the three-dimensional Navier-Stokes equations involving an immersed moving membrane journal February 2001
Immersed Boundary Method for Variable Viscosity and Variable Density Problems Using Fast Constant-Coefficient Linear Solvers I: Numerical Method and Results journal January 2013
A Numerical Method for the Incompressible Navier-Stokes Equations Based on an Approximate Projection journal March 1996
Adaptive mesh refinement for hyperbolic partial differential equations journal March 1984
Fully resolved viscoelastic particulate simulations using unstructured grids journal June 2017
The Immersed Boundary Method for Two-Dimensional Foam with Topological Changes journal August 2012
Immersed Boundary Method for Variable Viscosity and Variable Density Problems Using Fast Constant-Coefficient Linear Solvers II: Theory journal January 2014
Computational model of whole blood exhibiting lateral platelet motion induced by red blood cells
  • Crowl, Lindsay M.; Fogelson, Aaron L.
  • International Journal for Numerical Methods in Biomedical Engineering, Vol. 26, Issue 3-4 https://doi.org/10.1002/cnm.1274
journal March 2010
Lift Force and Dynamical Unbinding of Adhering Vesicles under Shear Flow journal July 1999
Dynamics of a Closed Rod with Twist and Bend in Fluid journal January 2008
A coupled level set projection method applied to ink jet simulation journal January 2003
Properties of Discrete Delta Functions and Local Convergence of the Immersed Boundary Method journal January 2012
Simulating flexible fiber suspensions using a scalable immersed boundary algorithm journal June 2015
Biomechanics of red blood cells in human spleen and consequences for physiology and disease journal June 2016

Cited By (3)

Parallel three-dimensional simulations of quasi-static elastoplastic solids text January 2019
Two-dimensional Finite Element Model of Breast Cancer Cell Motion Through a Microfluidic Channel journal January 2019
Coarse graining the dynamics of immersed and driven fiber assemblies journal July 2019