Fluid-structure Interaction Problems
Fluid-Structure Interaction Problems
Our work on Fluid-Structure Interaction Problems is done in the context of the Immersed Boundary (IB) Method as introduced by Peskin. There are several distinct components to our work. In one, we introduced provably unconditionally stable discretizations of the IB method and explored the effectiveness of various solvers for these discretizations as described in:
Elijah P. Newren, Aaron L. Fogelson, Robert D. Guy, and Robert M. Kirby, Unconditionally-stable discretizations of the Immersed Boundary Method, Journal of Computational Physics, 222, (2007), 702-719
Elijah P. Newren, Aaron L. Fogelson, Robert D. Guy, and Robert M. Kirby, A Comparison of Implicit Solvers for the Immersed Boundary Equations, Computer Methods in Applied Mechanics and Engineering, 197, (2008), 2290-2304.
This work was in collaboration with Elijah Newren (Utah), Robert M. Kirby (Utah), and Robert D. Guy (UC Davis) and was supported by DOE contract DE-FG02-97ER25308 and NSF Grants DMS-0139926 and DMS-0139926.
Another aspect of our work on the IB method is our development of an IB method for mixtures of two fluids of different viscosities. In this we combined an IB approach with the numerical methods for two-phase mixtures we developed. The method was applied to a two-fluid version of the Taylor sheet model of swimming by passing oscillating waves along a body:
Jian Du, Robert D. Guy, Aaron L. Fogelson, An Immersed Boundary Method for Two-fluid Mixtures, Journal of Computational Physics, 2014, 262, 231-243.
Jian Du, James P. Keener, Robert D. Guy, and Aaron L. Fogelson, Low Reynolds-number Swimming in Viscous Two-Phase Fluids, Physical Review E, 85, 036304 (2012).
This work was in collaboration with Jian Du (Florida Tech), Robert D. Guy (UC, Davis) and Jim Keener (Utah) and was support by NSF Grants DMS-0540779 and DMS-1160432 and NIGMS Grant RO1-GM090203.
Lattice-Boltzmann Immersed Boundary Method
We developed a hybrid Lattice-Boltzmann and Immersed Boundary (LB-IB) Method and applied it to study the flow of whole blood containing red blood cells and platelets. We sought to understand the process of platelet margination and to explore the effects of red blood cells on the rate of thrombus growth due to platelet deposition. The method and its application to understand platelet margination are described in:
Lindsay M. Crowl and Aaron L. Fogelson, Computational Model of Whole Blood Exhibiting Lateral Platelet Motion Induced by Red Blood Cells, International Journal for Numerical Methods in Biomedical Engineering, 26, 2010 471-487.
Lindsay M. Crowl and Aaron L. Fogelson, Analysis of Mechanisms for Platelet Near-wall Excess Under Arterial Blood Flow Conditions, Journal of Fluid Mechanics, 676, (2011) 348-375.
The application of the LB-IB method to investigate the effects of flowing red blood cells on platelet interactions with a porous thrombus is described in:
Tyler Skorczewski, Lindsay Crowl Erickson, and Aaron L. Fogelson, Platelet Motion near a Vessel Wall or Thrombus Surface in Two-dimensional Whole Blood Simulations, Biophysical Journal, 2013, 104(8), 1764-72
Use of the LB-IB method to give a mechanical basis for the in vivo and in vitro observations of an increased rate of thrombus growth with increasing hematocrit is part of the study reported in:
Bethany L. Walton, Marcus Lehmann, Tyler Skorczewski, Joan D. Beckman, Lori A. Holle, Jeremy A. Cribb, Micah J. Mooberry, Adam R. Wufsus, Brian C. Cooley, Jonathan W. Homeister, Michael R. Falvo, Aaron L. Fogelson, Keith B. Neeves, Alisa S. Wolberg, Elevated hematocrit promotes arterial thrombosis, Blood, 2017, 129, 2537-2546.
This work was done in collaboration with Lindsay Crowl (Utah), Tyler Skorczewski (Utah), Alisa Wolberg (UNC), Keith Neeves (Colorado School of Mines) and others and was supported by NSF training grants DMS-0354259 and DMS-0540779 and NIGMS Grant R01-GM090203.
A recent aspect of our IB work is in its application to study pumping in the lymphatic system as described in:
Hallie Elich, Aaron Barrett, Varun Shankar, Aaron L. Fogelson, Pump efficacy in a fluid-structure-interaction model of a chain of contracting lymphangions, Biomechanics and Mechanical Biology, 2021, doi: 10.1007/s10237-021-01486-w.
Another recent aspect of our IB work is in using RBF-based surface representations and Lagrangian force calculations in a three-dimensional IB study of platelet interactions with red blood cells and the undulating topography of a blood vessel wall:
Andrew Kassen, Aaron Barrett, Varun Shankar, Aaron L. Fogelson, Immersed boundary simulations of cell-cell interactions in whole blood, Journal of Computational Physics, 2021, submitted.
These works were done in collaboration with Hallie Elich, Andrew Kassen, Varun
Shankar, and Aaron Barrett, all at Utah