 |
Overview
There is tremendous interest in the development and application
of advanced computational techniques for simulating the motion of
an incompressible fluid driven by flexible immersed structures,
in large part owing to the multitude of applications in physiology
and biology. Active biological tissue is typically constructed of
fibers that are surrounded by fluid; the fibers not only hold the
tissue together but also transmit forces that ultimately result
in fluid motion. In other cases, the fluid may flow through flexible
conduits such as a blood vessels or airways that both react to and
affect the fluid dynamics. Additional examples arise in the context
of external fluid flows in biological and engineering applications,
such as dynamics of insect wings, flagellated or ciliated organisms,
suspensions of blood cells and other synthetic particles, parachute
dynamics, and so on.
The workshop will include two tutorials targeted to graduate students
and junior mathematicians, with the goal of providing training opportunities
to young scientists.
The meeting will be organized around three main themes:
- Formulation and analysis of the underlying governing equations.
- Algorithmic and computational issues related to increasing accuracy
and efficiency through use of adaptivity, novel time-stepping
schemes and parallelism.
- Applications to problems in the biological, physical and engineering
sciences.
Selected papers will be published in a special issue of Communications
in Computational Physics after the workshop.
Keynote Speakers
John Dolbow
(Duke University)
Recent Advances in Embedded Finite Element Methods
An emerging class of embedded finite element methods for evolving
boundary value problems in mechanics will be presented. These
methods have been designed to circumvent long-standing difficulties
with finite elements for Lagrangian simulations of deformable
media with complex geometry. Particularly for problems with significant
changes in topology, continuous remeshing strategies have simply
not proven sufficiently viable or robust. The embedded methods
provide a means for the geometry of features of interest, such
as sharp phase interfaces or fracture surfaces, to be represented
independently of the mesh. This relaxation between mesh and geometry
obviates the need for remeshing strategies in many cases and greatly
facilitates adaptivity in others. The approach is very similar
to the Eulerian methodologies developed by the finite difference
and level-set communities, but within a variational setting that
facilitates error and stability analysis. This talk will describe
the theory behind the embedded method and recent methodological
advances, as well as provide performance comparisons with the
state-of-the-art in fixed-grid finite-difference technologies.
Lisa Fauci (Tulane University)
Recent insights into swimming and pumping using an immersed
boundary framework
In many biological processes, elastic boundaries move through
a fluid or move the fluid itself. These elastic boundaries may
be passive or actuated, and may interact with a Newtonian fluid
or one that exhibits more complex constitutive properties. In
this talk, I will discuss successes and challenges in modeling
swimming of flagellated microorganisms, pumping and mixing of
complex fluids, and an integrative model of lamprey locomotion.
Zhilin Li (North Carolina State University)
The Augmented IIM and application to free boundary/moving interface
problems
The Immersed Interface Method (IIM) is an efficient numerical
method for interface, free boundary/moving interface problems,
and problems on irregular domains. The IIM is a sharp interface
method that enforces jump conditions either exactly or approximately.
In this talk, I will summarize some recent advances of the IIM,
particularly, the augmented approach and its application to incompressible
Stokes and Navier-Stokes equations with singular sources, discontinuous
viscosity, irregular domains, and free boundary and moving interfaces
using the augmented IIM. Particularly, I will explain the approach
for incompressible (or inextensible) interfaces in incompressible
flows. Most previous work has been done using Stokes equations
model by the boundary integral methods. The problem is essentially
an inverse problem in which one needs to find an unknown surface
tension such that the incompressible condition is satisfied in
the tangential direction. Geometrically, both the area and length
of the interface has to be preserved. Our method can be applied
to both the Stokes or Navier-Stokes equations. We propose a new
way to enforce the pressure jump condition. Some new numerical
simulation results will also be presented.
John Lowengrub (University
of California at Irvine)
Dynamics of multicomponent vesicles in a viscous fluid
We develop and investigate numerically a thermodynamically con-
sistent model of multicomponent vesicles in an incompressible
viscous fluid. The model is derived using an energy variation
approach that accounts for different lipid surface phases, the
excess energy (line energy) associated with surface phase domain
boundaries, bending energy, spontaneous curvature, local inextensibility
and fluid flow via the Stokes equations. The equations are high-order
(fourth
order) nonlinear and nonlocal due to incompressibility of the
fluid and the local inextensibility of the vesicle membrane. To
solve the equa- tions numerically, we develop a nonstiff, pseudo-spectral
boundary integral method that relies on an analysis of the equations
at small scales. The algorithm is closely related to that developed
very re- cently by Veerapaneni et al. for homogeneous vesicles
although we use a different and more efficient time stepping algorithm
and a reformulation of the inextensibility equation. We present
simulations of multicomponent vesicles in an initially quiescent
fluid and investigate the effect of varying the average surface
concentration of an initially unstable mixture of lipid phases.
The phases then redistribute and alter the morphology of the vesicle
and its dynamics. When an ap- plied shear is introduced, an initially
elliptical vesicle tank-treads and attains a steady shape and
surface phase distribution. A sufficiently elongated vesicle tumbles
and the presence of different surface phases with different bending
stiffnesses and spontaneous curvatures yields a complex evolution
of the vesicle morphology as the vesicle bends in regions where
the bending stiffness and spontaneous curvature are small.
Sheldon
Wang (Midwestern State University)
Current Challenges of Immersed Methods
In the study of micro aerial vehicles and biological systems,
the coupling of fluid and solid/structure plays an important role.
Traditionally, staggered iterations are used to link available
finite element codes with computational fluid dynamics codes.
Although this procedure is convenient, complex dynamical system
behaviors often get lost in the process. In order to derive corresponding
system model reduction procedures, and more importantly, effectively
and efficiently capture the system dynamical behaviors, we must
solve fluid-solid interaction (FSI) systems simultaneously as
a whole. Current development of immersed boundary/continuum methods
has demonstrated the feasibility and potential in handling complex
FSI systems with significant solid/structure motions.
Since its inception, the immersed boundary method has been extended
to a variety of problems. The initial application of this method
is for very flexible structures for which time step restriction
is not so severe. In current versions of immersed boundary methods,
complex nonlinear structures can be represented by both elastic
fiber and beam (rod) networks. In addition, sophisticated nonlinear
solid models have also be introduced in immersed finite element
formulations. The preliminary results of the implicit compressible
immersed continuum method have shown that reasonable time steps
can be used for stiff FSI systems. Moreover, it is possible to
apply immersed boundary/continuum methods to compressible fluid
flow problems. Nevertheless, many questions such as the efficient
matrix-free Newton-Krylov iterative procedure for the implicit
scheme, feasibility of multigrid solution procedures and the hierarchical
coarsening of discretized delta function, and stability and convergence
behaviors of immersed boundary/continuum methods coupled with
high speed compressible flows, still remain to be addressed. These
issues must be resolved before the full potential of immersed
methods can be finally realized.
Tutorial Speakers
Ming-Chih Lai (National Chiao Tung University)
Introduction to immersed boundary method
Anita Layton (Duke University
Immersed Interface Method
Deadlines
Contributed talk and poster submission --- May 23, 2010
Notification of acceptance --- June 14, 2010
Travel Support
Limited travel support is available to participants, with the final
amount pending the results of grant applications. Priority will
be given to students and postdoctoral fellows.
Deadline to apply was May 2, 2010. Notification of funding by June
21, 2010.
In addition to this application please have your advisor or supervisor
send a letter of recommendation to <fluid_motion@fields.utoronto.ca>
List of Participants as of July 27,
2010:
| Full Name |
University Name |
| Ashrafizadeh, Ali |
K.N. Toosi University of Technology |
| Beale, J. Thomas |
Duke University |
| Bennoune, Mounir |
University of Montreal |
| Bohun, C. Sean |
University of Ontario Institute of Technology |
| Bouzarth, Elizabeth |
Duke University |
| Chen, Duan |
Michigan State University |
| Chrispell, John |
Tulane University |
| Cohen, Sean |
North Carolina State University |
| Cooper, Lauren |
University of North Carolina at Chapel Hill |
| Dolbow, John |
Duke University |
| Donahue, Matthew |
Florida State University |
| Fauci, Lisa J. |
Tulane University |
| Gao, Peng |
University of British Columbia |
| Ghosh, Sudeshna |
Simon Fraser University |
| Griffith, Boyce |
New York University School of Medicine |
| Guy, Robert |
University of California, Davis |
| Hamlet, Christina |
University of North Carolina at Chapel Hill |
| He, Dongdong |
York University |
| Hou, Songming |
Louisiana Tech University |
| Hu, Langhua |
Michigan State University |
| Jackson, Ken |
University of Toronto |
| Khoo, Boo-Cheong |
National University of Singapore |
| Lai, Ming-Chih |
National Chiao Tung University |
| Layton, Anita |
Duke University |
| Lee, Wan Ho |
Konkuk University |
| Leiderman, Karin |
Duke University |
| Lewis, Owen |
University of California, Davis |
| Li, Zhilin |
North Carolina State University |
| Lim, Sookkyung |
University of Cincinnati |
| Liu, Yang |
University of Minnesota |
| Lowengrub, John |
University of California, Irvine |
| Mori, Yoichiro |
University of Minnesota |
| Nguyen, Hoa |
Tulane University |
| Nicholas, Michael |
Tulane University |
| Olson, Sarah |
Tulane University |
| Park, Jinkyoung |
Michigan State University |
| Peterson, Anne |
Duke University |
| Rawlins, Anthony |
Brunel University |
| Ren, Weiqing |
New York University |
| Seol, Yunchang |
Chung-Ang University |
| Sharma, Rajesh Kumar |
Indian Institute of Technology, Roorkee |
| Stockie, John |
Simon Fraser University |
| Strychalski, Wanda |
University of California, Davis |
| Sugiyama, Kazuyasu |
University of Tokyo |
| Takagi, Shu |
RIKEN/The University of Tokyo |
| Torres, Tedman |
Moffitt Cancer Center |
| Tsai, Peichun |
University of Twente |
| Wan Lung, Lee |
NUS |
| Wang, Jin |
Old Dominion University |
| Wang, X. Sheldon |
Midwestern State University |
| Wang, Xiao-Ping |
Hong Kong University of Science and Technology |
| Whidden, Mark |
Florida State University |
| Xia, Kelin |
Michigan State University |
| Xia, Qiong |
Michigan State University |
| Xu, Sheng |
Southern Methodist University |
| Yao, Pengfei |
University of Alabama |
| Yin, Shijun |
North Carolina State University |
| Young, Yuan-Nan |
New Jersey Institute of Technology |
| Zheng, Qiong |
Michigan State University |
| Zhu, Huibin |
Michigan State University |
| Zhu, Luoding |
IUPUI |
| TO BE CONFIRMED: |
| Bergmann, Michel |
INRIA |
| Cai, Xin |
Zhejiang University of Science and Technology |
| Devendran, Piriyadharshini |
Courant Institute of Mathematical Sciences |
| Huang, Huaxiong |
York University |
| Kim, Eun Heui |
California State University Long Beach |
| Kleshchonok, Andrii |
Kyiv National Taras Shevchenko University |
| Kumar, Binu |
BARC |
| Rejniak, Katarzyna |
University of South Florida |
| Zhao, Jianping |
Xi'an jiaotong University |
Back to top
|
|
