July 12, 2024

August 9-13, 2010
Workshop on Fluid Motion Driven by Immersed Structures

Walburg Building WB Rm 116 (map of campus)
184-200 College Street, University of Toronto

Workshop Organizers:  
Huaxiong Huang, York University
Anita Layton, Duke University
Zhilin Li, North Carolina State University
John Stockie, Simon Fraser University


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



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 <>

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
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

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