Table of Content

Recent Developments of Immersed Methods for Fluid-structure Interactions

Submission Deadline: 15 August 2018 (closed)

Guest Editors

Professor Zhilin Li, Ph.D., zhilin@math.ncsu.edu , (Zhilin Li got his Ph.D. in Applied Mathematics from University of Washington in Seattle, Washington. He was a CAM/Hedrick Assistant Professor at University of Californian at Los Angeles (UCLA) between1994-1996. He went to North Carolina State University in 1997 and was promoted to full professor in 2006. Zhilin Li's research area is in applied mathematics with applications in CFD, math biology. He is the main inventor of IIM, AIIM, IFEM and AIFEM methods. Has has published over 100 refereed publications, one monograph (SIAM Frontier Series 33), one textbook (Cambridge 2017). He has been PI or co-PI of external grants of NSF, ARO, NIH, AFOSR. Zhilin Li has had 12 PhD students graduated.);

Professor Sheldon Wang, Ph.D.,P.E., sheldon.wang@mwsu.edu, Dr. Sheldon Wang is a tenured full professor of the McCoy School of Engineering at the Midwestern State University (MSU). Dr. Wang has been teaching in higher education for over twenty-three years. He received his B.S. degree in Naval Architecture and Ocean Engineering in 1988 from Shanghai Jiao Tong University, M.S. in Ocean Engineering in 1993 and Ph.D. in Applied Mechanics in 1995 from Massachusetts Institute of Technology. Subsequently, he has worked in the Institute of Paper Science and Technology (currently part of GaTech), Polytechnic University (currently part of New York University), and Department of Mathematical Sciences of New Jersey Institute of Technology as a faculty member before joining MSU in 2009. Dr. Wang was selected by Polytechnic University in 2002 as one of the five founding Othmer Junior Faculty Fellows. He was also selected as the ASEE Air Force Summer Faculty Fellow in 2008 and 2009. His research interests include computational fluid and solid mechanics, fluid-solid interactions, quantitative modeling of biological systems, nonlinear dynamical systems, and complex systems. Dr. Wang is the author of around 40 journal papers with more than one thousand journal citations and an h-index 15 based on Researcher ID: C-4915-2008. He is also the author of a research monograph “Fundamentals of Fluid-Solid Interactions—Analytical and Computational Approaches” published by Elsevier Science in 2008. This book is available in nearly three hundred and twenty libraries around the world with 15 editions. Dr. Wang has served in the editorial boards of a number of journals and international conferences as well as review panels for National Science Foundation, US Department of Agriculture, and other governmental agencies. Dr. Wang has served as Chair of the McCoy School of Engineering at MSU from 2009 to 2014 and Chair of the Mechanical Engineering Tuning Committee of Texas Higher Education Coordinating Board (THECB) from 2010 to 2012. Dr. Wang is a licensed professional engineer in the State of Texas and current treasurer of MIT Club of Dallas/Fort Worth.

Prof. Lucy Zhang, zhanglucy@rpi.edu, (Prof. Lucy Zhang is currently an Associate Professor at the Department of Mechanical, Aerospace & Nuclear Engineering at Rensselaer Polytechnic Institute (RPI). She received her B.S. from Binghamton University in December of 1997, obtained her M.S. and Ph.D. from Northwestern University, IL in 2000 and 2003, respectively. Upon graduation, she joined Mechanical Engineering Department at Tulane as an assistant professor in July of 2003. In August 2006, she moved to Rensselaer Polytechnic Institute due to Hurricane Katrina and was promoted to Associate Professor in 2011. Her research interests are building advanced and robust computational tools and software framework for accurate and efficient multiphysics and multiscale simulations that can be used for engineering applications in biomechanics, micro and nano-mechanics, medicine, and defense projects involving impacts. She has published more than 40 highly cited peer-reviewed journals and more than 20 peer-reviewed conference papers. In 2016, she received Young Investigator Award at the International Conference for Computational Methods. She is currently developing a set of robust coupling technologies for a large variety of applications based on the immersed framework, and is developing an open-source multiphysics code, OpenIFEM, for multiphysics and multiscale simulations and analysis with minimum intrusive manipulation of existing solvers.)


Summary

Topics invited for this special issue include but are not limited to recent developments for: 

(1) Immersed Boundary Methods ;

(2) Immersed Finite Element Methods; 

(3) Immersed Isogeometric FSI Methods; 

(4) Immersed Interface Methods;

(5) Engineering Applications Using Immersed Strategies; 

(6) Numerical Methods and Algorithms for Immersed Strategies;

(7) Software Engineering of Immersed Framework.


Keywords

fluid-structure interactions; formulation; algorithm; immersed methods; numerical methods; applications; software engineering

Published Papers


  • Open Access

    EDITORIAL

    Preface: Simulation of Fluid-Structure Interaction Problems

    Zhilin Li, X.Sheldon Wang, LucyT. Zhang
    CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 1-3, 2019, DOI:10.32604/cmes.2019.06635
    (This article belongs to this Special Issue: Recent Developments of Immersed Methods for Fluid-structure Interactions)
    Abstract This article has no abstract. More >

  • Open Access

    ARTICLE

    Model Studies of Fluid-Structure Interaction Problems

    X.Sheldon Wang, Ye Yang, Tao Wu
    CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 5-34, 2019, DOI:10.32604/cmes.2019.04204
    (This article belongs to this Special Issue: Recent Developments of Immersed Methods for Fluid-structure Interactions)
    Abstract In this work, we employ fluid-structure interaction (FSI) systems with immersed flexible structures with or without free surfaces to explore both Singular Value Decomposition (SVD)-based model reduction methods and mode superposition methods. For acoustoelastic FSI systems, we adopt a three-field mixed finite element formulation with displacement, pressure, and vorticity moment unknowns to effectively enforce the irrotationality constraint. We also propose in this paper a new Inf-Sup test based on the lowest non-zero singular value of the coupling matrix for the selection of reliable sets of finite element discretizations for displacement and pressure as well as vorticity moment. Our numerical examples… More >

  • Open Access

    ARTICLE

    Distributed Lagrange Multiplier/Fictitious Domain Finite Element Method for a Transient Stokes Interface Problem with Jump Coefficients

    Andrew Lundberg, Pengtao Sun, Cheng Wang, Chen-song Zhang
    CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 35-62, 2019, DOI:10.32604/cmes.2019.04804
    (This article belongs to this Special Issue: Recent Developments of Immersed Methods for Fluid-structure Interactions)
    Abstract The distributed Lagrange multiplier/fictitious domain (DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients. The semi- and fully discrete DLM/FD-mixed finite element scheme are developed for the first time for this problem with a moving interface, where the arbitrary Lagrangian-Eulerian (ALE) technique is employed to deal with the moving and immersed subdomain. Stability and optimal convergence properties are obtained for both schemes. Numerical experiments are carried out for different scenarios of jump coefficients, and all theoretical results are validated. More >

  • Open Access

    ARTICLE

    An Augmented IB Method & Analysis for Elliptic BVP on Irregular Domains

    Zhilin Li, Baiying Dong, Fenghua Tong, Weilong Wang
    CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 63-72, 2019, DOI:10.32604/cmes.2019.04635
    (This article belongs to this Special Issue: Recent Developments of Immersed Methods for Fluid-structure Interactions)
    Abstract The immersed boundary method is well-known, popular, and has had vast areas of applications due to its simplicity and robustness even though it is only first order accurate near the interface. In this paper, an immersed boundary-augmented method has been developed for linear elliptic boundary value problems on arbitrary domains (exterior or interior) with a Dirichlet boundary condition. The new method inherits the simplicity, robustness, and first order convergence of the IB method but also provides asymptotic first order convergence of partial derivatives. Numerical examples are provided to confirm the analysis. More >

  • Open Access

    ARTICLE

    A Simple FEM for Solving Two-Dimensional Diffusion Equation with Nonlinear Interface Jump Conditions

    Liqun Wang, Songming Hou, Liwei Shi
    CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 73-90, 2019, DOI:10.32604/cmes.2019.04581
    (This article belongs to this Special Issue: Recent Developments of Immersed Methods for Fluid-structure Interactions)
    Abstract In this paper, we propose a numerical method for solving parabolic interface problems with nonhomogeneous flux jump condition and nonlinear jump condition. The main idea is to use traditional finite element method on semi-Cartesian mesh coupled with Newton’s method to handle nonlinearity. It is easy to implement even though variable coefficients are used in the jump condition instead of constant in previous work for elliptic interface problem. Numerical experiments show that our method is about second order accurate in the L norm. More >

  • Open Access

    ARTICLE

    OpenIFEM: A High Performance Modular Open-Source Software of the Immersed Finite Element Method for Fluid-Structure Interactions

    Jie Cheng, Feimi Yu, Lucy T. Zhang
    CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 91-124, 2019, DOI:10.32604/cmes.2019.04318
    (This article belongs to this Special Issue: Recent Developments of Immersed Methods for Fluid-structure Interactions)
    Abstract We present a high performance modularly-built open-source software - OpenIFEM. OpenIFEM is a C++ implementation of the modified immersed finite element method (mIFEM) to solve fluid-structure interaction (FSI) problems. This software is modularly built to perform multiple tasks including fluid dynamics (incompressible and slightly compressible fluid models), linear and nonlinear solid mechanics, and fully coupled fluid-structure interactions. Most of open-source software packages are restricted to certain discretization methods; some are under-tested, under-documented, and lack modularity as well as extensibility. OpenIFEM is designed and built to include a set of generic classes for users to adapt so that any fluid and… More >

  • Open Access

    ARTICLE

    An IB Method for Non-Newtonian-Fluid Flexible-Structure Interactions in Three-Dimensions

    Luoding Zhu
    CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 125-143, 2019, DOI:10.32604/cmes.2019.04828
    (This article belongs to this Special Issue: Recent Developments of Immersed Methods for Fluid-structure Interactions)
    Abstract Problems involving fluid flexible-structure interactions (FFSI) are ubiquitous in engineering and sciences. Peskin’s immersed boundary (IB) method is the first framework for modeling and simulation of such problems. This paper addresses a three-dimensional extension of the IB framework for non-Newtonian fluids which include power-law fluid, Oldroyd-B fluid, and FENE-P fluid. The motion of the non-Newtonian fluids are modelled by the lattice Boltzmann equations (D3Q19 model). The differential constitutive equations of Oldroyd-B and FENE-P fluids are solved by the D3Q7 model. Numerical results indicate that the new method is first-order accurate and conditionally stable. To show the capability of the new… More >

  • Open Access

    ARTICLE

    Multiscale Hybrid-Mixed Finite Element Method for Flow Simulation in Fractured Porous Media

    Philippe Devloo, Wenchao Teng, Chen-Song Zhang
    CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 145-163, 2019, DOI:10.32604/cmes.2019.04812
    (This article belongs to this Special Issue: Recent Developments of Immersed Methods for Fluid-structure Interactions)
    Abstract The multiscale hybrid-mixed (MHM) method is applied to the numerical approximation of two-dimensional matrix fluid flow in porous media with fractures. The two-dimensional fluid flow in the reservoir and the one-dimensional flow in the discrete fractures are approximated using mixed finite elements. The coupling of the two-dimensional matrix flow with the one-dimensional fracture flow is enforced using the pressure of the one-dimensional flow as a Lagrange multiplier to express the conservation of fluid transfer between the fracture flow and the divergence of the one-dimensional fracture flux. A zero-dimensional pressure (point element) is used to express conservation of mass where fractures… More >

  • Open Access

    ARTICLE

    An Immersed Method Based on Cut-Cells for the Simulation of 2D Incompressible Fluid Flows Past Solid Structures

    François Bouchon, Thierry Dubois, Nicolas James
    CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 165-184, 2019, DOI:10.32604/cmes.2019.04841
    (This article belongs to this Special Issue: Recent Developments of Immersed Methods for Fluid-structure Interactions)
    Abstract We present a cut-cell method for the simulation of 2D incompressible flows past obstacles. It consists in using the MAC scheme on cartesian grids and imposing Dirchlet boundary conditions for the velocity field on the boundary of solid structures following the Shortley-Weller formulation. In order to ensure local conservation properties, viscous and convecting terms are discretized in a finite volume way. The scheme is second order implicit in time for the linear part, the linear systems are solved by the use of the capacitance matrix method for non-moving obstacles. Numerical results of flows around an impulsively started circular cylinder are… More >

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