Year: 2012
Communications in Computational Physics, Vol. 12 (2012), Iss. 2 : pp. 401–432
Abstract
The immersed boundary (IB) method is an approach to problems of fluid-structure interaction in which an elastic structure is immersed in a viscous incompressible fluid. The IB formulation of such problems uses a Lagrangian description of the structure and an Eulerian description of the fluid. It is well known that some versions of the IB method can suffer from poor volume conservation. Methods have been introduced to improve the volume-conservation properties of the IB method, but they either have been fairly specialized, or have used complex, nonstandard Eulerian finite-difference discretizations. In this paper, we use quasi-static and dynamic benchmark problems to investigate the effect of the choice of Eulerian discretization on the volume-conservation properties of a formally second-order accurate IB method. We consider both collocated and staggered-grid discretization methods. For the tests considered herein, the staggered-grid IB scheme generally yields at least a modest improvement in volume conservation when compared to cell-centered methods, and in many cases considered in this work, the spurious volume changes exhibited by the staggered-grid IB method are more than an order of magnitude smaller than those of the collocated schemes. We also compare the performance of cell-centered schemes that use either exact or approximate projection methods. We find that the volume-conservation properties of approximate projection IB methods depend strongly on the formulation of the projection method. When used with the IB method, we find that pressure-free approximate projection methods can yield extremely poor volume conservation, whereas pressure-increment approximate projection methods yield volume conservation that is nearly identical to that of a cell-centered exact projection method.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.120111.300911s
Communications in Computational Physics, Vol. 12 (2012), Iss. 2 : pp. 401–432
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
-
Staggered scheme for the compressible fluctuating hydrodynamics of multispecies fluid mixtures
Srivastava, Ishan | Ladiges, Daniel R. | Nonaka, Andy J. | Garcia, Alejandro L. | Bell, John B.Physical Review E, Vol. 107 (2023), Iss. 1
https://doi.org/10.1103/PhysRevE.107.015305 [Citations: 3] -
A hybrid immersed boundary and immersed interface method for electrohydrodynamic simulations
Hu, Wei-Fan | Lai, Ming-Chih | Young, Yuan-NanJournal of Computational Physics, Vol. 282 (2015), Iss. P.47
https://doi.org/10.1016/j.jcp.2014.11.005 [Citations: 45] -
Adaptive Mesh Refinement for Immersed Boundary Methods
Vanella, Marcos | Posa, Antonio | Balaras, EliasJournal of Fluids Engineering, Vol. 136 (2014), Iss. 4
https://doi.org/10.1115/1.4026415 [Citations: 37] -
An operator splitting strategy for fluid–structure interaction problems with thin elastic structures in an incompressible Newtonian flow
Laadhari, Aymen
Applied Mathematics Letters, Vol. 81 (2018), Iss. P.35
https://doi.org/10.1016/j.aml.2018.01.001 [Citations: 8] -
An immersed interface method for discrete surfaces
Kolahdouz, Ebrahim M. | Bhalla, Amneet Pal Singh | Craven, Brent A. | Griffith, Boyce E.Journal of Computational Physics, Vol. 400 (2020), Iss. P.108854
https://doi.org/10.1016/j.jcp.2019.07.052 [Citations: 31] -
Benchmarking the immersed finite element method for fluid–structure interaction problems
Roy, Saswati | Heltai, Luca | Costanzo, FrancescoComputers & Mathematics with Applications, Vol. 69 (2015), Iss. 10 P.1167
https://doi.org/10.1016/j.camwa.2015.03.012 [Citations: 31] -
A sharp interface Lagrangian-Eulerian method for rigid-body fluid-structure interaction
Kolahdouz, E.M. | Bhalla, A.P.S. | Scotten, L.N. | Craven, B.A. | Griffith, B.E.Journal of Computational Physics, Vol. 443 (2021), Iss. P.110442
https://doi.org/10.1016/j.jcp.2021.110442 [Citations: 17] -
A numerical method for interaction problems between fluid and membranes with arbitrary permeability for fluid
Miyauchi, Suguru | Takeuchi, Shintaro | Kajishima, TakeoJournal of Computational Physics, Vol. 345 (2017), Iss. P.33
https://doi.org/10.1016/j.jcp.2017.05.006 [Citations: 16] -
A partitioned scheme for fluid–composite structure interaction problems
Bukač, M. | Čanić, S. | Muha, B.Journal of Computational Physics, Vol. 281 (2015), Iss. P.493
https://doi.org/10.1016/j.jcp.2014.10.045 [Citations: 46] -
Splitting Methods in Communication, Imaging, Science, and Engineering
An Operator Splitting Approach to the Solution of Fluid-Structure Interaction Problems in Hemodynamics
Bukač, Martina | Čanić, Sunčica | Muha, Boris | Glowinski, Roland2016
https://doi.org/10.1007/978-3-319-41589-5_22 [Citations: 5] -
Three-dimensional simulations of the cell growth and cytokinesis using the immersed boundary method
Li, Yibao | Kim, JunseokMathematical Biosciences, Vol. 271 (2016), Iss. P.118
https://doi.org/10.1016/j.mbs.2015.11.005 [Citations: 9] -
Inertial coupling for point particle fluctuating hydrodynamics
Usabiaga, F. Balboa | Pagonabarraga, I. | Delgado-Buscalioni, R.Journal of Computational Physics, Vol. 235 (2013), Iss. P.701
https://doi.org/10.1016/j.jcp.2012.10.045 [Citations: 34] -
Simulating Biofilm Deformation and Detachment with the Immersed Boundary Method
Sudarsan, Rangarajan | Ghosh, Sudeshna | Stockie, John M. | Eberl, Hermann J.Communications in Computational Physics, Vol. 19 (2016), Iss. 3 P.682
https://doi.org/10.4208/cicp.161214.021015a [Citations: 18] -
A Fourier spectral immersed boundary method with exact translation invariance, improved boundary resolution, and a divergence-free velocity field
Chen, Zhe | Peskin, Charles S.Journal of Computational Physics, Vol. 509 (2024), Iss. P.113048
https://doi.org/10.1016/j.jcp.2024.113048 [Citations: 0] -
Reference map technique for incompressible fluid–structure interaction
Rycroft, Chris H. | Wu, Chen-Hung | Yu, Yue | Kamrin, KenJournal of Fluid Mechanics, Vol. 898 (2020), Iss.
https://doi.org/10.1017/jfm.2020.353 [Citations: 20] -
Numerical Analysis of the Immersed Boundary Method for Cell-Based Simulation
Cooper, Fergus R. | Baker, Ruth E. | Fletcher, Alexander G.SIAM Journal on Scientific Computing, Vol. 39 (2017), Iss. 5 P.B943
https://doi.org/10.1137/16M1092246 [Citations: 10] -
A Review of Interface-Driven Adaptivity for Phase-Field Modeling of Fluid–Structure Interaction
Rath, Biswajeet | Mao, Xiaoyu | Jaiman, RajeevJournal of the Indian Institute of Science, Vol. 104 (2024), Iss. 1 P.303
https://doi.org/10.1007/s41745-024-00422-y [Citations: 2] -
An interface preserving and residual-based adaptivity for phase-field modeling of fully Eulerian fluid-structure interaction
Rath, Biswajeet | Mao, Xiaoyu | Jaiman, Rajeev K.Journal of Computational Physics, Vol. 488 (2023), Iss. P.112188
https://doi.org/10.1016/j.jcp.2023.112188 [Citations: 3] -
A robust incompressible Navier-Stokes solver for high density ratio multiphase flows
Nangia, Nishant | Griffith, Boyce E. | Patankar, Neelesh A. | Bhalla, Amneet Pal SinghJournal of Computational Physics, Vol. 390 (2019), Iss. P.548
https://doi.org/10.1016/j.jcp.2019.03.042 [Citations: 63] -
Vesicle electrohydrodynamic simulations by coupling immersed boundary and immersed interface method
Hu, Wei-Fan | Lai, Ming-Chih | Seol, Yunchang | Young, Yuan-NanJournal of Computational Physics, Vol. 317 (2016), Iss. P.66
https://doi.org/10.1016/j.jcp.2016.04.035 [Citations: 25] -
Non-body-fitted fluid–structure interaction: Divergence-conforming B-splines, fully-implicit dynamics, and variational formulation
Casquero, Hugo | Zhang, Yongjie Jessica | Bona-Casas, Carles | Dalcin, Lisandro | Gomez, HectorJournal of Computational Physics, Vol. 374 (2018), Iss. P.625
https://doi.org/10.1016/j.jcp.2018.07.020 [Citations: 29] -
An immersed peridynamics model of fluid-structure interaction accounting for material damage and failure
Kim, Keon Ho | Bhalla, Amneet P.S. | Griffith, Boyce E.Journal of Computational Physics, Vol. 493 (2023), Iss. P.112466
https://doi.org/10.1016/j.jcp.2023.112466 [Citations: 3] -
High-order fluid solver based on a combined compact integrated RBF approximation and its fluid structure interaction applications
Tien, C.M.T. | Ngo-Cong, D. | Mai-Duy, N. | Tran, C.-D. | Tran-Cong, T.Computers & Fluids, Vol. 131 (2016), Iss. P.151
https://doi.org/10.1016/j.compfluid.2016.03.021 [Citations: 2] -
Implicit finite element methodology for the numerical modeling of incompressible two-fluid flows with moving hyperelastic interface
Laadhari, Aymen
Applied Mathematics and Computation, Vol. 333 (2018), Iss. P.376
https://doi.org/10.1016/j.amc.2018.03.074 [Citations: 6] -
Accuracy improvement for immersed boundary method using Lagrangian velocity interpolation
Amiri, Farhad A. | Le, Guigao | Chen, Qing | Zhang, JunfengJournal of Computational Physics, Vol. 423 (2020), Iss. P.109800
https://doi.org/10.1016/j.jcp.2020.109800 [Citations: 7] -
Immersed boundary simulations of flows driven by moving thin membranes
Lauber, Marin | Weymouth, Gabriel D. | Limbert, GeorgesJournal of Computational Physics, Vol. 457 (2022), Iss. P.111076
https://doi.org/10.1016/j.jcp.2022.111076 [Citations: 9] -
An efficient parallel immersed boundary algorithm using a pseudo-compressible fluid solver
Wiens, Jeffrey K. | Stockie, John M.Journal of Computational Physics, Vol. 281 (2015), Iss. P.917
https://doi.org/10.1016/j.jcp.2014.10.058 [Citations: 17] -
Geometric multigrid for an implicit-time immersed boundary method
Guy, Robert D. | Philip, Bobby | Griffith, Boyce E.Advances in Computational Mathematics, Vol. 41 (2015), Iss. 3 P.635
https://doi.org/10.1007/s10444-014-9380-1 [Citations: 8] -
An Interface-Driven Adaptive Variational Procedure for Fully Eulerian Fluid-Structure Interaction Via Phase-Field Modeling
Rath, Biswajeet | Mao, Xiaoyu | Jaiman, Rajeev KumarSSRN Electronic Journal , Vol. (2022), Iss.
https://doi.org/10.2139/ssrn.4047634 [Citations: 0] -
A numerical study of the benefits of driving jellyfish bells at their natural frequency
Hoover, Alexander | Miller, LauraJournal of Theoretical Biology, Vol. 374 (2015), Iss. P.13
https://doi.org/10.1016/j.jtbi.2015.03.016 [Citations: 41] -
Modeling deformable capsules in viscous flow using immersed boundary method
Tran, S. B. Q. | Le, Q. T. | Leong, F. Y. | Le, D. V.Physics of Fluids, Vol. 32 (2020), Iss. 9
https://doi.org/10.1063/5.0016302 [Citations: 14] -
Neuromechanical wave resonance in jellyfish swimming
Hoover, Alexander P. | Xu, Nicole W. | Gemmell, Brad J. | Colin, Sean P. | Costello, John H. | Dabiri, John O. | Miller, Laura A.Proceedings of the National Academy of Sciences, Vol. 118 (2021), Iss. 11
https://doi.org/10.1073/pnas.2020025118 [Citations: 20] -
On the Lagrangian-Eulerian coupling in the immersed finite element/difference method
Lee, Jae H. | Griffith, Boyce E.Journal of Computational Physics, Vol. 457 (2022), Iss. P.111042
https://doi.org/10.1016/j.jcp.2022.111042 [Citations: 10] -
Quasi‐static image‐based immersed boundary‐finite element model of left ventricle under diastolic loading
Gao, Hao | Wang, Huiming | Berry, Colin | Luo, Xiaoyu | Griffith, Boyce E.International Journal for Numerical Methods in Biomedical Engineering, Vol. 30 (2014), Iss. 11 P.1199
https://doi.org/10.1002/cnm.2652 [Citations: 51] -
Stabilization approaches for the hyperelastic immersed boundary method for problems of large-deformation incompressible elasticity
Vadala-Roth, Ben | Acharya, Shashank | Patankar, Neelesh A. | Rossi, Simone | Griffith, Boyce E.Computer Methods in Applied Mechanics and Engineering, Vol. 365 (2020), Iss. P.112978
https://doi.org/10.1016/j.cma.2020.112978 [Citations: 20] -
An immersed interface-lattice Boltzmann method for fluid-structure interaction
Qin, Jianhua | Kolahdouz, Ebrahim M. | Griffith, Boyce E.Journal of Computational Physics, Vol. 428 (2021), Iss. P.109807
https://doi.org/10.1016/j.jcp.2020.109807 [Citations: 17] -
Variational implementation of immersed finite element methods
Heltai, Luca | Costanzo, FrancescoComputer Methods in Applied Mechanics and Engineering, Vol. 229-232 (2012), Iss. P.110
https://doi.org/10.1016/j.cma.2012.04.001 [Citations: 30] -
Fully Eulerian finite element approximation of a fluid‐structure interaction problem in cardiac cells
Laadhari, A. | Ruiz‐Baier, R. | Quarteroni, A.International Journal for Numerical Methods in Engineering, Vol. 96 (2013), Iss. 11 P.712
https://doi.org/10.1002/nme.4582 [Citations: 20] -
Numerical methods for immersed FSI with thin-walled structures
Boilevin-Kayl, Ludovic | Fernández, Miguel A. | Gerbeau, Jean-FrédéricComputers & Fluids, Vol. 179 (2019), Iss. P.744
https://doi.org/10.1016/j.compfluid.2018.05.024 [Citations: 15] -
Hybrid finite difference/finite element immersed boundary method
Griffith, Boyce E | Luo, XiaoyuInternational Journal for Numerical Methods in Biomedical Engineering, Vol. 33 (2017), Iss. 12
https://doi.org/10.1002/cnm.2888 [Citations: 101] -
An immersed boundary energy-based method for incompressible viscoelasticity
Devendran, Dharshi | Peskin, Charles S.Journal of Computational Physics, Vol. 231 (2012), Iss. 14 P.4613
https://doi.org/10.1016/j.jcp.2012.02.020 [Citations: 36] -
Numerical method for modeling photosynthesis of algae on pulsing soft corals
Santiago, Matea | Mitchell, Kevin A. | Khatri, ShilpaPhysical Review Fluids, Vol. 7 (2022), Iss. 3
https://doi.org/10.1103/PhysRevFluids.7.033102 [Citations: 2] -
Fluid-Structure Interaction and Biomedical Applications
Fluid–Structure Interaction in Hemodynamics: Modeling, Analysis, and Numerical Simulation
Čanić, Sunčica | Muha, Boris | Bukač, Martina2014
https://doi.org/10.1007/978-3-0348-0822-4_2 [Citations: 8] -
An immersed boundary method for rigid bodies
Kallemov, Bakytzhan | Bhalla, Amneet | Griffith, Boyce | Donev, AleksandarCommunications in Applied Mathematics and Computational Science, Vol. 11 (2016), Iss. 1 P.79
https://doi.org/10.2140/camcos.2016.11.79 [Citations: 72] -
A Monolithic Approach to Fluid–Composite Structure Interaction
Forti, Davide | Bukac, Martina | Quaini, Annalisa | Canic, Suncica | Deparis, SimoneJournal of Scientific Computing, Vol. 72 (2017), Iss. 1 P.396
https://doi.org/10.1007/s10915-017-0363-5 [Citations: 18] -
Study of drafting, kissing and tumbling process of two particles with different sizes using immersed boundary method in a confined medium
Ghosh, Sudeshna | Kumar, ManishMathematics and Computers in Simulation, Vol. 177 (2020), Iss. P.341
https://doi.org/10.1016/j.matcom.2020.04.029 [Citations: 11] -
A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction
Kolahdouz, Ebrahim M. | Wells, David R. | Rossi, Simone | Aycock, Kenneth I. | Craven, Brent A. | Griffith, Boyce E.Journal of Computational Physics, Vol. 488 (2023), Iss. P.112174
https://doi.org/10.1016/j.jcp.2023.112174 [Citations: 3] -
An unfitted mesh semi‐implicit coupling scheme for fluid‐structure interaction with immersed solids
Fernández, Miguel A. | Gerosa, Fannie M.International Journal for Numerical Methods in Engineering, Vol. 122 (2021), Iss. 19 P.5384
https://doi.org/10.1002/nme.6449 [Citations: 6] -
An immersed-boundary/isogeometric method for fluid–structure interaction involving thin shells
Nitti, Alessandro | Kiendl, Josef | Reali, Alessandro | de Tullio, Marco D.Computer Methods in Applied Mechanics and Engineering, Vol. 364 (2020), Iss. P.112977
https://doi.org/10.1016/j.cma.2020.112977 [Citations: 35] -
A scalable method to model large suspensions of colloidal phoretic particles with arbitrary shapes
Delmotte, Blaise | Usabiaga, Florencio BalboaJournal of Computational Physics, Vol. 518 (2024), Iss. P.113321
https://doi.org/10.1016/j.jcp.2024.113321 [Citations: 0] -
An Immersed Boundary method with divergence-free velocity interpolation and force spreading
Bao, Yuanxun | Donev, Aleksandar | Griffith, Boyce E. | McQueen, David M. | Peskin, Charles S.Journal of Computational Physics, Vol. 347 (2017), Iss. P.183
https://doi.org/10.1016/j.jcp.2017.06.041 [Citations: 41] -
Staggered Schemes for Fluctuating Hydrodynamics
Balboa, Florencio | Bell, John B. | Delgado-Buscalioni, Rafael | Donev, Aleksandar | Fai, Thomas G. | Griffith, Boyce E. | Peskin, Charles S.Multiscale Modeling & Simulation, Vol. 10 (2012), Iss. 4 P.1369
https://doi.org/10.1137/120864520 [Citations: 98] -
An effective preconditioning strategy for volume penalized incompressible/low Mach multiphase flow solvers
Thirumalaisamy, Ramakrishnan | Khedkar, Kaustubh | Ghysels, Pieter | Bhalla, Amneet Pal SinghJournal of Computational Physics, Vol. 490 (2023), Iss. P.112325
https://doi.org/10.1016/j.jcp.2023.112325 [Citations: 4] -
Influence of the vessel wall geometry on the wall-induced migration of red blood cells
Zhang, Ying | Fai, Thomas G. | Beard, Daniel APLOS Computational Biology, Vol. 19 (2023), Iss. 7 P.e1011241
https://doi.org/10.1371/journal.pcbi.1011241 [Citations: 5] -
Lubricated immersed boundary method in two dimensions
Fai, Thomas G. | Rycroft, Chris H.Journal of Computational Physics, Vol. 356 (2018), Iss. P.319
https://doi.org/10.1016/j.jcp.2017.11.029 [Citations: 10] -
A Forced Damped Oscillation Framework for Undulatory Swimming Provides New Insights into How Propulsion Arises in Active and Passive Swimming
Bhalla, Amneet Pal Singh | Griffith, Boyce E. | Patankar, Neelesh A. | Goldman, DanielPLoS Computational Biology, Vol. 9 (2013), Iss. 6 P.e1003097
https://doi.org/10.1371/journal.pcbi.1003097 [Citations: 52] -
Eulerian weakly compressible smoothed particle hydrodynamics (SPH) with the immersed boundary method for thin slender bodies
Nasar, A.M.A. | Rogers, B.D. | Revell, A. | Stansby, P.K. | Lind, S.J.Journal of Fluids and Structures, Vol. 84 (2019), Iss. P.263
https://doi.org/10.1016/j.jfluidstructs.2018.11.005 [Citations: 28] -
Patient–Specific Immersed Finite Element–Difference Model of Transcatheter Aortic Valve Replacement
Brown, Jordan A. | Lee, Jae H. | Smith, Margaret Anne | Wells, David R. | Barrett, Aaron | Puelz, Charles | Vavalle, John P. | Griffith, Boyce E.Annals of Biomedical Engineering, Vol. 51 (2023), Iss. 1 P.103
https://doi.org/10.1007/s10439-022-03047-3 [Citations: 13] -
A modular, operator‐splitting scheme for fluid–structure interaction problems with thick structures
Bukač, M. | Čanić, S. | Glowinski, R. | Muha, B. | Quaini, A.International Journal for Numerical Methods in Fluids, Vol. 74 (2014), Iss. 8 P.577
https://doi.org/10.1002/fld.3863 [Citations: 34] -
Image-based fluid–structure interaction model of the human mitral valve
Ma, Xingshuang | Gao, Hao | Griffith, Boyce E. | Berry, Colin | Luo, XiaoyuComputers & Fluids, Vol. 71 (2013), Iss. P.417
https://doi.org/10.1016/j.compfluid.2012.10.025 [Citations: 46] -
Image-based immersed boundary model of the aortic root
Hasan, Ali | Kolahdouz, Ebrahim M. | Enquobahrie, Andinet | Caranasos, Thomas G. | Vavalle, John P. | Griffith, Boyce E.Medical Engineering & Physics, Vol. 47 (2017), Iss. P.72
https://doi.org/10.1016/j.medengphy.2017.05.007 [Citations: 19] -
The divergence-conforming immersed boundary method: Application to vesicle and capsule dynamics
Casquero, Hugo | Bona-Casas, Carles | Toshniwal, Deepesh | Hughes, Thomas J.R. | Gomez, Hector | Zhang, Yongjie JessicaJournal of Computational Physics, Vol. 425 (2021), Iss. P.109872
https://doi.org/10.1016/j.jcp.2020.109872 [Citations: 27]