Local divergence-free immersed finite element-difference method using composite B-splines
In the class of immersed boundary (IB) methods, the choice of the regularized delta function plays a crucial role in transferring information between fluid and solid domains through interpolation and spreading operators. Most prior work using the IB method has used isotropic kernels that do not pres...
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| Published in: | Advances in Computational Science and Engineering Vol. 4; pp. 16 - 56 |
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| Language: | English |
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01.06.2025
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| ISSN: | 2837-1739, 2837-1739 |
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| Abstract | In the class of immersed boundary (IB) methods, the choice of the regularized delta function plays a crucial role in transferring information between fluid and solid domains through interpolation and spreading operators. Most prior work using the IB method has used isotropic kernels that do not preserve the divergence-free condition of the velocity field, leading to loss of incompressibility of the solid when interpolating the Eulerian velocity to Lagrangian markers. One approach to addressing this issue in IB simulations involving large deformations of immersed incompressible elastic structures is to use a volumetric stabilization approach, such as adding a volumetric energy term and using modified invariants in the structure's constitutive model. Composite B-spline (CBS) kernels offer an alternative approach by inherently maintaining the discrete divergence-free property. This work evaluates the performance of CBS kernels in terms of their volume conservation and accuracy, comparing them with several traditional isotropic kernel functions using a construction introduced by Peskin (referred to as IB kernels) and B-spline (BS) kernels. Benchmark tests include pressure-loaded and shear-dominated flows, such as an elastic band under differential pressure loads, a pressurized membrane, a compressed block, Cook's membrane, a slanted channel flow, and a modified Turek-Hron problem. Additionally, we validate our methodology using a complex fluid-structure interaction model of bioprosthetic heart valve dynamics in a pulse duplicator. Results demonstrate that CBS kernels achieve superior volume conservation compared to conventional isotropic kernels, eliminating the need for additional volumetric stabilization techniques typically required to address instabilities arising from volume conservation errors. Further, it is common that the accuracy provided by CBS kernels on coarser grids is comparable to that provided by IB and BS kernels on finer grids. Unlike IB and BS kernels, which perform better with larger mesh ratio factors between solid and fluid grids, CBS kernels show improved results with smaller mesh ratio factors. Additionally, the study reveals that although wider kernels provide more accurate results across all methods, CBS kernels are less sensitive to variations in relative grid spacings than isotropic kernels. This study highlights the advantages of CBS kernels in achieving stable, accurate, and efficient FSI simulations without requiring specialized volumetric stabilization treatments when simulating large deformations of elastic solids immersed in fluid. |
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| AbstractList | In the class of immersed boundary (IB) methods, the choice of the regularized delta function plays a crucial role in transferring information between fluid and solid domains through interpolation and spreading operators. Most prior work using the IB method has used isotropic kernels that do not preserve the divergence-free condition of the velocity field, leading to loss of incompressibility of the solid when interpolating the Eulerian velocity to Lagrangian markers. One approach to addressing this issue in IB simulations involving large deformations of immersed incompressible elastic structures is to use a volumetric stabilization approach, such as adding a volumetric energy term and using modified invariants in the structure's constitutive model. Composite B-spline (CBS) kernels offer an alternative approach by inherently maintaining the discrete divergence-free property. This work evaluates the performance of CBS kernels in terms of their volume conservation and accuracy, comparing them with several traditional isotropic kernel functions using a construction introduced by Peskin (referred to as IB kernels) and B-spline (BS) kernels. Benchmark tests include pressure-loaded and shear-dominated flows, such as an elastic band under differential pressure loads, a pressurized membrane, a compressed block, Cook's membrane, a slanted channel flow, and a modified Turek-Hron problem. Additionally, we validate our methodology using a complex fluid-structure interaction model of bioprosthetic heart valve dynamics in a pulse duplicator. Results demonstrate that CBS kernels achieve superior volume conservation compared to conventional isotropic kernels, eliminating the need for additional volumetric stabilization techniques typically required to address instabilities arising from volume conservation errors. Further, it is common that the accuracy provided by CBS kernels on coarser grids is comparable to that provided by IB and BS kernels on finer grids. Unlike IB and BS kernels, which perform better with larger mesh ratio factors between solid and fluid grids, CBS kernels show improved results with smaller mesh ratio factors. Additionally, the study reveals that although wider kernels provide more accurate results across all methods, CBS kernels are less sensitive to variations in relative grid spacings than isotropic kernels. This study highlights the advantages of CBS kernels in achieving stable, accurate, and efficient FSI simulations without requiring specialized volumetric stabilization treatments when simulating large deformations of elastic solids immersed in fluid. In the class of immersed boundary (IB) methods, the choice of the regularized delta function plays a crucial role in transferring information between fluid and solid domains through interpolation and spreading operators. Most prior work using the IB method has used isotropic kernels that do not preserve the divergence-free condition of the velocity field, leading to loss of incompressibility of the solid when interpolating the Eulerian velocity to Lagrangian markers. One approach to addressing this issue in IB simulations involving large deformations of immersed incompressible elastic structures is to use a volumetric stabilization approach, such as adding a volumetric energy term and using modified invariants in the structure's constitutive model. Composite B-spline (CBS) kernels offer an alternative approach by inherently maintaining the discrete divergence-free property. This work evaluates the performance of CBS kernels in terms of their volume conservation and accuracy, comparing them with several traditional isotropic kernel functions using a construction introduced by Peskin (referred to as IB kernels) and B-spline (BS) kernels. Benchmark tests include pressure-loaded and shear-dominated flows, such as an elastic band under differential pressure loads, a pressurized membrane, a compressed block, Cook's membrane, a slanted channel flow, and a modified Turek-Hron problem. Additionally, we validate our methodology using a complex fluid-structure interaction model of bioprosthetic heart valve dynamics in a pulse duplicator. Results demonstrate that CBS kernels achieve superior volume conservation compared to conventional isotropic kernels, eliminating the need for additional volumetric stabilization techniques typically required to address instabilities arising from volume conservation errors. Further, it is common that the accuracy provided by CBS kernels on coarser grids is comparable to that provided by IB and BS kernels on finer grids. Unlike IB and BS kernels, which perform better with larger mesh ratio factors between solid and fluid grids, CBS kernels show improved results with smaller mesh ratio factors. Additionally, the study reveals that although wider kernels provide more accurate results across all methods, CBS kernels are less sensitive to variations in relative grid spacings than isotropic kernels. This study highlights the advantages of CBS kernels in achieving stable, accurate, and efficient FSI simulations without requiring specialized volumetric stabilization treatments when simulating large deformations of elastic solids immersed in fluid.In the class of immersed boundary (IB) methods, the choice of the regularized delta function plays a crucial role in transferring information between fluid and solid domains through interpolation and spreading operators. Most prior work using the IB method has used isotropic kernels that do not preserve the divergence-free condition of the velocity field, leading to loss of incompressibility of the solid when interpolating the Eulerian velocity to Lagrangian markers. One approach to addressing this issue in IB simulations involving large deformations of immersed incompressible elastic structures is to use a volumetric stabilization approach, such as adding a volumetric energy term and using modified invariants in the structure's constitutive model. Composite B-spline (CBS) kernels offer an alternative approach by inherently maintaining the discrete divergence-free property. This work evaluates the performance of CBS kernels in terms of their volume conservation and accuracy, comparing them with several traditional isotropic kernel functions using a construction introduced by Peskin (referred to as IB kernels) and B-spline (BS) kernels. Benchmark tests include pressure-loaded and shear-dominated flows, such as an elastic band under differential pressure loads, a pressurized membrane, a compressed block, Cook's membrane, a slanted channel flow, and a modified Turek-Hron problem. Additionally, we validate our methodology using a complex fluid-structure interaction model of bioprosthetic heart valve dynamics in a pulse duplicator. Results demonstrate that CBS kernels achieve superior volume conservation compared to conventional isotropic kernels, eliminating the need for additional volumetric stabilization techniques typically required to address instabilities arising from volume conservation errors. Further, it is common that the accuracy provided by CBS kernels on coarser grids is comparable to that provided by IB and BS kernels on finer grids. Unlike IB and BS kernels, which perform better with larger mesh ratio factors between solid and fluid grids, CBS kernels show improved results with smaller mesh ratio factors. Additionally, the study reveals that although wider kernels provide more accurate results across all methods, CBS kernels are less sensitive to variations in relative grid spacings than isotropic kernels. This study highlights the advantages of CBS kernels in achieving stable, accurate, and efficient FSI simulations without requiring specialized volumetric stabilization treatments when simulating large deformations of elastic solids immersed in fluid. |
| Author | Li, Lianxia Gruninger, Cole Lee, Jae H. Griffith, Boyce E. |
| AuthorAffiliation | 4 Computational Medicine Program, University of North Carolina School of Medicine, Chapel Hill, NC, USA 2 Department of Biomedical Engineering, University of North Carolina, Chapel Hill, NC, USA 5 McAllister Heart Institute, University of North Carolina School of Medicine, Chapel Hill, NC, USA 1 Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA 3 Carolina Center for Interdisciplinary Applied Mathematics, University of North Carolina, Chapel Hill, NC, USA |
| AuthorAffiliation_xml | – name: 3 Carolina Center for Interdisciplinary Applied Mathematics, University of North Carolina, Chapel Hill, NC, USA – name: 2 Department of Biomedical Engineering, University of North Carolina, Chapel Hill, NC, USA – name: 1 Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA – name: 4 Computational Medicine Program, University of North Carolina School of Medicine, Chapel Hill, NC, USA – name: 5 McAllister Heart Institute, University of North Carolina School of Medicine, Chapel Hill, NC, USA |
| Author_xml | – sequence: 1 givenname: Lianxia surname: Li fullname: Li, Lianxia email: llianxia@unc.edu organization: Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA – sequence: 2 givenname: Cole surname: Gruninger fullname: Gruninger, Cole email: coleco@live.unc.edu organization: Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA – sequence: 3 givenname: Jae H. surname: Lee fullname: Lee, Jae H. email: jaeholee@live.unc.edu organization: Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA – sequence: 4 givenname: Boyce E. surname: Griffith fullname: Griffith, Boyce E. email: boyceg@email.unc.edu organization: Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA |
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| Cites_doi | 10.1371/journal.pbio.1002123 10.1137/S1064827502414060 10.1016/j.jcp.2016.04.024 10.1007/s00366-006-0049-3 10.1016/j.jcp.2018.07.020 10.1006/jcph.1999.6293 10.1016/j.jtbi.2015.07.035 10.1017/jfm.2013.434 10.1017/jfm.2017.3 10.1016/0021-9991(72)90065-4 10.1016/j.jcp.2022.111890 10.1063/1.1761178 10.1016/j.cma.2020.112978 10.1016/j.cma.2003.12.044 10.1016/j.jcp.2022.111500 10.1016/j.jcp.2006.08.019 10.1016/0021-9991(84)90143-8 10.1142/S1758825109000113 10.1016/j.jcp.2013.08.043 10.1002/cnm.2888 10.1016/j.jcp.2017.06.041 10.1017/jfm.2011.54 10.1002/cpe.652 10.1016/j.cma.2003.12.024 10.1016/j.jcp.2024.112831 10.1016/j.jcp.2009.07.001 10.1002/cnm.3240 10.1016/j.cma.2016.07.028 10.1002/fld.1650200824 10.4208/cicp.120111.300911s 10.1090/qam/16705 10.1142/S0218202512500583 10.1016/j.cma.2007.09.015 10.1016/j.jcp.2007.02.023 10.1016/j.jcp.2024.112888 10.1006/jcph.2000.6502 10.1109/18.119742 10.1098/rsif.2005.0073 10.1016/j.jcp.2020.109872 10.1016/j.jcp.2012.02.020 10.1006/jcph.1993.1051 10.1017/S0962492902000077 10.1016/j.jcp.2022.111042 10.1039/tf9615700829 10.1007/s10439-020-02466-4 10.1371/journal.pone.0179727 10.1002/cnm.1445 10.1093/imanum/4.4.491 10.3390/fluids3030045 10.1016/j.zool.2013.10.011 10.1142/S0218202513500139 10.1007/3-540-34596-5_15 10.1016/j.jbiomech.2016.03.009 10.1007/978-1-4612-1986-6_8 10.1007/978-1-4612-6333-3 10.1093/pnasnexus/pgae392 10.1002/9780470558027.ch7 10.1137/1.9781611970555 10.2172/2337606 10.1007/BFb0064470 |
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| Keywords | isotropic kernel fluid-structure interaction immersed finite element-finite difference method volume conservation Immersed boundary composite B-spline kernels (CBS) volumetric stabilization Secondary: 53C35 Primary: 58F15, 58F17 |
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| References | Jones Laurenza Hedrick Griffith Miller (38) 2015; 384 Lee Rygg Kolahdouz Rossi Retta Duraiswamy Scotten Craven Griffith (43) 2020; 48 Santhanakrishnan Jones Dickson Peek Kasoju Dickinson Miller (54) 2018; 3 Bale Neveln Bhalla MacIver Patankar (5) 2015; 13 Kirk Peterson Stogner Carey (41) 2006; 22 Casquero Zhang Bona-Casas Dalcin Gomez (12) 2018; 374 Zhang Gerstenberger Wang Liu (64) 2004; 193 Handscomb (33) 1984; 4 M. Davey, C. Puelz, S. Rossi, M. A. Smith, D. R. Wells, G. M. Sturgeon, W. P. Segars, J. P. Vavalle, C. S. Peskin and B. E. Griffith, Simulating cardiac fluid dynamics in the human heart, PNAS Nexus, 3 (2024), pgae392. Wells Vadala-Roth Lee Griffith (63) 2023; 477 Wang Liu (62) 2004; 193 Flory (22) 1961; 57 Tytell Hsu Fauci (59) 2014; 117 Evans Hughes (20) 2013; 23 Peskin (47) 1972; 10 Lee Griffith (42) 2022; 457 S. Balay, W. D. Gropp, L. C. McInnes and B. F. Smith, Efficient management of parallelism in object oriented numerical software libraries, in Modern Software Tools in Scientific Computing, Birkhäuser Press, (1997), 163-202. P. A. Raviart and J. M. Thomas, A mixed finite element method for second-order elliptic problems, in Mathematical Aspects of Finite Element Methods, Lecture Notes in Mathematics, Springer, Berlin, Heidelberg, 606 (1977), 292-315. Gruninger Barrett Fang Forest Griffith (31) 2024; 506 Rider Greenough Kamm (51) 2007; 225 Roma Peskin Berger (52) 1999; 153 Hoover Griffith Miller (36) 2017; 813 B. E. Griffith, R. D. Hornung, D. M. McQueen and C. S. Peskin, Parallel and adaptive simulation of cardiac fluid dynamics, in Advanced Computational Infrastructures for Parallel and Distributed Adaptive Applications, (2009), 105-130. Liu Jun Zhang (45) 1995; 20 Colella Woodward (14) 1984; 54 S. Balay, S. Abhyankar, M.F. Adams, S. Benson, J. Brown, P. Brune, K. Buschelman, E. M. Constantinescu, L. o Dalcin, A. Dener, V. Eijkhout, J. Faibussowitsch, W. D. Gropp, V. Hapla, T. Isaac, P. Jolivet, D. Karpeev, D. Kaushik, M. G. Knepley, F. Kong, S. Kruger, D. A. May, L. C. McInnes, R. T. Mills, L. Mitchell, T. Munson, J. E. Roman, K. Rupp, P. Sanan, J. Sarich, B. F. Smith, S. Zampini, H. Zhang, H. Zhang and J. Zhang, PETSc Web page, Available from: https://petsc.org/, 2024. Griffith (26) 2012; 28 Hasan Kolahdouz Enquobahrie Caranasos Vavalle Griffith (35) 2017; 47 Alben Miller Peng (1) 2013; 733 Cortez Minion (15) 2000; 161 Devendran Peskin (19) 2012; 231 Evans Hughes (21) 2013; 23 I. J. Schoenberg, Cardinal Spline Interpolation, Society for Industrial and Applied Mathematics, 1973. Gasser Ogden Holzapfel (23) 2006; 3 Lee LeVeque (44) 2003; 25 Roy-Chowdhury Shinar Schroeder (53) 2024; 503 Bao Kaye Peskin (7) 2016; 316 S. Turek and J. Hron, Proposal for numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow, in Fluid-Structure Interaction, Springer Berlin Heidelberg, Berlin, Heidelberg, 53 (2006), 371-385. W. W. Chen, H. Gao, X. Y. Luo and N. A. Hill, Study of cardiovascular function using a coupled left ventricle and systemic circulation model, Journal of Biomechanics, 49 (2016), 2445-2454, Cardiovascular Biomechanics in Health and Disease. Nangia Bale Chen Hanna Patankar (46) 2017; 12 Casquero Bona-Casas Toshniwal Hughes Gomez Zhang (11) 2021; 425 Bhalla Bale Griffith Patankar (8) 2014; 256 Crowl Fogelson (16) 2011; 676 C. de Boor, A Practical Guide to Splines, Springer-Verlag, New York, 1978. Unser Aldroubi Eden (60) 1992; 38 Kaiser McQueen Peskin (39) 2019; 35 Peskin (48) 2002; 11 Griffith Luo McQueen Peskin (30) 2009; 1 Peskin Printz (49) 1993; 105 Bao Donev Griffith McQueen Peskin (6) 2017; 347 Griffith (25) 2012; 12 Griffith Luo (29) 2017; 33 S. Balay, S. Abhyankar, M. F. Adams, S. Benson, J. Brown, P. Brune, K. Buschelman, E. M. Constantinescu, L. Dalcin, A. Dener, V. Eijkhout, J. Faibussowitsch, W. D. Gropp, V. Hapla, T. Isaac, P. Jolivet, D. Karpeev, D. Kaushik, M. G. Knepley, F. Kong, S. Kruger, D. A. May, L. C. McInnes, R. T. Mills, L. Mitchell, T. Munson, J. E. Roman, K. Rupp, P. Sanan, J. Sarich, B. F. Smith, S. Zampini, H. Zhang, H. Zhang and J. Zhang, PETSc/TAO Users Manual, Technical Report ANL-21/39 - Revision 3.22, Argonne National Laboratory, 2024. Boffi Gastaldi Heltai Peskin (9) 2008; 197 Kamensky Hsu Yu Evans Sacks Hughes (40) 2017; 314 Schoenberg (55) 1946; 4 Griffith (24) 2009; 228 Schroeder Roy-Chowdhury Shinar (57) 2022; 468 Harlow Welch (34) 1965; 8 IBAMR Web page, Available from: http://ibamr.github.io/. C. Gruninger and B. E. Griffith, Local divergence-free velocity interpolation for the immersed boundary method using composite B-splines, preprint, arXiv: : 408.08280, 2024. Griffith Hornung McQueen Peskin (27) 2007; 223 Hornung Kohn (37) 2002; 14 Vadala-Roth Acharya Patankar Rossi Griffith (61) 2020; 365 key-10.3934/acse.2025011-40 key-10.3934/acse.2025011-41 key-10.3934/acse.2025011-42 key-10.3934/acse.2025011-47 key-10.3934/acse.2025011-48 key-10.3934/acse.2025011-49 key-10.3934/acse.2025011-43 key-10.3934/acse.2025011-44 key-10.3934/acse.2025011-45 key-10.3934/acse.2025011-46 key-10.3934/acse.2025011-50 key-10.3934/acse.2025011-51 key-10.3934/acse.2025011-52 key-10.3934/acse.2025011-53 key-10.3934/acse.2025011-14 key-10.3934/acse.2025011-58 key-10.3934/acse.2025011-15 key-10.3934/acse.2025011-59 key-10.3934/acse.2025011-16 key-10.3934/acse.2025011-17 key-10.3934/acse.2025011-10 key-10.3934/acse.2025011-54 key-10.3934/acse.2025011-11 key-10.3934/acse.2025011-55 key-10.3934/acse.2025011-12 key-10.3934/acse.2025011-56 key-10.3934/acse.2025011-13 key-10.3934/acse.2025011-57 key-10.3934/acse.2025011-18 key-10.3934/acse.2025011-19 key-10.3934/acse.2025011-9 key-10.3934/acse.2025011-3 key-10.3934/acse.2025011-61 key-10.3934/acse.2025011-4 key-10.3934/acse.2025011-62 key-10.3934/acse.2025011-1 key-10.3934/acse.2025011-63 key-10.3934/acse.2025011-2 key-10.3934/acse.2025011-20 key-10.3934/acse.2025011-64 key-10.3934/acse.2025011-7 key-10.3934/acse.2025011-8 key-10.3934/acse.2025011-5 key-10.3934/acse.2025011-6 key-10.3934/acse.2025011-60 key-10.3934/acse.2025011-25 key-10.3934/acse.2025011-26 key-10.3934/acse.2025011-27 key-10.3934/acse.2025011-28 key-10.3934/acse.2025011-21 key-10.3934/acse.2025011-65 key-10.3934/acse.2025011-22 key-10.3934/acse.2025011-23 key-10.3934/acse.2025011-24 key-10.3934/acse.2025011-29 key-10.3934/acse.2025011-30 key-10.3934/acse.2025011-31 key-10.3934/acse.2025011-36 key-10.3934/acse.2025011-37 key-10.3934/acse.2025011-38 key-10.3934/acse.2025011-39 key-10.3934/acse.2025011-32 key-10.3934/acse.2025011-33 key-10.3934/acse.2025011-34 key-10.3934/acse.2025011-35 |
| References_xml | – volume: 13 start-page: 1 year: 2015 end-page: 22 ident: 5 article-title: Convergent evolution of mechanically optimal locomotion in aquatic invertebrates and vertebrates publication-title: PLOS Biology doi: 10.1371/journal.pbio.1002123 – volume: 25 start-page: 832 year: 2003 end-page: 856 ident: 44 article-title: An immersed interface method for incompressible navier–stokes equations publication-title: SIAM Journal on Scientific Computing doi: 10.1137/S1064827502414060 – volume: 316 start-page: 139 year: 2016 end-page: 144 ident: 7 article-title: A Gaussian-like immersed-boundary kernel with three continuous derivatives and improved translational invariance publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2016.04.024 – volume: 47 start-page: 72 year: 2017 end-page: 84 ident: 35 article-title: Image-based immersed boundary model of the aortic root publication-title: Medical Engineering and Physics – volume: 22 start-page: 237 year: 2006 end-page: 254 ident: 41 article-title: IibMesh: A C++ library for parallel adaptive mesh refinement/coarsening simulations publication-title: Engineering with Computers doi: 10.1007/s00366-006-0049-3 – volume: 374 start-page: 625 year: 2018 end-page: 653 ident: 12 article-title: Non-body-fitted fluid–structure interaction: Divergence-conforming B-splines, fully-implicit dynamics and variational formulation publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2018.07.020 – reference: M. Davey, C. Puelz, S. Rossi, M. A. Smith, D. R. Wells, G. M. Sturgeon, W. P. Segars, J. P. Vavalle, C. S. Peskin and B. E. Griffith, Simulating cardiac fluid dynamics in the human heart, PNAS Nexus, 3 (2024), pgae392. – volume: 153 start-page: 509 year: 1999 end-page: 534 ident: 52 article-title: An adaptive version of the immersed boundary method publication-title: Journal of Computational Physics doi: 10.1006/jcph.1999.6293 – volume: 384 start-page: 105 year: 2015 end-page: 120 ident: 38 article-title: Lift vs. drag based mechanisms for vertical force production in the smallest flying insects publication-title: Journal of Theoretical Biology doi: 10.1016/j.jtbi.2015.07.035 – volume: 733 start-page: 100 year: 2013 end-page: 133 ident: 1 article-title: Efficient kinematics for jet-propelled swimming publication-title: Journal of Fluid Mechanics doi: 10.1017/jfm.2013.434 – volume: 813 start-page: 1112 year: 2017 end-page: 1155 ident: 36 article-title: Quantifying performance in the medusan mechanospace with an actively swimming three-dimensional jellyfish model publication-title: Journal of Fluid Mechanics doi: 10.1017/jfm.2017.3 – volume: 10 start-page: 252 year: 1972 end-page: 271 ident: 47 article-title: Flow patterns around heart valves: A numerical method publication-title: Journal of Computational Physics doi: 10.1016/0021-9991(72)90065-4 – reference: P. A. Raviart and J. M. Thomas, A mixed finite element method for second-order elliptic problems, in Mathematical Aspects of Finite Element Methods, Lecture Notes in Mathematics, Springer, Berlin, Heidelberg, 606 (1977), 292-315. – volume: 477 start-page: 111890 year: 2023 ident: 63 article-title: A nodal immersed finite element-finite difference method publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2022.111890 – volume: 8 start-page: 2182 year: 1965 end-page: 2189 ident: 34 article-title: Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface publication-title: Physics of Fluids doi: 10.1063/1.1761178 – volume: 365 start-page: 112978 year: 2020 ident: 61 article-title: Stabilization approaches for the hyperelastic immersed boundary method for problems of large-deformation incompressible elasticity publication-title: Computer Methods in Applied Mechanics and Engineering doi: 10.1016/j.cma.2020.112978 – volume: 193 start-page: 2051 year: 2004 end-page: 2067 ident: 64 article-title: Immersed finite element method publication-title: Computer Methods in Applied Mechanics and Engineering doi: 10.1016/j.cma.2003.12.044 – volume: 468 start-page: 111500 year: 2022 ident: 57 article-title: Local divergence-free polynomial interpolation on MAC grids publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2022.111500 – volume: 223 start-page: 10 year: 2007 end-page: 49 ident: 27 article-title: An adaptive, formally second order accurate version of the immersed boundary method publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2006.08.019 – volume: 54 start-page: 174 year: 1984 end-page: 201 ident: 14 article-title: The piecewise parabolic method (PPM) for gas-dynamical simulations publication-title: Journal of Computational Physics doi: 10.1016/0021-9991(84)90143-8 – volume: 1 start-page: 137 year: 2009 end-page: 177 ident: 30 article-title: Simulating the fluid dynamics of natural and prosthetic heart valves using the immersed boundary method publication-title: International Journal of Applied Mechanics doi: 10.1142/S1758825109000113 – volume: 256 start-page: 88 year: 2014 end-page: 108 ident: 8 article-title: Fully resolved immersed electrohydrodynamics for particle motion, electrolocation and self-propulsion publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2013.08.043 – reference: I. J. Schoenberg, Cardinal Spline Interpolation, Society for Industrial and Applied Mathematics, 1973. – volume: 33 start-page: e2888 year: 2017 ident: 29 article-title: Hybrid finite difference/finite element immersed boundary method publication-title: International Journal for Numerical Methods in Biomedical Engineering doi: 10.1002/cnm.2888 – volume: 347 start-page: 183 year: 2017 end-page: 206 ident: 6 article-title: An immersed boundary method with divergence-free velocity interpolation and force spreading publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2017.06.041 – volume: 676 start-page: 348 year: 2011 end-page: 375 ident: 16 article-title: Analysis of mechanisms for platelet near-wall excess under arterial blood flow conditions publication-title: Journal of Fluid Mechanics doi: 10.1017/jfm.2011.54 – volume: 14 start-page: 347 year: 2002 end-page: 368 ident: 37 article-title: Managing application complexity in the SAMRAI object-oriented framework publication-title: Concurrency and Computation: Practice and Experience doi: 10.1002/cpe.652 – reference: C. Gruninger and B. E. Griffith, Local divergence-free velocity interpolation for the immersed boundary method using composite B-splines, preprint, arXiv: : 408.08280, 2024. – volume: 193 start-page: 1305 year: 2004 end-page: 1321 ident: 62 article-title: Extended immersed boundary method using FEM and RKPM publication-title: Computer Methods in Applied Mechanics and Engineering doi: 10.1016/j.cma.2003.12.024 – volume: 503 start-page: 112831 year: 2024 ident: 53 article-title: Higher order divergence-free and curl-free interpolation on MAC grids publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2024.112831 – volume: 228 start-page: 7565 year: 2009 end-page: 7595 ident: 24 article-title: An accurate and efficient method for the incompressible Navier-Stokes equations using the projection method as a preconditioner publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2009.07.001 – volume: 35 start-page: e3240 year: 2019 ident: 39 article-title: Modeling the mitral valve publication-title: International Journal for Numerical Methods in Biomedical Engineering doi: 10.1002/cnm.3240 – volume: 314 start-page: 408 year: 2017 end-page: 472 ident: 40 article-title: Immersogeometric cardiovascular fluid–structure interaction analysis with divergence-conforming B-splines publication-title: Computer Methods in Applied Mechanics and Engineering doi: 10.1016/j.cma.2016.07.028 – volume: 20 start-page: 1081 year: 1995 end-page: 1106 ident: 45 article-title: Reproducing kernel particle methods publication-title: International Journal for Numerical Methods in Fluids doi: 10.1002/fld.1650200824 – reference: S. Balay, S. Abhyankar, M. F. Adams, S. Benson, J. Brown, P. Brune, K. Buschelman, E. M. Constantinescu, L. Dalcin, A. Dener, V. Eijkhout, J. Faibussowitsch, W. D. Gropp, V. Hapla, T. Isaac, P. Jolivet, D. Karpeev, D. Kaushik, M. G. Knepley, F. Kong, S. Kruger, D. A. May, L. C. McInnes, R. T. Mills, L. Mitchell, T. Munson, J. E. Roman, K. Rupp, P. Sanan, J. Sarich, B. F. Smith, S. Zampini, H. Zhang, H. Zhang and J. Zhang, PETSc/TAO Users Manual, Technical Report ANL-21/39 - Revision 3.22, Argonne National Laboratory, 2024. – volume: 12 start-page: 401 year: 2012 end-page: 432 ident: 25 article-title: On the volume conservation of the immersed boundary method publication-title: Communications in Computational Physics doi: 10.4208/cicp.120111.300911s – volume: 4 start-page: 112 year: 1946 end-page: 141 ident: 55 article-title: Contributions to the problem of approximation of equidistant data by analytic functions. Part A.- On the problem of smoothing or graduation. A first class of analytic approximation formulae. Part B.- On the second problem of osculatory interpolation. A second class of analytic approximation formulae publication-title: Quaterly of Applied Mathematics doi: 10.1090/qam/16705 – reference: S. Balay, W. D. Gropp, L. C. McInnes and B. F. Smith, Efficient management of parallelism in object oriented numerical software libraries, in Modern Software Tools in Scientific Computing, Birkhäuser Press, (1997), 163-202. – volume: 23 start-page: 671 year: 2013 end-page: 741 ident: 21 article-title: Isogeometric divergence-conforming B-Splines for the Darcy–Stokes–Brinkman equations publication-title: Mathematical Models and Methods in Applied Sciences doi: 10.1142/S0218202512500583 – volume: 197 start-page: 2210 year: 2008 end-page: 2231 ident: 9 article-title: On the hyper-elastic formulation of the immersed boundary method publication-title: Computer Methods in Applied Mechanics and Engineering doi: 10.1016/j.cma.2007.09.015 – reference: C. de Boor, A Practical Guide to Splines, Springer-Verlag, New York, 1978. – volume: 225 start-page: 1827 year: 2007 end-page: 1848 ident: 51 article-title: Accurate monotonicity- and extrema-preserving methods through adaptive nonlinear hybridizations publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2007.02.023 – volume: 506 start-page: 112888 year: 2024 ident: 31 article-title: Benchmarking the immersed boundary method for viscoelastic flows publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2024.112888 – volume: 161 start-page: 428 year: 2000 end-page: 453 ident: 15 article-title: The blob projection method for immersed boundary problems publication-title: Journal of Computational Physics doi: 10.1006/jcph.2000.6502 – volume: 38 start-page: 864 year: 1992 end-page: 872 ident: 60 article-title: On the asymptotic convergence of B-spline wavelets to Gabor functions publication-title: IEEE Transactions on Information Theory doi: 10.1109/18.119742 – volume: 3 start-page: 15 year: 2006 end-page: 35 ident: 23 article-title: Hyperelastic modelling of arterial layers with distributed collagen fibre orientations publication-title: Journal of The Royal Society Interface doi: 10.1098/rsif.2005.0073 – volume: 425 start-page: 109872 year: 2021 ident: 11 article-title: The divergence-conforming immersed boundary method: Application to vesicle and capsule dynamics publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2020.109872 – volume: 231 start-page: 4613 year: 2012 end-page: 4642 ident: 19 article-title: An immersed boundary energy-based method for incompressible viscoelasticity publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2012.02.020 – reference: W. W. Chen, H. Gao, X. Y. Luo and N. A. Hill, Study of cardiovascular function using a coupled left ventricle and systemic circulation model, Journal of Biomechanics, 49 (2016), 2445-2454, Cardiovascular Biomechanics in Health and Disease. – volume: 105 start-page: 33 year: 1993 end-page: 46 ident: 49 article-title: Improved volume conservation in the computation of flows with immersed elastic boundaries publication-title: Journal of Computational Physics doi: 10.1006/jcph.1993.1051 – volume: 11 start-page: 479 year: 2002 end-page: 517 ident: 48 article-title: The immersed boundary method publication-title: Acta Numerica doi: 10.1017/S0962492902000077 – volume: 457 start-page: 111042 year: 2022 ident: 42 article-title: On the Lagrangian-Eulerian coupling in the immersed finite element/difference method publication-title: Journal of Computational Physics doi: 10.1016/j.jcp.2022.111042 – reference: S. Turek and J. Hron, Proposal for numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow, in Fluid-Structure Interaction, Springer Berlin Heidelberg, Berlin, Heidelberg, 53 (2006), 371-385. – volume: 57 start-page: 829 year: 1961 end-page: 838 ident: 22 article-title: Thermodynamic relations for high elastic materials publication-title: Transactions of the Faraday Society doi: 10.1039/tf9615700829 – reference: IBAMR Web page, Available from: http://ibamr.github.io/. – reference: B. E. Griffith, R. D. Hornung, D. M. McQueen and C. S. Peskin, Parallel and adaptive simulation of cardiac fluid dynamics, in Advanced Computational Infrastructures for Parallel and Distributed Adaptive Applications, (2009), 105-130. – volume: 48 start-page: 1475 year: 2020 end-page: 1490 ident: 43 article-title: Fluid–structure interaction models of bioprosthetic heart valve dynamics in an experimental pulse duplicator publication-title: Annals of Biomedical Engineering doi: 10.1007/s10439-020-02466-4 – reference: S. Balay, S. Abhyankar, M.F. Adams, S. Benson, J. Brown, P. Brune, K. Buschelman, E. M. Constantinescu, L. o Dalcin, A. Dener, V. Eijkhout, J. Faibussowitsch, W. D. Gropp, V. Hapla, T. Isaac, P. Jolivet, D. Karpeev, D. Kaushik, M. G. Knepley, F. Kong, S. Kruger, D. A. May, L. C. McInnes, R. T. Mills, L. Mitchell, T. Munson, J. E. Roman, K. Rupp, P. Sanan, J. Sarich, B. F. Smith, S. Zampini, H. Zhang, H. Zhang and J. Zhang, PETSc Web page, Available from: https://petsc.org/, 2024. – volume: 12 start-page: 1 year: 2017 end-page: 23 ident: 46 article-title: Optimal specific wavelength for maximum thrust production in undulatory propulsion publication-title: PLOS ONE doi: 10.1371/journal.pone.0179727 – volume: 28 start-page: 317 year: 2012 end-page: 345 ident: 26 article-title: Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions publication-title: International Journal for Numerical Methods in Biomedical Engineering doi: 10.1002/cnm.1445 – volume: 4 start-page: 491 year: 1984 end-page: 502 ident: 33 article-title: Spline representation of incompressible flow publication-title: IMA Journal of Numerical Analysis doi: 10.1093/imanum/4.4.491 – volume: 3 year: 2018 ident: 54 article-title: Flow structure and force generation on flapping wings at low reynolds numbers relevant to the flight of tiny insects publication-title: Fluids doi: 10.3390/fluids3030045 – volume: 117 start-page: 48 year: 2014 end-page: 56 ident: 59 article-title: The role of mechanical resonance in the neural control of swimming in fishes publication-title: Zoology doi: 10.1016/j.zool.2013.10.011 – volume: 23 start-page: 1421 year: 2013 end-page: 1478 ident: 20 article-title: Isogeometric divergence-conforming B-splines for the steady Navier-Stokes equations publication-title: Mathematical Models and Methods in Applied Sciences doi: 10.1142/S0218202513500139 – ident: key-10.3934/acse.2025011-52 doi: 10.1006/jcph.1999.6293 – ident: key-10.3934/acse.2025011-51 doi: 10.1016/j.jcp.2007.02.023 – ident: key-10.3934/acse.2025011-65 – ident: key-10.3934/acse.2025011-58 doi: 10.1007/3-540-34596-5_15 – ident: key-10.3934/acse.2025011-43 doi: 10.1007/s10439-020-02466-4 – ident: key-10.3934/acse.2025011-27 doi: 10.1016/j.jcp.2006.08.019 – ident: key-10.3934/acse.2025011-44 doi: 10.1137/S1064827502414060 – ident: key-10.3934/acse.2025011-8 doi: 10.1016/j.jcp.2013.08.043 – ident: key-10.3934/acse.2025011-29 doi: 10.1002/cnm.2888 – ident: key-10.3934/acse.2025011-49 doi: 10.1006/jcph.1993.1051 – ident: key-10.3934/acse.2025011-23 doi: 10.1098/rsif.2005.0073 – ident: key-10.3934/acse.2025011-20 doi: 10.1142/S0218202513500139 – ident: key-10.3934/acse.2025011-31 doi: 10.1016/j.jcp.2024.112888 – ident: key-10.3934/acse.2025011-55 doi: 10.1090/qam/16705 – ident: key-10.3934/acse.2025011-10 – ident: key-10.3934/acse.2025011-60 doi: 10.1109/18.119742 – ident: key-10.3934/acse.2025011-12 doi: 10.1016/j.jcp.2018.07.020 – ident: key-10.3934/acse.2025011-25 doi: 10.4208/cicp.120111.300911s – ident: key-10.3934/acse.2025011-21 doi: 10.1142/S0218202512500583 – ident: key-10.3934/acse.2025011-37 doi: 10.1002/cpe.652 – ident: key-10.3934/acse.2025011-13 doi: 10.1016/j.jbiomech.2016.03.009 – ident: key-10.3934/acse.2025011-64 doi: 10.1016/j.cma.2003.12.044 – ident: key-10.3934/acse.2025011-4 doi: 10.1007/978-1-4612-1986-6_8 – ident: key-10.3934/acse.2025011-39 doi: 10.1002/cnm.3240 – ident: key-10.3934/acse.2025011-47 doi: 10.1016/0021-9991(72)90065-4 – ident: key-10.3934/acse.2025011-3 – ident: key-10.3934/acse.2025011-59 doi: 10.1016/j.zool.2013.10.011 – ident: key-10.3934/acse.2025011-5 doi: 10.1371/journal.pbio.1002123 – ident: key-10.3934/acse.2025011-18 doi: 10.1007/978-1-4612-6333-3 – ident: key-10.3934/acse.2025011-45 doi: 10.1002/fld.1650200824 – ident: key-10.3934/acse.2025011-53 doi: 10.1016/j.jcp.2024.112831 – ident: key-10.3934/acse.2025011-26 doi: 10.1002/cnm.1445 – ident: key-10.3934/acse.2025011-9 doi: 10.1016/j.cma.2007.09.015 – ident: key-10.3934/acse.2025011-33 doi: 10.1093/imanum/4.4.491 – ident: key-10.3934/acse.2025011-38 doi: 10.1016/j.jtbi.2015.07.035 – ident: key-10.3934/acse.2025011-17 doi: 10.1093/pnasnexus/pgae392 – ident: key-10.3934/acse.2025011-48 doi: 10.1017/S0962492902000077 – ident: key-10.3934/acse.2025011-11 doi: 10.1016/j.jcp.2020.109872 – ident: key-10.3934/acse.2025011-63 doi: 10.1016/j.jcp.2022.111890 – ident: key-10.3934/acse.2025011-36 doi: 10.1017/jfm.2017.3 – ident: key-10.3934/acse.2025011-28 doi: 10.1002/9780470558027.ch7 – ident: key-10.3934/acse.2025011-16 doi: 10.1017/jfm.2011.54 – ident: key-10.3934/acse.2025011-35 – ident: key-10.3934/acse.2025011-40 doi: 10.1016/j.cma.2016.07.028 – ident: key-10.3934/acse.2025011-57 doi: 10.1016/j.jcp.2022.111500 – ident: key-10.3934/acse.2025011-34 doi: 10.1063/1.1761178 – ident: key-10.3934/acse.2025011-61 doi: 10.1016/j.cma.2020.112978 – ident: key-10.3934/acse.2025011-15 doi: 10.1006/jcph.2000.6502 – ident: key-10.3934/acse.2025011-22 doi: 10.1039/tf9615700829 – ident: key-10.3934/acse.2025011-19 doi: 10.1016/j.jcp.2012.02.020 – ident: key-10.3934/acse.2025011-24 doi: 10.1016/j.jcp.2009.07.001 – ident: key-10.3934/acse.2025011-41 doi: 10.1007/s00366-006-0049-3 – ident: key-10.3934/acse.2025011-46 doi: 10.1371/journal.pone.0179727 – ident: key-10.3934/acse.2025011-14 doi: 10.1016/0021-9991(84)90143-8 – ident: key-10.3934/acse.2025011-56 doi: 10.1137/1.9781611970555 – ident: key-10.3934/acse.2025011-1 doi: 10.1017/jfm.2013.434 – ident: key-10.3934/acse.2025011-62 doi: 10.1016/j.cma.2003.12.024 – ident: key-10.3934/acse.2025011-7 doi: 10.1016/j.jcp.2016.04.024 – ident: key-10.3934/acse.2025011-30 doi: 10.1142/S1758825109000113 – ident: key-10.3934/acse.2025011-42 doi: 10.1016/j.jcp.2022.111042 – ident: key-10.3934/acse.2025011-2 doi: 10.2172/2337606 – ident: key-10.3934/acse.2025011-6 doi: 10.1016/j.jcp.2017.06.041 – ident: key-10.3934/acse.2025011-54 doi: 10.3390/fluids3030045 – ident: key-10.3934/acse.2025011-32 – ident: key-10.3934/acse.2025011-50 doi: 10.1007/BFb0064470 |
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