메뉴 건너뛰기




Volumn 12, Issue 2, 2012, Pages 401-432

On the volume conservation of the immersed boundary method

Author keywords

Approximate projection method; Collocated discretization; Exact projection method; Fluid structure interaction; Immersed boundary method; Staggered grid discretization; Volume conservation

Indexed keywords


EID: 84857571345     PISSN: 18152406     EISSN: 19917120     Source Type: Journal    
DOI: 10.4208/cicp.120111.300911s     Document Type: Article
Times cited : (79)

References (41)
  • 1
    • 33751544551 scopus 로고    scopus 로고
    • The immersed boundary method
    • C. S. Peskin. The immersed boundary method. Acta Numer., 11:479-517, 2002.
    • (2002) Acta Numer. , vol.11 , pp. 479-517
    • Peskin, C.S.1
  • 2
    • 0002795289 scopus 로고
    • Improved volume conservation in the computation of flows with immersed elastic boundaries
    • C. S. Peskin and B. F. Printz. Improved volume conservation in the computation of flows with immersed elastic boundaries. J. Comput. Phys., 105(1):33-46, 1993.
    • (1993) J. Comput. Phys. , vol.105 , Issue.1 , pp. 33-46
    • Peskin, C.S.1    Printz, B.F.2
  • 3
    • 0001123374 scopus 로고    scopus 로고
    • The blob projection method for immersed boundary problems
    • R. Cortez and M. L. Minion. The blob projection method for immersed boundary problems. J. Comput. Phys., 161(2):428-453, 2000.
    • (2000) J. Comput. Phys. , vol.161 , Issue.2 , pp. 428-453
    • Cortez, R.1    Minion, M.L.2
  • 4
    • 77951623237 scopus 로고    scopus 로고
    • Simulating the dynamics of inextensible vesicles by the penalty immersed boundary method
    • Y. Kim and M.-C. Lai. Simulating the dynamics of inextensible vesicles by the penalty immersed boundary method. J. Comput. Phys., 229(12):4840-4853, 2010.
    • (2010) J. Comput. Phys. , vol.229 , Issue.12 , pp. 4840-4853
    • Kim, Y.1    Lai, M.-C.2
  • 5
    • 77952426384 scopus 로고    scopus 로고
    • Numerical simulations of two-dimensional foam by the immersed boundary method
    • Y. Kim, M.-C. Lai, and C. S. Peskin. Numerical simulations of two-dimensional foam by the immersed boundary method. J. Comput. Phys., 229(13):5194-5207, 2010.
    • (2010) J. Comput. Phys. , vol.229 , Issue.13 , pp. 5194-5207
    • Kim, Y.1    Lai, M.-C.2    Peskin, C.S.3
  • 6
    • 77952429010 scopus 로고    scopus 로고
    • Flow-induced vibrations of a deformable ring
    • K. Shoele and Q. Zhu. Flow-induced vibrations of a deformable ring. J. Fluid Mech., 650:343-362, 2010.
    • (2010) J. Fluid Mech. , vol.650 , pp. 343-362
    • Shoele, K.1    Zhu, Q.2
  • 8
    • 67349246069 scopus 로고    scopus 로고
    • Modelling and simulation of porous immersed boundaries
    • J. A. Stockie. Modelling and simulation of porous immersed boundaries. Comput. Struct., 87(11-12):701-709, 2009.
    • (2009) Comput. Struct. , vol.87 , Issue.11-12 , pp. 701-709
    • Stockie, J.A.1
  • 9
    • 33749190078 scopus 로고
    • Numerical calculation of time-dependent viscous incompresible flow of fluid with free surface
    • F. H. Harlow and J. E. Welch. Numerical calculation of time-dependent viscous incompresible flow of fluid with free surface. Phys. Fluid, 8(12):2182-2189, 1965.
    • (1965) Phys. Fluid , vol.8 , Issue.12 , pp. 2182-2189
    • Harlow, F.H.1    Welch, J.E.2
  • 10
    • 34547537336 scopus 로고    scopus 로고
    • Accurate monotonicity-and extremapreserving methods through adaptive nonlinear hybridizations
    • W. J. Rider, J. A. Greenough, and J. R. Kamm. Accurate monotonicity-and extremapreserving methods through adaptive nonlinear hybridizations. J. Comput. Phys., 225(2):1827-1848, 2007.
    • (2007) J. Comput. Phys. , vol.225 , Issue.2 , pp. 1827-1848
    • Rider, W.J.1    Greenough, J.A.2    Kamm, J.R.3
  • 11
    • 34547419627 scopus 로고
    • The piecewise parabolic method (PPM) for gas-dynamical simulations
    • P. Colella and P. R. Woodward. The piecewise parabolic method (PPM) for gas-dynamical simulations. J. Comput. Phys., 54(1):174-201, 1984.
    • (1984) J. Comput. Phys. , vol.54 , Issue.1 , pp. 174-201
    • Colella, P.1    Woodward, P.R.2
  • 12
    • 84968510911 scopus 로고
    • Numerical solution of the Navier-Stokes equations
    • A. J. Chorin. Numerical solution of the Navier-Stokes equations. Math. Comput., 22(104):745-762, 1968.
    • (1968) Math. Comput. , vol.22 , Issue.104 , pp. 745-762
    • Chorin, A.J.1
  • 13
    • 84968483581 scopus 로고
    • On the convergence of discrete approximations to the Navier-Stokes equations
    • A. J. Chorin. On the convergence of discrete approximations to the Navier-Stokes equations. Math. Comput., 23(106):341-353, 1969.
    • (1969) Math. Comput. , vol.23 , Issue.106 , pp. 341-353
    • Chorin, A.J.1
  • 14
    • 46549092989 scopus 로고
    • Application of a fractional-step method to incompressible Navier-Stokes equations
    • J. Kim and P. Moin. Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys., 59(2):308-323, 1985.
    • (1985) J. Comput. Phys. , vol.59 , Issue.2 , pp. 308-323
    • Kim, J.1    Moin, P.2
  • 15
    • 0001608079 scopus 로고
    • A second-order projection method for the incompressible Navier-Stokes equations
    • J. B. Bell, P. Colella, and H. M. Glaz. A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys., 85(2):257-283, 1989.
    • (1989) J. Comput. Phys. , vol.85 , Issue.2 , pp. 257-283
    • Bell, J.B.1    Colella, P.2    Glaz, H.M.3
  • 16
    • 0000310338 scopus 로고    scopus 로고
    • A numerical method for the incompressible Navier-Stokes equations based on an approximate projection
    • A. S. Almgren, J. B. Bell, and W. G. Szymczak. A numerical method for the incompressible Navier-Stokes equations based on an approximate projection. SIAM J. Sci. Comput., 17(2):358-369, 1996. (Pubitemid 126610882)
    • (1996) SIAM Journal of Scientific Computing , vol.17 , Issue.2 , pp. 358-369
    • Almgren, A.S.1    Bell, J.B.2    Szymczak, W.G.3
  • 17
    • 0008688174 scopus 로고    scopus 로고
    • A conservative adaptive projection method for the variable density incompressible navier-stokes equations
    • DOI 10.1006/jcph.1998.5890, PII S0021999198958909
    • A. S. Almgren, J. B. Bell, P. Colella, L. H. Howell, and M. L. Welcome. A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations. J. Comput. Phys., 142(1):1-46, 1998. (Pubitemid 128344797)
    • (1998) Journal of Computational Physics , vol.142 , Issue.1 , pp. 1-46
    • Almgren, A.S.1    Bell, J.B.2    Colella, P.3    Howell, L.H.4    Welcome, M.L.5
  • 18
    • 0034883943 scopus 로고    scopus 로고
    • Approximate projection methods: Part I. Inviscid analysis
    • DOI 10.1137/S1064827599357024, PII S1064827599357024
    • A. S. Almgren, J. B. Bell, and W. Y. Crutchfield. Approximate projection methods: Part I. Inviscid analysis. SIAM J. Sci. Comput., 22(4):1139-1159, 2000. (Pubitemid 32748646)
    • (2001) SIAM Journal of Scientific Computing , vol.22 , Issue.4 , pp. 1139-1159
    • Almgren, A.S.1    Bell, J.B.2    Crutchfield, W.Y.3
  • 19
    • 0000037930 scopus 로고    scopus 로고
    • A cell-centered adaptive projection method for the incompressible Euler equations
    • D. F. Martin and P. Colella. A cell-centered adaptive projection method for the incompressible Euler equations. J. Comput. Phys., 163(2):271-312, 2000.
    • (2000) J. Comput. Phys. , vol.163 , Issue.2 , pp. 271-312
    • Martin, D.F.1    Colella, P.2
  • 20
    • 0000135764 scopus 로고    scopus 로고
    • Accurate projection methods for the incompressible navier-stokes equations
    • DOI 10.1006/jcph.2001.6715, PII S0021999101967154
    • D. L. Brown, R. Cortez, and M. L. Minion. Accurate projection methods for the incompressible Navier-Stokes equations. J. Comput. Phys., 168(2):464-499, 2001. (Pubitemid 33663736)
    • (2001) Journal of Computational Physics , vol.168 , Issue.2 , pp. 464-499
    • Brown, D.L.1    Cortez, R.2    Minion, M.L.3
  • 21
    • 37249089366 scopus 로고    scopus 로고
    • A cell-centered adaptive projection method for the incompressible Navier-Stokes equations in three dimensions
    • D. F. Martin, P. Colella, and D. Graves. A cell-centered adaptive projection method for the incompressible Navier-Stokes equations in three dimensions. J. Comput. Phys., 227(3):1863-1886, 2008.
    • (2008) J. Comput. Phys. , vol.227 , Issue.3 , pp. 1863-1886
    • Martin, D.F.1    Colella, P.2    Graves, D.3
  • 22
    • 19044361846 scopus 로고    scopus 로고
    • On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems
    • DOI 10.1016/j.jcp.2005.02.011, PII S0021999105000835
    • B. E. Griffith and C. S. Peskin. On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems. J. Comput. Phys., 208(1):75-105, 2005. (Pubitemid 40714214)
    • (2005) Journal of Computational Physics , vol.208 , Issue.1 , pp. 75-105
    • Griffith, B.E.1    Peskin, C.S.2
  • 23
    • 33947217364 scopus 로고    scopus 로고
    • An adaptive, formally second order accurate version of the immersed boundary method
    • B. E. Griffith, R. D. Hornung, D. M. McQueen, and C. S. Peskin. An adaptive, formally second order accurate version of the immersed boundary method. J. Comput. Phys., 223(1):10-49, 2007.
    • (2007) J. Comput. Phys. , vol.223 , Issue.1 , pp. 10-49
    • Griffith, B.E.1    Hornung, R.D.2    McQueen, D.M.3    Peskin, C.S.4
  • 24
    • 33847017264 scopus 로고    scopus 로고
    • Unconditionally stable discretizations of the immersed boundary equations
    • E. P. Newren, A. L. Fogelson, R. D. Guy, and R. M. Kirby. Unconditionally stable discretizations of the immersed boundary equations. J. Comput. Phys., 222(2):702-719, 2007.
    • (2007) J. Comput. Phys. , vol.222 , Issue.2 , pp. 702-719
    • Newren, E.P.1    Fogelson, A.L.2    Guy, R.D.3    Kirby, R.M.4
  • 25
    • 69049112963 scopus 로고    scopus 로고
    • Simulating the fluid dynamics of natural and prosthetic heart valves using the immersed boundary method
    • B. E. Griffith, X. Luo, D. M. McQueen, and C. S. Peskin. Simulating the fluid dynamics of natural and prosthetic heart valves using the immersed boundary method. Int. J. Appl. Mech., 1(1):137-177, 2009.
    • (2009) Int. J. Appl. Mech. , vol.1 , Issue.1 , pp. 137-177
    • Griffith, B.E.1    Luo, X.2    McQueen, D.M.3    Peskin, C.S.4
  • 27
    • 69049084381 scopus 로고    scopus 로고
    • An accurate and efficient method for the incompressible Navier-Stokes equations using the projection method as a preconditioner
    • B. E. Griffith. An accurate and efficient method for the incompressible Navier-Stokes equations using the projection method as a preconditioner. J. Comput. Phys., 228(20):7565-7595, 2009.
    • (2009) J. Comput. Phys. , vol.228 , Issue.20 , pp. 7565-7595
    • Griffith, B.E.1
  • 28
    • 0000810173 scopus 로고    scopus 로고
    • An adaptive version of the immersed boundary method
    • A. M. Roma, C. S. Peskin, and M. J. Berger. An adaptive version of the immersed boundary method. J. Comput. Phys., 153(2):509-534, 1999.
    • (1999) J. Comput. Phys. , vol.153 , Issue.2 , pp. 509-534
    • Roma, A.M.1    Peskin, C.S.2    Berger, M.J.3
  • 29
    • 84858400633 scopus 로고    scopus 로고
    • Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions
    • To appear
    • B. E. Griffith. Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions. Int. J. Numer. Meth. Biomed. Eng., To appear.
    • Int. J. Numer. Meth. Biomed. Eng.
    • Griffith, B.E.1
  • 32
    • 0037171879 scopus 로고    scopus 로고
    • Managing application complexity in the SAMRAI object-oriented framework
    • DOI 10.1002/cpe.652
    • R. D. Hornung and S. R. Kohn. Managing application complexity in the SAMRAI objectoriented framework. Concurrency Comput. Pract. Ex., 14(5):347-368, 2002. (Pubitemid 34491380)
    • (2002) Concurrency Computation Practice and Experience , vol.14 , Issue.5 , pp. 347-368
    • Hornung, R.D.1    Kohn, S.R.2
  • 33
    • 34249930796 scopus 로고    scopus 로고
    • Managing complex data and geometry in parallel structured AMR applications
    • R. D. Hornung, A. M. Wissink, and S. R. Kohn. Managing complex data and geometry in parallel structured AMR applications. Eng. Comput., 22(3-4):181-195, 2006.
    • (2006) Eng. Comput. , vol.22 , Issue.3-4 , pp. 181-195
    • Hornung, R.D.1    Wissink, A.M.2    Kohn, S.R.3
  • 36
    • 0002515487 scopus 로고    scopus 로고
    • Efficient management of parallelism in object oriented numerical software libraries
    • E. Arge, A. M. Bruaset, and H. P. Langtangen, editors, Birkhäuser Press
    • S. Balay, V. Eijkhout, W. D. Gropp, L. C. McInnes, and B. F. Smith. Efficient management of parallelism in object oriented numerical software libraries. In E. Arge, A. M. Bruaset, and H. P. Langtangen, editors, Modern Software Tools in Scientific Computing, pages 163-202. Birkhäuser Press, 1997.
    • (1997) Modern Software Tools in Scientific Computing , pp. 163-202
    • Balay, S.1    Eijkhout, V.2    Gropp, W.D.3    McInnes, L.C.4    Smith, B.F.5
  • 38
    • 84886852494 scopus 로고    scopus 로고
    • Hypre: A library of high performance preconditioners
    • P. M. A. Sloot, C. J. K. Tan, J. J. Dongarra, and A. G. Hoekstra, editors, Springer-Verlag, Also available as LLNL Technical Report UCRL-JC-146175
    • R. D. Falgout and U. M. Yang. hypre: a library of high performance preconditioners. In P. M. A. Sloot, C. J. K. Tan, J. J. Dongarra, and A. G. Hoekstra, editors, Computational Science - ICCS 2002 Part III, volume 2331 of Lecture Notes in Computer Science, pages 632-641. Springer-Verlag, 2002. Also available as LLNL Technical Report UCRL-JC-146175.
    • (2002) Computational Science - ICCS 2002 Part III, Volume 2331 of Lecture Notes in Computer Science , pp. 632-641
    • Falgout, R.D.1    Yang, U.M.2
  • 41
    • 0037055773 scopus 로고    scopus 로고
    • Divergence-and curl-preserving prolongation and restriction formulas
    • G. Tóth and P. L. Roe. Divergence-and curl-preserving prolongation and restriction formulas. J. Comput. Phys., 180(2):736-750, 2002.
    • (2002) J. Comput. Phys. , vol.180 , Issue.2 , pp. 736-750
    • Tóth, G.1    Roe, P.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.