메뉴 건너뛰기




Volumn 223, Issue 1, 2007, Pages 10-49

An adaptive, formally second order accurate version of the immersed boundary method

Author keywords

Adaptive mesh refinement; Blood flow; Cardiac mechanics; Convergence; Fluid structure interaction; Hemodynamics; Immersed boundary method; Projection method

Indexed keywords

BLOOD; BLOOD VESSELS; BOUNDARY LAYERS; COMPUTATIONAL FLUID DYNAMICS; HEART; HEMODYNAMICS; INCOMPRESSIBLE FLOW; NUMERICAL METHODS; TURBULENT FLOW; VISCOUS FLOW;

EID: 33947217364     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.08.019     Document Type: Article
Times cited : (326)

References (55)
  • 1
    • 85190571834 scopus 로고    scopus 로고
    • A.M. Roma, A multilevel self adaptive version of the immersed boundary method, Ph.D. Thesis, Courant Institute of Mathematical Sciences, New York University, 1996.
  • 2
    • 0000810173 scopus 로고    scopus 로고
    • An adaptive version of the immersed boundary method
    • Roma A.M., Peskin C.S., and Berger M.J. An adaptive version of the immersed boundary method. J. Comput. Phys. 153 2 (1999) 509-534
    • (1999) J. Comput. Phys. , vol.153 , Issue.2 , pp. 509-534
    • Roma, A.M.1    Peskin, C.S.2    Berger, M.J.3
  • 3
    • 19044361846 scopus 로고    scopus 로고
    • On the order of accuracy of the immersed boundary method: higher order convergence rates for sufficiently smooth problems
    • Griffith B.E., and Peskin C.S. On the order of accuracy of the immersed boundary method: higher order convergence rates for sufficiently smooth problems. J. Comput. Phys. 208 1 (2005) 75-105
    • (2005) J. Comput. Phys. , vol.208 , Issue.1 , pp. 75-105
    • Griffith, B.E.1    Peskin, C.S.2
  • 4
    • 45149143078 scopus 로고
    • A three-dimensional computational method for blood flow in the heart. I. Immersed elastic fibers in a viscous incompressible fluid
    • Peskin C.S., and McQueen D.M. A three-dimensional computational method for blood flow in the heart. I. Immersed elastic fibers in a viscous incompressible fluid. J. Comput. Phys. 81 2 (1989) 372-405
    • (1989) J. Comput. Phys. , vol.81 , Issue.2 , pp. 372-405
    • Peskin, C.S.1    McQueen, D.M.2
  • 5
    • 45149145362 scopus 로고
    • A three-dimensional computational method for blood flow in the heart. II. Contractile fibers
    • McQueen D.M., and Peskin C.S. A three-dimensional computational method for blood flow in the heart. II. Contractile fibers. J. Comput. Phys. 82 2 (1989) 289-297
    • (1989) J. Comput. Phys. , vol.82 , Issue.2 , pp. 289-297
    • McQueen, D.M.1    Peskin, C.S.2
  • 6
    • 0028144286 scopus 로고
    • Mechanical equilibrium determines the fractal fiber architecture of aortic heart valve leaflets
    • Peskin C.S., and McQueen D.M. Mechanical equilibrium determines the fractal fiber architecture of aortic heart valve leaflets. Am. J. Physiol. Heart Circ. Physiol. 266 1 (1994) H319-H328
    • (1994) Am. J. Physiol. Heart Circ. Physiol. , vol.266 , Issue.1
    • Peskin, C.S.1    McQueen, D.M.2
  • 7
    • 0002680335 scopus 로고    scopus 로고
    • Fluid dynamics of the heart and its valves
    • Othmer H.G., Adler F.R., Lewis M.A., and Dallon J.C. (Eds), Prentice-Hall, Englewood Cliffs, NJ, USA
    • Peskin C.S., and McQueen D.M. Fluid dynamics of the heart and its valves. In: Othmer H.G., Adler F.R., Lewis M.A., and Dallon J.C. (Eds). Case Studies in Mathematical Modeling: Ecology, Physiology, and Cell Biology (1996), Prentice-Hall, Englewood Cliffs, NJ, USA 309-337
    • (1996) Case Studies in Mathematical Modeling: Ecology, Physiology, and Cell Biology , pp. 309-337
    • Peskin, C.S.1    McQueen, D.M.2
  • 8
    • 0002329803 scopus 로고    scopus 로고
    • A three-dimensional computer model of the human heart for studying cardiac fluid dynamics
    • McQueen D.M., and Peskin C.S. A three-dimensional computer model of the human heart for studying cardiac fluid dynamics. Comput. Graphics 34 1 (2000) 56-60
    • (2000) Comput. Graphics , vol.34 , Issue.1 , pp. 56-60
    • McQueen, D.M.1    Peskin, C.S.2
  • 10
    • 85190567326 scopus 로고    scopus 로고
    • C.S. Peskin, Flow patterns around heart valves: a digital computer method for solving the equations of motion, Ph.D. Thesis, Albert Einstein College of Medicine, 1972.
  • 11
    • 0017424014 scopus 로고
    • Numerical analysis of blood flow in the heart
    • Peskin C.S. Numerical analysis of blood flow in the heart. J. Comput. Phys. 25 3 (1977) 220-252
    • (1977) J. Comput. Phys. , vol.25 , Issue.3 , pp. 220-252
    • Peskin, C.S.1
  • 12
    • 48749141209 scopus 로고
    • Adaptive mesh refinement for hyperbolic partial-differential equations
    • Berger M.J., and Oliger J. Adaptive mesh refinement for hyperbolic partial-differential equations. J. Comput. Phys. 53 3 (1984) 484-512
    • (1984) J. Comput. Phys. , vol.53 , Issue.3 , pp. 484-512
    • Berger, M.J.1    Oliger, J.2
  • 13
    • 11744289966 scopus 로고
    • Local adaptive mesh refinement for shock hydrodynamics
    • Berger M.J., and Colella P. Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82 1 (1989) 64-84
    • (1989) J. Comput. Phys. , vol.82 , Issue.1 , pp. 64-84
    • Berger, M.J.1    Colella, P.2
  • 14
    • 0035273564 scopus 로고    scopus 로고
    • Strong stability-preserving high-order time discretization methods
    • Gottlieb S., Shu C.-W., and Tadmor E. Strong stability-preserving high-order time discretization methods. SIAM Rev. 43 1 (2001) 89-112
    • (2001) SIAM Rev. , vol.43 , Issue.1 , pp. 89-112
    • Gottlieb, S.1    Shu, C.-W.2    Tadmor, E.3
  • 15
    • 21444442511 scopus 로고    scopus 로고
    • 0-stable methods for the heat equation with time-dependent boundary conditions
    • 0-stable methods for the heat equation with time-dependent boundary conditions. Adv. Comput. Math. 6 3-4 (1996) 333-352
    • (1996) Adv. Comput. Math. , vol.6 , Issue.3-4 , pp. 333-352
    • Twizell, E.H.1    Gumel, A.B.2    Arigu, M.A.3
  • 16
    • 0035505590 scopus 로고    scopus 로고
    • A Cartesian grid embedded boundary method for the heat equation on irregular domains
    • McCorquodale P., Colella P., and Johansen H. A Cartesian grid embedded boundary method for the heat equation on irregular domains. J. Comput. Phys. 173 2 (2001) 620-635
    • (2001) J. Comput. Phys. , vol.173 , Issue.2 , pp. 620-635
    • McCorquodale, P.1    Colella, P.2    Johansen, H.3
  • 17
    • 26844455510 scopus 로고
    • Multidimensional upwind methods for hyperbolic conservation laws
    • Colella P. Multidimensional upwind methods for hyperbolic conservation laws. J. Comput. Phys. 87 1 (1989) 171-200
    • (1989) J. Comput. Phys. , vol.87 , Issue.1 , pp. 171-200
    • Colella, P.1
  • 18
    • 0030078729 scopus 로고    scopus 로고
    • On the stability of Godunov-projection methods for incompressible flow
    • Minion M.L. On the stability of Godunov-projection methods for incompressible flow. J. Comput. Phys. 123 2 (1996) 435-449
    • (1996) J. Comput. Phys. , vol.123 , Issue.2 , pp. 435-449
    • Minion, M.L.1
  • 19
    • 0030210485 scopus 로고    scopus 로고
    • A projection method for locally refined grids
    • Minion M.L. A projection method for locally refined grids. J. Comput. Phys. 127 1 (1996) 158-178
    • (1996) J. Comput. Phys. , vol.127 , Issue.1 , pp. 158-178
    • Minion, M.L.1
  • 20
    • 0000037930 scopus 로고    scopus 로고
    • A cell-centered adaptive projection method for the incompressible Euler equations
    • Martin D.F., and Colella P. A cell-centered adaptive projection method for the incompressible Euler equations. J. Comput. Phys. 163 2 (2000) 271-312
    • (2000) J. Comput. Phys. , vol.163 , Issue.2 , pp. 271-312
    • Martin, D.F.1    Colella, P.2
  • 21
    • 84968510911 scopus 로고
    • Numerical solution of the Navier-Stokes equations
    • Chorin A.J. Numerical solution of the Navier-Stokes equations. Math. Comput. 22 104 (1968) 745-762
    • (1968) Math. Comput. , vol.22 , Issue.104 , pp. 745-762
    • Chorin, A.J.1
  • 22
    • 84968483581 scopus 로고
    • On the convergence of discrete approximations to the Navier-Stokes equations
    • Chorin A.J. On the convergence of discrete approximations to the Navier-Stokes equations. Math. Comput. 23 106 (1969) 341-353
    • (1969) Math. Comput. , vol.23 , Issue.106 , pp. 341-353
    • Chorin, A.J.1
  • 23
    • 0001608079 scopus 로고
    • A second-order projection method for the incompressible Navier-Stokes equations
    • Bell J.B., Colella P., and Glaz H.M. A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 85 2 (1989) 257-283
    • (1989) J. Comput. Phys. , vol.85 , Issue.2 , pp. 257-283
    • Bell, J.B.1    Colella, P.2    Glaz, H.M.3
  • 24
    • 0008688174 scopus 로고    scopus 로고
    • A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations
    • Almgren A.S., Bell J.B., Colella P., Howell L.H., and Welcome M.L. A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations. J. Comput. Phys. 142 1 (1998) 1-46
    • (1998) J. Comput. Phys. , 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
  • 25
    • 0034883943 scopus 로고    scopus 로고
    • Approximate projection methods: Part I. Inviscid analysis
    • Almgren A.S., Bell J.B., and Crutchfield W.Y. Approximate projection methods: Part I. Inviscid analysis. SIAM J. Sci. Comput. 22 4 (2000) 1139-1159
    • (2000) SIAM J. Sci. Comput. , vol.22 , Issue.4 , pp. 1139-1159
    • Almgren, A.S.1    Bell, J.B.2    Crutchfield, W.Y.3
  • 26
    • 84966249747 scopus 로고
    • Local refinement techniques for elliptic problems on cell-centered grids I. Error analysis
    • Ewing R.E., Lazarov R.D., and Vassilevski P.S. Local refinement techniques for elliptic problems on cell-centered grids I. Error analysis. Math. Comput. 56 194 (1991) 437-461
    • (1991) Math. Comput. , vol.56 , Issue.194 , pp. 437-461
    • Ewing, R.E.1    Lazarov, R.D.2    Vassilevski, P.S.3
  • 27
    • 85190567452 scopus 로고    scopus 로고
    • B.E. Griffith, Simulating the blood-muscle-valve mechanics of the heart by an adaptive and parallel version of the immersed boundary method, Ph.D. Thesis, Courant Institute of Mathematical Sciences, New York University, 2005 also available from .
  • 28
    • 85190569639 scopus 로고    scopus 로고
    • M.-C. Lai, Simulations of the flow past an array of circular cylinders as a test of the immersed boundary method, Ph.D. Thesis, Courant Institute of Mathematical Sciences, New York University, 1998.
  • 29
    • 0000868581 scopus 로고    scopus 로고
    • An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
    • Lai M.-C., and Peskin C.S. An immersed boundary method with formal second-order accuracy and reduced numerical viscosity. J. Comput. Phys. 160 2 (2000) 705-719
    • (2000) J. Comput. Phys. , vol.160 , Issue.2 , pp. 705-719
    • Lai, M.-C.1    Peskin, C.S.2
  • 30
    • 33751544551 scopus 로고    scopus 로고
    • The immersed boundary method
    • Peskin C.S. The immersed boundary method. Acta Numer. 11 (2002) 479-517
    • (2002) Acta Numer. , vol.11 , pp. 479-517
    • Peskin, C.S.1
  • 31
    • 0036646919 scopus 로고    scopus 로고
    • Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method
    • Zhu L., and Peskin C.S. Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method. J. Comput. Phys. 179 2 (2002) 452-468
    • (2002) J. Comput. Phys. , vol.179 , Issue.2 , pp. 452-468
    • Zhu, L.1    Peskin, C.S.2
  • 32
    • 0041324691 scopus 로고    scopus 로고
    • Interaction of two flapping filaments in a flowing soap film
    • Zhu L., and Peskin C.S. Interaction of two flapping filaments in a flowing soap film. Phys. Fluids 15 7 (2003) 1954-1960
    • (2003) Phys. Fluids , vol.15 , Issue.7 , pp. 1954-1960
    • Zhu, L.1    Peskin, C.S.2
  • 33
    • 0026226856 scopus 로고
    • An algorithm for point clustering and grid generation
    • Berger M.J., and Rigoutsos I. An algorithm for point clustering and grid generation. IEEE Trans. Syst. Man Cybernet. 21 5 (1991) 1278-1286
    • (1991) IEEE Trans. Syst. Man Cybernet. , vol.21 , Issue.5 , pp. 1278-1286
    • Berger, M.J.1    Rigoutsos, I.2
  • 34
    • 33749190078 scopus 로고
    • Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface
    • Harlow F.H., and Welch J.E. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8 12 (1965) 2182-2189
    • (1965) Phys. Fluids , vol.8 , Issue.12 , pp. 2182-2189
    • Harlow, F.H.1    Welch, J.E.2
  • 35
    • 0000310338 scopus 로고    scopus 로고
    • A numerical method for the incompressible Navier-Stokes equations based on an approximate projection
    • Almgren A.S., Bell J.B., and Szymczak W.G. A numerical method for the incompressible Navier-Stokes equations based on an approximate projection. SIAM J. Sci. Comput. 17 2 (1996) 358-369
    • (1996) SIAM J. Sci. Comput. , vol.17 , Issue.2 , pp. 358-369
    • Almgren, A.S.1    Bell, J.B.2    Szymczak, W.G.3
  • 36
    • 85190570663 scopus 로고    scopus 로고
    • M.F. Lai, A projection method for reacting flow in the zero mach number limit, Ph.D. Thesis, University of California at Berkeley, 1993.
  • 37
    • 7244250225 scopus 로고    scopus 로고
    • Numerical approximations of singular source terms in differential equations
    • Tornberg A.-K., and Engquist B. Numerical approximations of singular source terms in differential equations. J. Comput. Phys. 200 2 (2004) 462-488
    • (2004) J. Comput. Phys. , vol.200 , Issue.2 , pp. 462-488
    • Tornberg, A.-K.1    Engquist, B.2
  • 38
    • 0031173537 scopus 로고    scopus 로고
    • An adaptive mesh projection method for viscous incompressible flow
    • Howell L.H., and Bell J.B. An adaptive mesh projection method for viscous incompressible flow. SIAM J. Sci. Comput. 18 4 (1997) 996-1013
    • (1997) SIAM J. Sci. Comput. , vol.18 , Issue.4 , pp. 996-1013
    • Howell, L.H.1    Bell, J.B.2
  • 39
    • 0002531306 scopus 로고
    • An unsplit 3D upwind method for hyperbolic conservation laws
    • Saltzman J. An unsplit 3D upwind method for hyperbolic conservation laws. J. Comput. Phys. 115 1 (1994) 153-168
    • (1994) J. Comput. Phys. , vol.115 , Issue.1 , pp. 153-168
    • Saltzman, J.1
  • 40
    • 0000135764 scopus 로고    scopus 로고
    • Accurate projection methods for the incompressible Navier-Stokes equations
    • Brown D.L., Cortez R., and Minion M.L. Accurate projection methods for the incompressible Navier-Stokes equations. J. Comput. Phys. 168 2 (2001) 464-499
    • (2001) J. Comput. Phys. , vol.168 , Issue.2 , pp. 464-499
    • Brown, D.L.1    Cortez, R.2    Minion, M.L.3
  • 42
    • 0000714458 scopus 로고
    • Stability and instability in the computation of flows with moving immersed boundaries: a comparison of three methods
    • Tu C., and Peskin C.S. Stability and instability in the computation of flows with moving immersed boundaries: a comparison of three methods. SIAM J. Sci. Stat. Comput. 13 6 (1992) 1361-1376
    • (1992) SIAM J. Sci. Stat. Comput. , vol.13 , Issue.6 , pp. 1361-1376
    • Tu, C.1    Peskin, C.S.2
  • 43
    • 0001417748 scopus 로고
    • An implicit numerical method for fluid dynamics problems with immersed elastic boundaries
    • Fluid Dynamics in Biology: Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference. Cheer A.Y., and van Dam C.P. (Eds), American Mathematical Society, Providence, RI, USA
    • Mayo A.A., and Peskin C.S. An implicit numerical method for fluid dynamics problems with immersed elastic boundaries. In: Cheer A.Y., and van Dam C.P. (Eds). Fluid Dynamics in Biology: Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference. Contemporary Mathematics vol. 140 (1993), American Mathematical Society, Providence, RI, USA 261-277
    • (1993) Contemporary Mathematics , vol.140 , pp. 261-277
    • Mayo, A.A.1    Peskin, C.S.2
  • 44
    • 0031129202 scopus 로고    scopus 로고
    • Immersed interface methods for Stokes flow with elastic boundaries or surface tension
    • LeVeque R.J., and Li Z. Immersed interface methods for Stokes flow with elastic boundaries or surface tension. SIAM J. Sci. Comput. 18 3 (1997) 709-735
    • (1997) SIAM J. Sci. Comput. , vol.18 , Issue.3 , pp. 709-735
    • LeVeque, R.J.1    Li, Z.2
  • 45
    • 2942543066 scopus 로고    scopus 로고
    • An immersed interface method for incompressible Navier-Stokes equations
    • Lee L., and LeVeque R.J. An immersed interface method for incompressible Navier-Stokes equations. SIAM J. Sci. Comput. 25 3 (2003) 832-856
    • (2003) SIAM J. Sci. Comput. , vol.25 , Issue.3 , pp. 832-856
    • Lee, L.1    LeVeque, R.J.2
  • 47
    • 85190570830 scopus 로고    scopus 로고
    • SAMRAI: structured adaptive mesh refinement application infrastructure. Available from: .
  • 48
    • 85190567927 scopus 로고    scopus 로고
    • A.M. Wissink, R.D. Hornung, S.R. Kohn, S.G.S.N. Elliott, Large scale parallel structured AMR calculations using the SAMRAI framework, in: Proceedings of the SC01 Conference on High Performance Networking and Computing, Denver, CO, USA, 2001, also available as LLNL Technical Report UCRL-JC-144755.
  • 49
    • 0037171879 scopus 로고    scopus 로고
    • Managing application complexity in the SAMRAI object-oriented framework
    • Hornung R.D., and Kohn S.R. Managing application complexity in the SAMRAI object-oriented framework. Concurr. Comp.: Pract. E. 14 5 (2002) 347-368
    • (2002) Concurr. Comp.: Pract. E. , vol.14 , Issue.5 , pp. 347-368
    • Hornung, R.D.1    Kohn, S.R.2
  • 50
    • 1142305194 scopus 로고    scopus 로고
    • Enhancing scalability of parallel structured AMR calculations
    • ACM Press, New York, NY, USA also available as LLNL Technical Report UCRL-JC-151791
    • Wissink A.M., Hysom D., and Hornung R.D. Enhancing scalability of parallel structured AMR calculations. Proceedings of the 17th ACM International Conference on Supercomputing (ICS03) (2003), ACM Press, New York, NY, USA 336-347 also available as LLNL Technical Report UCRL-JC-151791
    • (2003) Proceedings of the 17th ACM International Conference on Supercomputing (ICS03) , pp. 336-347
    • Wissink, A.M.1    Hysom, D.2    Hornung, R.D.3
  • 51
    • 85190572717 scopus 로고    scopus 로고
    • S. Balay, K. Buschelman, W.D. Gropp, D. Kaushik, M.G. Knepley, L.C. McInnes, B.F. Smith, H. Zhang, PETSc Web page, http://www.mcs.anl.gov/petsc.
  • 52
    • 85190570170 scopus 로고    scopus 로고
    • S. Balay, K. Buschelman, V. Eijkhout, W.D. Gropp, D. Kaushik, M.G. Knepley, L.C. McInnes, B.F. Smith, H. Zhang, PETSc users manual, Technical Report ANL-95/11 - Revision 2.1.5, Argonne National Laboratory, 2004.
  • 53
    • 0002515487 scopus 로고    scopus 로고
    • Efficient management of parallelism in object oriented numerical software libraries
    • Arge E., Bruaset A.M., and Langtangen H.P. (Eds), Birkhäuser, Basel
    • Balay S., Eijkhout V., Gropp W.D., McInnes L.C., and Smith B.F. Efficient management of parallelism in object oriented numerical software libraries. In: Arge E., Bruaset A.M., and Langtangen H.P. (Eds). Modern Software Tools in Scientific Computing (1997), Birkhäuser, Basel 163-202
    • (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
  • 54
    • 85190569266 scopus 로고    scopus 로고
    • hypre: High performance preconditioners. Available from: .
  • 55
    • 84886852494 scopus 로고    scopus 로고
    • hypre: a library of high performance preconditioners
    • Computational Science - ICCS 2002 Part III. Sloot P.M.A., Tan C.J.K., Dongarra J.J., and Hoekstra A.G. (Eds), Springer, Berlin also available as LLNL Technical Report UCRL-JC-146175
    • Falgout R.D., and Yang U.M. hypre: a library of high performance preconditioners. In: Sloot P.M.A., Tan C.J.K., Dongarra J.J., and Hoekstra A.G. (Eds). Computational Science - ICCS 2002 Part III. Lecture Notes in Computer Science vol. 2331 (2002), Springer, Berlin 632-641 also available as LLNL Technical Report UCRL-JC-146175
    • (2002) Lecture Notes in Computer Science , vol.2331 , pp. 632-641
    • Falgout, R.D.1    Yang, U.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.