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Some new finite difference methods for Helmholtz equations on irregular domains or with interfaces
An augmented immersed interface method for moving structures with mass
1. | Department of Mathematics, Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695, United States, United States, United States |
References:
[1] |
R. Glowinski, T.-W. Pan, T. I. Hesla, D. D. Joseph and J. Périaux, A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: Application to particulate flow, J. Comput. Phys., 169 (2001), 363-426.
doi: 10.1006/jcph.2000.6542. |
[2] |
J. Hao, T.-W. Pan, R. Glowinski and D. D. Joseph, A fictitious domain/distributed Lagrange multiplier method for the particulate flow of Oldroyd-B fluids: A positive definiteness preserving approach, J. Non-Newtonian Fluid Mech., 156 (2009), 95-111.
doi: 10.1016/j.jnnfm.2008.07.006. |
[3] |
J. Hao, T.-W. Pan, S. Čanić, R. Glowinski and D. Rosenstrauch, A fluid-cell interaction and adhesion algorithm for tissue-coating of cardiovascular implants, Multiscale Model. Simul., 7 (2009), 1669-1694.
doi: 10.1137/080733188. |
[4] |
J. Hao and L. Zhu, A lattice Boltzmann based implicit immersed boundary method for fluid-structure interaction, Comp. Math. Appl., 59 (2010), 185-193.
doi: 10.1016/j.camwa.2009.06.055. |
[5] |
J. Hao and L. Zhu, A lattice Boltzmann based implicit immersed boundary method in three dimensions,, submitted., ().
|
[6] |
T. Y. Hou and Z. Shi, An efficient semi-implicit immersed boundary method for the Navier-Stokes equations, J. Comput. Phys., 227 (2008), 8968-8991.
doi: 10.1016/j.jcp.2008.07.005. |
[7] |
K. Ito, M.-C. Lai and Z. Li, A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains, J. Comput. Phys., 228 (2009), 2616-2628.
doi: 10.1016/j.jcp.2008.12.028. |
[8] |
S. W. Jung, K. Mareck, M. Shelley and J. Zhang, Dynamics of a deformable body in a fast flowing soap film, Phys. Rev. Lett., 97 (2006), 134502.
doi: 10.1103/PhysRevLett.97.134502. |
[9] |
Y. Kim and C. S. Peskin, Penalty immersed boundary method for an elastic boundary with mass, Phys. Fluids, 19 (2007), 053103.
doi: 10.1063/1.2734674. |
[10] |
Y. Kim, L. Zhu, X. Wang and C. S. Peskin, On various techniques for computer simulation of boundaries with mass, in "Computational Fluid and Solid Mechanics" (eds. K. J. Bathe), Elsevier, (2003), 1746-1750. |
[11] |
R. J. LeVeque and Z. Li, Immersed interface methods for Stokes flow with elastic boundaries or surface tension, SIAM J. Sci. Comput., 18 (1997), 709-735.
doi: 10.1137/S1064827595282532. |
[12] |
Z. Li, "The Immersed Interface Method-A Numerical Approach for Partial Differential Equations with Interfaces," Ph.D thesis, University of Washington, 1994. |
[13] |
Z. Li and K. Ito, "The Immersed Interface Method. Numerical Solutions of PDEs Involving Interfaces and Irregular Domains," Frontiers in Applied Mathematics, 33, SIAM, Philadelphia, PA, 2006. |
[14] |
Z. Li and M.-C. Lai, The immersed interface method for the Navier-Stokes equations with singular forces, J. Comput. Phys., 171 (2001), 822-842.
doi: 10.1006/jcph.2001.6813. |
[15] |
Z. Li and M.-C. Lai, New finite difference methods based on IIM for inextensible interfaces in incompressible flows, East Asian J. Applied Math., 1 (2011), 155-171. |
[16] |
Y. Mori and C. S. Peskin, Implicit second-order immersed boundary methods with boundary mass, Comput. Methods Appl. Mech. Engrg., 197 (2008), 2049-2067.
doi: 10.1016/j.cma.2007.05.028. |
[17] |
T.-W. Pan and R. Glowinski, Direct simulation of the motion of neutrally buoyant circular cylinders in plane Poiseuille flow, J. Comput. Phys., 181 (2002), 260-279.
doi: 10.1006/jcph.2002.7123. |
[18] |
C. S. Peskin, "Flow Patterns Around Heart Valves: A Digital Computer Method for Solving the Equations of Motion," Ph.D thesis, Albert Einstein Coll. Med., 1972. |
[19] |
C. S. Peskin, Numerical analysis of blood flow in the heart, J. Comput. Phys., 25 (1977), 220-252.
doi: 10.1016/0021-9991(77)90100-0. |
[20] |
C. S. Peskin, The immersed boundary method, Acta Numerica, 11 (2002), 479-517.
doi: 10.1017/S0962492902000077. |
[21] |
K. Shoele and Q. Zhu, Flow-induced vibrations of a deformable ring, J. Fluid Mech., 650 (2010), 343-362.
doi: 10.1017/S0022112009993697. |
[22] |
X. S. Wang, An iterative matrix-free method in implicit immersed boundary/continuum methods, Computers and Structures, 85 (2007), 739-748.
doi: 10.1016/j.compstruc.2007.01.017. |
[23] |
J. Zhang, S. Childress, A. Libchaber and M. Shelley, Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind, Nature, 408 (2000), 835.
doi: 10.1038/35048530. |
[24] |
L. Zhu, Scaling laws for drag of a compliant body in an incompressible viscous flow, J. Fluid Mech., 607 (2008), 387-400. |
[25] |
L. Zhu and C. S. Peskin, Interaction of two flexible filaments in a flowing soap film, Phys. Fluids, 15 (2003), 1954-1960.
doi: 10.1063/1.1582476. |
[26] |
L. Zhu and C. S. Peskin, Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method, J. Comput. Phys., 179 (2002), 452-468.
doi: 10.1006/jcph.2002.7066. |
show all references
References:
[1] |
R. Glowinski, T.-W. Pan, T. I. Hesla, D. D. Joseph and J. Périaux, A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: Application to particulate flow, J. Comput. Phys., 169 (2001), 363-426.
doi: 10.1006/jcph.2000.6542. |
[2] |
J. Hao, T.-W. Pan, R. Glowinski and D. D. Joseph, A fictitious domain/distributed Lagrange multiplier method for the particulate flow of Oldroyd-B fluids: A positive definiteness preserving approach, J. Non-Newtonian Fluid Mech., 156 (2009), 95-111.
doi: 10.1016/j.jnnfm.2008.07.006. |
[3] |
J. Hao, T.-W. Pan, S. Čanić, R. Glowinski and D. Rosenstrauch, A fluid-cell interaction and adhesion algorithm for tissue-coating of cardiovascular implants, Multiscale Model. Simul., 7 (2009), 1669-1694.
doi: 10.1137/080733188. |
[4] |
J. Hao and L. Zhu, A lattice Boltzmann based implicit immersed boundary method for fluid-structure interaction, Comp. Math. Appl., 59 (2010), 185-193.
doi: 10.1016/j.camwa.2009.06.055. |
[5] |
J. Hao and L. Zhu, A lattice Boltzmann based implicit immersed boundary method in three dimensions,, submitted., ().
|
[6] |
T. Y. Hou and Z. Shi, An efficient semi-implicit immersed boundary method for the Navier-Stokes equations, J. Comput. Phys., 227 (2008), 8968-8991.
doi: 10.1016/j.jcp.2008.07.005. |
[7] |
K. Ito, M.-C. Lai and Z. Li, A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains, J. Comput. Phys., 228 (2009), 2616-2628.
doi: 10.1016/j.jcp.2008.12.028. |
[8] |
S. W. Jung, K. Mareck, M. Shelley and J. Zhang, Dynamics of a deformable body in a fast flowing soap film, Phys. Rev. Lett., 97 (2006), 134502.
doi: 10.1103/PhysRevLett.97.134502. |
[9] |
Y. Kim and C. S. Peskin, Penalty immersed boundary method for an elastic boundary with mass, Phys. Fluids, 19 (2007), 053103.
doi: 10.1063/1.2734674. |
[10] |
Y. Kim, L. Zhu, X. Wang and C. S. Peskin, On various techniques for computer simulation of boundaries with mass, in "Computational Fluid and Solid Mechanics" (eds. K. J. Bathe), Elsevier, (2003), 1746-1750. |
[11] |
R. J. LeVeque and Z. Li, Immersed interface methods for Stokes flow with elastic boundaries or surface tension, SIAM J. Sci. Comput., 18 (1997), 709-735.
doi: 10.1137/S1064827595282532. |
[12] |
Z. Li, "The Immersed Interface Method-A Numerical Approach for Partial Differential Equations with Interfaces," Ph.D thesis, University of Washington, 1994. |
[13] |
Z. Li and K. Ito, "The Immersed Interface Method. Numerical Solutions of PDEs Involving Interfaces and Irregular Domains," Frontiers in Applied Mathematics, 33, SIAM, Philadelphia, PA, 2006. |
[14] |
Z. Li and M.-C. Lai, The immersed interface method for the Navier-Stokes equations with singular forces, J. Comput. Phys., 171 (2001), 822-842.
doi: 10.1006/jcph.2001.6813. |
[15] |
Z. Li and M.-C. Lai, New finite difference methods based on IIM for inextensible interfaces in incompressible flows, East Asian J. Applied Math., 1 (2011), 155-171. |
[16] |
Y. Mori and C. S. Peskin, Implicit second-order immersed boundary methods with boundary mass, Comput. Methods Appl. Mech. Engrg., 197 (2008), 2049-2067.
doi: 10.1016/j.cma.2007.05.028. |
[17] |
T.-W. Pan and R. Glowinski, Direct simulation of the motion of neutrally buoyant circular cylinders in plane Poiseuille flow, J. Comput. Phys., 181 (2002), 260-279.
doi: 10.1006/jcph.2002.7123. |
[18] |
C. S. Peskin, "Flow Patterns Around Heart Valves: A Digital Computer Method for Solving the Equations of Motion," Ph.D thesis, Albert Einstein Coll. Med., 1972. |
[19] |
C. S. Peskin, Numerical analysis of blood flow in the heart, J. Comput. Phys., 25 (1977), 220-252.
doi: 10.1016/0021-9991(77)90100-0. |
[20] |
C. S. Peskin, The immersed boundary method, Acta Numerica, 11 (2002), 479-517.
doi: 10.1017/S0962492902000077. |
[21] |
K. Shoele and Q. Zhu, Flow-induced vibrations of a deformable ring, J. Fluid Mech., 650 (2010), 343-362.
doi: 10.1017/S0022112009993697. |
[22] |
X. S. Wang, An iterative matrix-free method in implicit immersed boundary/continuum methods, Computers and Structures, 85 (2007), 739-748.
doi: 10.1016/j.compstruc.2007.01.017. |
[23] |
J. Zhang, S. Childress, A. Libchaber and M. Shelley, Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind, Nature, 408 (2000), 835.
doi: 10.1038/35048530. |
[24] |
L. Zhu, Scaling laws for drag of a compliant body in an incompressible viscous flow, J. Fluid Mech., 607 (2008), 387-400. |
[25] |
L. Zhu and C. S. Peskin, Interaction of two flexible filaments in a flowing soap film, Phys. Fluids, 15 (2003), 1954-1960.
doi: 10.1063/1.1582476. |
[26] |
L. Zhu and C. S. Peskin, Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method, J. Comput. Phys., 179 (2002), 452-468.
doi: 10.1006/jcph.2002.7066. |
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