參考文獻 |
[1] T. Allen and P. Cullis, Drug delivery systems: entering the mainstream, Science,
303 (2004), pp. 1818-1822.
[2] J. B. Bell, P. Colella, and H. M. Glaz, A second-order projection method for the incompressible
Navier-Stokes equations, Journal of Computational Physics, 85 (1989),
pp. 257-283.
[3] I. Borazjani, Fluid-structure interaction, immersed boundary-finite element
method simulations of bio-prosthetic heart valves, Computer Methods in Applied
Mechanics and Engineering, 257 (2013), pp. 103-116.
[4] D. L. Brown, R. Cortez, and M. L. Minion, Accurate projection methods for the incompressible
Navier-Stokes equations, Journal of Computational Physics, 168 (2001),
pp. 464-499.
[5] D. Calhoun, A Cartesian grid method for solving the two-dimensional
streamfunction-vorticity equations in irregular regions, Journal of Computational
Physics, 176 (2002), pp. 231-275.
[6] M.-J. Chern, Y.-H. Kuan, G. Nugroho, G.-T. Lu, and T.-L. Horng, Direct-forcing
immersed boundary modeling of vortex-induced vibration of a circular cylinder,
Journal of Wind Engineering and Industrial Aerodynamics, 134 (2014), pp. 109-121.
[7] M.-J. Chern, D. Z. Noor, C.-B. Liao, and T.-L. Horng, Direct-forcing immersed
boundary method for mixed heat transfer, Communications in Computational
Physics, 18 (2015), pp.1072-1094.
[8] M.-J. Chern,W.-C. Shiu, and T.-L. Horng, Immersed boundary modeling for interaction
of oscillatory flow with cylinder array under effects of flow direction and
cylinder arrangement, Journal of Fluids and Structures, 43 (2013), pp. 325-346.
[9] P. H. Chiu, R. K. Lin, and T.W. H. Sheu, A differentially interpolated direct forcing
immersed boundary method for predicting incompressible Navier-Stokes equations
in time-varying complex geometries, Journal of Computational Physics, 229
(2010), pp. 4476-4500.
[10] H. Choi and P. Moin, Effects of the computational time step on numerical solutions
of turbulent flow, Journal of Computational Physics, 113 (1994), pp. 1-4.
[11] J.-I. Choi, R. C. Oberoi, J. R. Edwards, and J. A. Rosati, An immersed boundary
method for complex incompressible flows, Journal of Computational Physics, 224
(2007), pp. 757-784.
[12] A. J. Chorin, Numerical solution of the Navier-Stokes equations, Mathematics of
Computation, 22 (1968), pp. 745-762.
[13] A. J. Chorin, On the convergence of discrete approximations to Navier-Stokes
equations, Mathematics of Computation, 23 (1969), pp. 341-353.
[14] A. J. Chorin and J. E. Marsden, A Mathematical Introduction to Fluid Mechanics, 2nd
Edition, Springer-Verlag, New York, 1990.
[15] R. Cortez and M. Minion, The blob projection method for immersed boundary
problems, Journal of Computational Physics, 161 (2000), pp. 428-453.
[16] M. Coutanceau and R. Bouard, Experimental determination of the main features
of the viscous flow in the wake of a circular cylinder in uniform translation. Part
1. steady flow, Journal of Fluid Mechanics, 79 (1977), pp. 231-256.
[17] F. Domenichini, On the consistency of the direct forcing method in the fractional
step solution of the Navier-Stokes equations, Journal of Computational Physics, 227
(2008), pp. 6372-6384.
[18] E. A. Fadlun, R. Verzicco, P. Orlandi, and J. Mohd-Yusof, Combined immersedboundary
finite-difference methods for three-dimensional complex flow simulations,
Journal of Computational Physics, 161 (2000), pp. 35-60.
[19] L. J. Fauci and A. L. Fogelson, Truncated Newton methods and the modeling of
complex immersed elastic structures, Communications on Pure and Applied Mathematics,
66 (1993), pp. 787-818.
[20] D. A. Fedosov, B. Caswell, and G. E. Karniadakis, A multiscale red blood cell
model with accurate mechanics, rheology, and dynamics, Biophysical Journal, 98
(2010), pp. 2215-2225.
[21] D. Goldstein, R. Handler, and L. Sirovich, Modeling a no-slip flow boundary with
an external force field, Journal of Computational Physics, 105 (1993), pp. 354-366.
[22] B. E. Griffith, An accurate and efficient method for the incompressible Navier-
Stokes equations using the projection method as a preconditioner, Journal of Computational
Physics, 228 (2009), pp. 7565-7595.
[23] J. L. Guermond, P. Minev, and J. Shen, An overview of projection methods for
incompressible flows, Computer Methods in Applied Mechanics and Engineering, 195
(2006), pp. 6011-6045.
[24] R. D. Guy and D. A. Hartenstine, On the accuracy of direct forcing immersed
boundary methods with projection methods, Journal of Computational Physics, 229
(2010), pp. 2479-2496.
[25] K. H. de Haas, C. Blom, D. van den Ende, M. H. G. Duits, and J. Mellema, Deformation
of giant lipid bilayer vesicles in shear flow, Physical Review E, 56 (1997),
pp. 7132-7137.
[26] F. H. Harlow and J. E. Welsh, Numerical calculation of time-dependent viscous
incompressible flow of fluid with a free surface, Physics of Fluids, 8 (1965), pp.
2181-2189.
[27] T.-L. Horng, P.-W. Hsieh, S.-Y. Yang, and C.-S. You, A simple direct-forcing immersed
boundary projection method with prediction-correction for fluid-solid interaction
problems, preprint, 2016.
[28] P.-W. Hsieh, M.-C. Lai, S.-Y. Yang, and C.-S. You, An unconditionally energy stable
penalty immersed boundary method for simulating the dynamics of an inextensible
interface interacting with a solid particle, Journal of Scientific Computing, 64
(2015), pp. 289-316.
[29] M.-C. Hsu and Y. Bazilevs, Fluid-structure interaction modeling of wind turbines:
simulating the full machine, Computational Mechanics, 50 (2012), pp. 821-833.
[30] T. J. R. Hughes, W. K. Liu, and A. Brooks, Finite element analysis of incompressible
viscous flows by the penalty function formulation, Journal of Computational
Physics, 30 (1979), pp. 1-60.
[31] S. E. Hurlbut, M. L. Spaulding, and F. M. White, Numerical solution for laminar
two dimensional flow about a cylinder oscillating in a uniform stream, Journal of
Fluids Engineering, 104 (1982), pp. 214-220.
[32] C. Ji, A. Munjiza, and J. J. R. Williams, A novel iterative direct-forcing immersed
boundary method and its finite volume applications, Journal of Computational
Physics, 231 (2012), pp. 1797-1821.
[33] J. van Kan, A second-order accurate pressure-correction scheme for viscous incompressible
flow, SIAM Journal on Scientific and Statistical Computing, 7 (1986),
pp. 870-891.
[34] V. Kantsler and V. Steinberg, Orientation and dynamics of a vesicle in tanktreading
motion in shear flow, Physical Review Letters, 95 (2005), 258101.
[35] S. R. Keller and R. Skalak, Motion of a tank-treading ellipsoidal particle in a shear
flow, Journal of Fluid Mechanics, 120 (1982), pp. 27-47.
[36] J. Kim, D. Kim, and H. Choi, An immersed-boundary finite-volume method for
simulations of flow in complex geometries, Journal of Computational Physics, 171
(2001), pp. 132-150.
[37] J. Kim and P. Moin, Application of a fractional-step method to incompressible
Navier-Stokes equations, Journal of Computational Physics, 59 (1985), pp. 308-323.
[38] Y. Kim and M.-C. Lai, Simulating the dynamics of inextensible vesicles by the
penalty immersed boundary method, Journal of Computational Physics, 229 (2010),
pp. 4840-4853.
[39] Y. Kim, C. S. Peskin, Penalty immersed boundary method for an elastic boundary
with mass, Physics of Fluids, 19 (2007), 053103.
[40] M. Kraus, W. Wintz, U. Seifert, and R. Lipowsky, Fluid vesicles in shear flow,
Physical Review Letters, 77 (1996), pp. 3685-3688.
[41] M.-C. Lai,W.-F. Hu, andW.-W. Lin, A fractional step immersed boundary method
for stokes flow with an inextensible interface enclosing a solid particle, SIAM Journal
on Scientific Computing, 34 (2012), pp. B692-B710.
[42] M.-C. Lai and C. S. Peskin, An Immersed boundary method with formal secondorder
accuracy and reduced numerical viscosity, Journal of Computational Physics,
160 (2000), pp. 705-719.
[43] M.-C. Lai, Y.-H. Tseng, and H. Huang, An immersed boundary method for interfacial
flow with insoluble surfactant, Journal of Computational Physics, 227 (2008),
pp. 7279-7293.
[44] D. V. Le, B. C. Khoo, and K. M. Lim, An implicit-forcing immersed boundary
method for simulating viscous flows in irregular domains, Computer Methods in
Applied Mechanics and Engineering, 1 97 (2008), pp. 2119-2130.
[45] R. J. Leveque and Z. Li, Immersed interface methods for Stokes flow with elastic
boundaries or surface tension, SIAM Journal on Scientific Computing, 18 (1997), pp.
709-735.
[46] Z. Li and M.-C. Lai, New finite difference methods based on IIM for inextensible
interfaces in incompressible flows, East Asian Journal on Applied Mathematics, 1
(2011), pp. 155-171.
[47] C.-C. Liao, Y.-W. Chang, C.-A. Lin, and J. M. McDonough, Simulating flows with
moving rigid boundary using immersed-boundary method, Computers & Fluids,
39 (2010), pp. 152-167.
[48] A. L. F. Lima E Silva, A. Silveira-Neto, and J. J. R. Damasceno, Numerical simulation
of two-dimensional flows over a circular cylinder using the immersed boundary
method, Journal of Computational Physics, 189 (2003), pp. 351-370.
[49] M. N. Linnick and H. F. Fasel, A high-order immersed interface method for simulating
unsteady incompressible flows on irregular domains, Journal of Computational
Physics, 204 (2005), pp.157-192.
[50] C. Liu, X. Zheng, and C. H. Sung, Preconditioned multigrid methods for unsteady
incompressible flows, Journal of Computational Physics, 139 (1998), pp. 35-57.
[51] H. Luo, H. Dai, P. J. S. A. Ferreira de Sousa, and B. Yin, On the numerical oscillation
of the direct-forcing immersed-boundary method for moving boundaries,
Computers & Fluids, 56 (2012), pp. 61-76.
[52] A. A. Mayo and C. S. Peskin, An implicit numerical method for fluid dynamics
problems with immersed elastic boundaries, Contemporary Mathematics, 141
(1993), pp. 261-277.
[53] C. Misbah, Vacillating breathing and tumbling of vesicles under shear flow, Physical
Review Letters, 96 (2006), 028104.
[54] R. Mittal and G. Iaccarino, Immersed boundary methods, Annual Review of Fluid
Mechanics, 37 (2005), pp. 239-261.
[55] J. Mohd-Yusof, Interaction of Massive Particles with Turbulence, Ph.D. Dissertation,
Department of Mechanical and Aerospace Engineering, Cornell University, 1996.
[56] E. P. Newren, A. L. Fogelson, R. D. Guy, and R. M. Kirby, Unconditionally stable
discretizations of the immersed boundary equations, Journal of Computational
Physics, 222 (2007) pp. 702-719.
[57] H. Noguchi and G. Gompper, Swinging and tumbling of fluid vesicles in shear
flow, Physical Review Letters, 98 (2007), 128103.
[58] D. Z. Noor, M.-J. Chern, and T.-L. Horng, An immersed boundary method to solve
fluid-solid interaction problems, Computational Mechanics, 44 (2009), pp. 447-453.
[59] C. S. Peskin, Flow patterns around heart valves: a numerical method, Journal of
Computational Physics, 10 (1972), pp. 252-271.
[60] C. S. Peskin, The immersed boundary method, Acta Numerica, 11 (2002), pp. 479-
51
[61] D. Russell and Z. J.Wang, A Cartesian grid method for modeling multiple moving
objects in 2D incompressible viscous flow, Journal of Computational Physics, 191
(2003), pp. 177-205.
[62] E. M. Saiki and S. Biringen, Numerical simulation of a cylinder in uniform flow:
application of a virtual boundary method, Journal of Computational Physics, 123
(1996), pp. 450-465.
[63] J. S. Sohn, Y.-H. Tseng, S. Li, A. Voigt, and J. S. Lowengrub, Dynamics of multicomponent
vesicles in a viscous fluid, Journal of Computational Physics, 229 (2010),
pp. 119-144.
[64] J. M. Stockie and B. R. Wetton, Analysis of stiffness in the immersed boundary
method and implications for time-stepping schemes, Journal of Computational
Physics, 154 (1999), pp. 41-64.
[65] S.-W. Su, M.-C. Lai, and C.-A. Lin, An immersed boundary technique for simulating
complex flows with rigid boundary, Computers & Fluids, 36 (2007), pp. 313-324.
[66] K. Taira and T. Colonius, The immersed boundary method: a projection approach,
Journal of Computational Physics, 225 (2007), pp. 2118-2137.
[67] R. Temam, Sur l’approximation de la solution des ´equations de Navier-Stokes par
la m´ethode des pas fractionnaires II, Archive for Rational Mechanics and Analysis, 33
(1969), pp. 377-385.
[68] R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis, Revised Ed., Elsevier
Science Publishers B.V., Amsterdam, 1984.
[69] D. J. Tritton, Experiments on the flow past a circular cylinder at low Reynolds
numbers, Journal of Fluid Mechanics, 6 (1959), pp. 547-567.
[70] Y.-H. Tseng and J. H. Ferziger A ghost-cell immersed boundary method for flow
in complex geometry, Journal of Computational Physics, 192 (2003), pp. 593-623.
[71] C. Tu and C. S. Peskin, Stability and instability in the computation of flows with
moving immersed boundaries: a comparison of three methods, SIAM Journal on
Scientific and Statistical Computing, 13 (1992), pp. 1361-1376.
[72] M. Uhlmann, An immersed boundary method with direct forcing for the simulation
of particulate flows, Journal of Computational Physics, 209 (2005), pp. 448-476.
[73] M. Vanella, P. Rabenold, and E. Balaras, A direct-forcing embedded-boundary
method with adaptive mesh refinement for fluid-structure interaction problems,
Journal of Computational Physics, 229 (2010), pp. 6427-6449.
[74] H. A. van der Vorst, Bi-CGSTAB: a fast and smoothly converging variant of Bi-
CG for the solution of nonsymmetric linear systems, SIAM Journal on Scientific and
Statistical Computing, 13 (1992), pp. 631-644.
[75] S. K. Veerapaneni, D. Gueyffier, D. Zorin, and G. Biros, A boundary integral
method for simulating the dynamics of inextensible vesicles suspended in a viscous
fluid in 2D, Journal of Computational Physics, 228 (2009), pp. 2334-2353.
[76] S. K. Veerapaneni, Y.-N. Young, P. M. Vlahovska, and J. Blawzdziewicz, Dynamics
of a compound vesicle in shear flow, Physical Review Letters, 106 (2011), 158103.
[77] Z.Wang, J. Fan, and K. Luo, Combined multi-direct forcing and immersed boundary
method for simulating flows with moving particles, International Journal of
Multiphase Flow, 34 (2008), pp. 283-302.
[78] S. Xu and Z. J.Wang, An immersed interface method for simulating the interaction
of a fluid with moving boundaries, Journal of Computational Physics, 216 (2006), pp.
454-493.
[79] X. Yang, X. Zhang, Z. Li, and G.-W. He, A smoothing technique for discrete delta
functions with application to immersed boundary method in moving boundary
simulations, Journal of Computational Physics, 228 (2009), pp. 7821-7836.
[80] T. Ye, R. Mittal, H. S. Udaykumar, and W. Shyy, An accurate Cartesian grid
method for viscous incompressible flows with complex immersed boundaries,
Journal of Computational Physics, 156 (1999), pp.209-240.
[81] N. Zhang and Z. C. Zheng, An improved direct-forcing immersed-boundary
method for finite difference applications, Journal of Computational Physics, 221
(2007), pp. 250-268.
[82] Z. Zheng and L. Petzold, Runge-Kutta-Chebyshev projection method, Journal of
Computational Physics, 219 (2006), pp. 976-991.
[83] H. Zhou and C. Pozrikidis, Deformation of liquid capsules with incompressible
interfaces in simple shear flow, Journal of Fluid Mechanics, 283 (1995), pp. 175-200. |