The immersed molecular finite element method

Computer Methods in Applied Mechanics and Engineering

Volumn 233-236, Issue , 2012, Pages 28-39

  Kopacz, Adrian M ^a   Patankar, Neelesh A ^a   Liu, Wing K ^a  

^a Northwestern University   (United States)

Author keywords

Fluctuating hydrodynamics; Fluid structure interaction; Immersed molecular finite element method; Molecular phenomena; Nanodiamond self assembly; Nanoscale computational fluidics

Indexed keywords

ANALYTIC SOLUTION; COULOMB POTENTIAL; DIAGNOSTIC APPLICATIONS; FLUCTUATION DISSIPATION THEOREM; FLUID EQUATIONS; FORCE FIELDS; HYDRODYNAMIC FORCES; IMMERSED FINITE ELEMENT METHOD; IMMERSED OBJECTS; INTEGRATED SIMULATIONS; MOLECULAR PHENOMENA; NANO DIAMOND; NANO SCALE; NANOSCALE STRUCTURE; SELF ASSEMBLY PROCESS; THERMAL FLUCTUATIONS; TIME STEP;

BROWNIAN MOVEMENT; ELECTRIC FIELDS; FLUID STRUCTURE INTERACTION; FLUIDICS; HYDRODYNAMICS; NANODIAMONDS; NANOTECHNOLOGY; SELF ASSEMBLY;

FINITE ELEMENT METHOD;

EID: 84860691257     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2012.04.005     Document Type: Article

References (69)

1. D Boal. Mechanics of the cell. Cambridge University Press, 2001.
2. Crocker J.C., Valentine M.T., Weeks E.R., Gisler T., Kaplan P.D., Yodh A.G., Crocker J.C., Weitz D.A. Two-point microrheology of inhomogeneous soft materials. Physical Review Letters 2000, 85(4):888-891.
3. Fall C., Marland E., Wagner J., Tyson J. Computational Cell Biology 2002, Springer.
4. Neuman K.C., Block S.M. Optical Trapping Review of Scientific Instruments 2004, 75(9):2787-2809.
5. Berg-Sorensen K., Flyvbjerg H. Power spectrum analysis for optical tweezers. Review of Scientific Instruments 2004, 75(3):594-612.
6. Watari N., Doi M., Larson R.G. Fluidic trapping of deformable polymers in microflows. Physical Review E 2008, 78(1):011801.
7. Moffitt J.R., Chemla Y.R., Smith S.B., Bustamante C. Recent advances in optical tweezers. Annual Review of Biochemistry 2008, 77:205-228.
8. Alberts B., Johnson A., Lewis J., Raff M., Roberts K., Walter P. Molecular Biology of the Cell 2002, Garland Science.
9. Yanagida T., Ueda M., Murata T., Esaki S., Ishil Y. Brownian next term motion, fluctuation and life. Biosystems 2007, 88(3):228-242.
10. Napoli M., Eijkel J.C.T., Pennathur S. Nanofluidic technology for biomolecule applications a critical review. Lab on a Chip 2010, 10:957-985.
11. Einstein A. Investigations on the Theory of Brownian Movement 1956, Dover, New York.
12. Squires T.M., Quake S.R. Microfluidics: fluid physics at the nanoliter scale. Reviews of Modern Physics 2005, 77(3):977-1026.
13. Coffey W.T., Kalmykov Y.P., Titov S.V. Langevin equation method for the rotational Brownian motion and orientational relaxation in liquids. Journal of Physics A: Mathematical and General 2002, 35(32):6789-6803.
14. Kalmykov Y.P., Titov S.V., Coffey W.T. Langevin equation method for the rotational Brownian motion and orientational relaxation in liquids: spherical top molecules. Journal of Molecular Liquids 2005, 116(3):119-123.
15. Bixon M., Zwanzig R. Boltzmann-Langevin equation and hydrodynamic fluctuations. Physical Review 1969, 187(1):267-272.
16. Ermak D.L., McCammon J.A. Brownian dynamics with hydrodynamic interactions. Journal of Chemical Physics 1978, 69(4):1352-1360.
17. Brady J.F., Bossis G. Stokesian dynamics. Annual Review of Fluid Mechanics 1988, 20:111-157.
18. Sierou A., Brady J.F. Accelerated Stokesian dynamics simulations. Journal of Fluid Mechanics 2001, 448:115-146.
19. Banchio A.J., Brady J.F. Accelerated Stokesian dynamics: Brownian motion. Journal of Chemical Physics 2003, 118(22):10323-10332.
20. Kramer P.R., Majda A.J. Stochastic mode reduction for the immersed boundary method. SIAM Journal on Applied Mathematics 2003, 64(2):369-400.
21. Atzberger P.J., Kramer P.R., Peskin C.S. A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales. Journal of Computational Physics 2007, 224:1255-1292.
22. Kramer P.R., Peskin C.S., Atzberger P.J. On the foundations of the stochastic immersed boundary method. Computer Methods in Applied Mechanics and Engineering 2008, 197:2232-2249.
23. Atzberger P.J. Stochastic Eulerian Lagrangian methods for fluid-structure interactions with thermal fluctuations. Journal of Computational Physics 2011, 230:2821-2837.
24. L.D. Landau, E.M. Lifshitz, Fluid Mechanics, Pergamon Press, 1959.
25. Zwanzig R. Hydrodynamic fluctuations and Stokes' law friction. Journal of Research of the National Bureau of Standards 1964, 68B:143-145.
26. Sharma N., Patankar N.A. Direct numerical simulation of the Brownian motion of particles by using fluctuating hydrodynamic equations. Journal of Computational Physics 2004, 201(2):466-486.
27. Peskin C.S. Flow patterns around heart valves: a numerical method. Journal of Computational Physics 1972, 10(2):252-271.
28. Arienti M., Hung P., Morano E., Shepherd J.E. A level set approach to Eulerian-Lagrangian coupling. Journal of Computational Physics 2003, 185(1):213-251.
29. Wang X., Liu W.K. Extended immersed boundary method using FEM and RKPM. Computer Methods in Applied Mechanics and Engineering 2004, 193(12-14):1305-1321.
30. Zhang L., Gerstenberger A., Wang X., Liu W.K. Immersed finite element method. Computer Methods in Applied Mechanics and Engineering 2004, 193(21-22):2051-2067.
31. Bodard N., Deville M.O. Fluid-structure interaction by the spectral element method. Journal of Scientific Computing 2006, 27(1):123-136.
32. Kim Y., Peskin C.S. Penalty immersed boundary method for an elastic boundary with mass. Physics of Fluids 2007, 19(5):53103-53118.
33. J.B. Bell, A.L. Garcia, S.A. Williams, Computational fluctuating fluid dynamics, ESAIM Mathematical Modelling and Numerical Analysis (44) (2010) 1085-1105.
34. W.K. Liu, D.W. Kim, S. Tang, Mathematical foundations of the immersed finite element method, Computational Mechanics (2006) 1-12.
35. Peskin C.S., McQueen D.M. A three-dimensional computational method for blood flow in the heart. I. Immersed elastic fibers in a viscous incompressible fluid. Journal of Computational Physics 1989, 81(2):372-405.
36. C.S. Peskin, D.M. McQueen, Computational biofluid dynamics, Contemproary Mathematics 141 (1993) 161-186.
37. T.J.R. Hughes, The Finite Element Method, Prentice Hall, 1987.
38. W.K. Liu, H. Chang, J. Chen, T. Belytschko, Arbitrary Lagrangian-Eulerian Petrov-Galerkin finite elements for nonlinear continua, Computer Methods in Applied Mechanics and Engineering 68 (1988) 259-310.
39. T. Belytschko, W.K. Liu, B. Moran, Nonlinear Finite Elements for Continua and Structures, John Wiley and Sons, 2000.
40. Li S., Liu W.K. Meshfree and particle methods and their applications. Applied Mechanics Review 2002, 55:1-34.
41. S. Li, W.K. Liu, Meshfree Particle Method, Springer, 2004.
42. Y. Liu, W.K. Liu, T. Belytschko, N. Patankar, A.C. To, A.M. Kopacz, J.H. Chung, Immersed electrokinetic finite element method, International Journal for Numerical Methods in Engineering 71 (2007) 379-405.
43. Y. Liu, K. Oh, J.G. Bai, C.L. Chang, W. Yeo, J.H. Chung, K.H. Lee, W.K. Liu, Manipulation of nanoparticles and biomolecules by electric field and surface tension, Computer Methods in Applied Mechanics and Engineering 197 (2008) 2156-2172.
44. Liu Y., Liu W.K. Rheology of red blood cell aggregation by computer simulation. Journal of Computational Physics 2006, 220(1):139-154.
45. W.K. Liu, Y. Liu, D. Farrell, L. Zhang, X.S. Wang, Y. Fukui, N. Patankar, Y. Zhang, C. Bajaj, J. Lee, J. Hong, X. Chen, H. Hsua, Immersed finite element method and its applications to biological systems, Computer Methods in Applied Mechanics and Engineering 195 (2006) 1722-1749.
46. Kopacz A.M., Liu W.K., Liu S.Q. Simulation and prediction of endothelial cell adhesion modulated by molecular engineering. Computer Methods in Applied Mechanics and Engineering 2008, 197(25-28):2340-2352.
47. Liu W.K., Jun S., Zhang Y.F. Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids 1995, 20:1081-1106.
48. Liu W.K., Jun S., Zhang Y.F. Generalized multiple scale reproducing kernel particle methods. Computer Methods in Applied Mechanics and Engineering 1996, 139:91-158.
49. Kubo R. The fluctuation-dissipation theorem. Reports on Progress in Physics 1966, 29:255-293.
50. Fox R.F., Uhlenbeck G.E. Contributions to nonequilibrium thermodynamics. II. Fluctuation theory for the boltzmann equation. Physics of Fluids 1970, 13(12):1893-1902.
51. Tezduyar T.E. Stabilized finite element formulations for incompressible flow computations. Advances in Applied Mechanics 1991, 28:1-44.
52. Tezduyar T.E., Mittal S., Ray S.E., Shih R. Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Computer Methods in Applied Mechanics and Engineering 1992, 95:221-242.
53. Tezduyar T.E. Finite element methods for flow problems with moving boundaries and interfaces. Archives of Computational Methods in Engineering 2001, 8(2):83-130.
54. C W Gardiner, Handbook of stochastic methods: for physics, chemistry and the natural sciences. Springer, 1996.
55. T.J.R. Hughes, L.P. Franca, M. Balestra, A new finite element formulation for computational fluid dynamics: circumventing the Babuska-Brezzi condition: a stable Petrov-Galerkin formulation of the stokes problem accommodating equal-order interpolations, Computer Methods in Applied Mechanics and Engineering 59 (1986) 85-99.
56. Tezduyar E., Osawa Y. Finite element stabilization parameters computed from element matrices and vectors. Computer Methods in Applied Mechanics and Engineering 2000, 190:411-430.
57. Tezduyar T.E., Sathe S. Stabilization parameters in SUPG and PSPG formulations. Journal of Computational and Applied Mechanics 2003, 4(1):71-88.
58. Saad Y., Schultz M.H. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 1986, 7(3):856-869.
59. Zhang T., Wagner G.J., Liu W.K. A parallelized meshfree method with boundary enrichment for large-scale CFD. Journal of Computational Physics 2002, 176:483-506.
60. Paul G.L., Pusey P.N. Observation of a long-time tail in Brownian motion. Journal of Physics A: Mathematical and General 1981, 14(12):3301-3327.
61. Atzberger P.J. Velocity correlations of a thermally fluctuating Brownian particle: a novel model of the hydrodynamic coupling. Physics Letters A 2006, 351(4):225-230.
62. Hauge E.H., Martin-Lof A. Fluctuating hydrodynamics and Brownian motion. Journal of Statistical Physics 1973, 7(3):259-281.
63. Alder B.J., Wainwright T.E. Decay of the velocity autocorrelation function. Physical Review A 1970, 1(1):18-21.
64. Dorfman J.R., Cohen E.G.D. Velocity-correlation functions in two and three dimensions. II. Higher density. Physical Review A 1975, 12(1):292-316.
65. Li A., Ahmadi G. Dispersion and deposition of spherical particles from point sources in a turbulent channel flow. Aerosol Science and Technology 1992, 16(4):209-226.
66. Hasimoto H. On the periodic fundamental solution of the stokes equations and their application to viscous flow past a cubic array of spheres. Journal of Fluid Mechanics 1959, 6:317-328.
67. Zick A., Homsy G.M. Stokes flow through periodic arrays of spheres. Journal of Fluid Mechanics 1982, 115:13-26.
68. Liu Y., Zhang L., Wang X., Liu W.K. Coupling of Navier-Stokes equations with protein molecular dynamics and its application to hemodynamics. International Journal for Numerical Methods in Fluids 2004, 46:1237-1252.
69. Liu W.K., Adnan A., Kopacz A.M., Hallikainen M., Ho D., Lam R., Lee J., Belytschko T., Schatz G., Tzeng Y., Kim Y.J., Baik S., Kim M.K., Kim T., Lee J., Hwang E.S., Im S., Osawa E., Barnard A., Chang H.C., Chang C.C., Onate E. Design of nanodiamond based drug delivery patch for cancer therapeutics and imaging applications. Nanodiamonds: Applications in Biology and Nanoscale Medicine 2010, 249-285. Springer, New York.