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Hydrodynamic effects of mucus on swimming performance of an undulatory foil by using the DSD/SST method

  • Fang-Bao TianEmail author
Original Paper
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Abstract

This paper presents a DSD/SST study of the hydrodynamic effects of mucus on swimming performance of an undulatory foil in a non-Newtonian uniform flow. As the non-Newtonian effects are dominant in the boundary layer, this model can be taken as a simple strategy to study the hydrodynamic effects of fish mucus. Based on the simulations by varying the power-law fluid behavior index, some propulsive properties including the drag coefficients, the power coefficients, and the flow fields are analyzed in detail. It is found that in addition to other biological functions, the fish mucus serves to reduce the friction, enhance the thrust, save hydrodynamic power, reduce the force oscillations, and reduce the swimming sound. This work provides a better understanding of the fish mucus effects from the point of view of hydrodynamics.

Keywords

Non-Newtonian flow Fish mucus Fish swimming Travelling wave DSD/SST method 

Notes

Acknowledgements

Dr. F.-B. Tian is the recipient of an Australian Research Council Discovery Early Career Researcher Award (Project Number DE160101098). Simulations were partially undertaken with computational resources on the National Computational Infrastructure National Facility through the National Computational Merit Allocation Scheme supported by the Australian Government.

References

  1. 1.
    Videler JJ (1993) Fish swimming. Chapman and Hall, LondonCrossRefGoogle Scholar
  2. 2.
    Triantafyllou MS, Triantafyllou GS, Yue DKP (2000) Hydrodynamics of fish swimming. Annu Rev Fluid Mech 32:33–53zbMATHCrossRefGoogle Scholar
  3. 3.
    Fish FE, Lauder GV (2006) Passive and active flow control by swimming fishes and mammals. Annu Rev Fluid Mech 38:193–224MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Tytell ED, Borazjani I, Sotiropoulos F, Baker TV, Anderson EJ, Lauder GV (2010) Disentangling the functional roles of morphology and motion in the swimming of fish. Integr Comput Biol 50:1140–1154CrossRefGoogle Scholar
  5. 5.
    Deng HB, Xu YQ, Chen DD, Dai H, Wu J, Tian FB (2013) On numerical modeling of animal swimming and flight. Comput Mech 52:1221–1242MathSciNetCrossRefGoogle Scholar
  6. 6.
    Ling SC, Ling TYJ (1974) Anomalous drag-reducing phenomenon at a water/fish-mucus or polymer interface. J Fluid Mech 65:499–512CrossRefGoogle Scholar
  7. 7.
    Shephard KL (1994) Functions for fish mucus. Rev Fish Biol Fish 4:401–429CrossRefGoogle Scholar
  8. 8.
    Müller UK, van den Heuvel BLE, Stamhuis EJ, Videler JJ (1997) Fish foot prints: morphology and energetics of the wake behind a continuously swimming mullet ( chelon labrosus risso). J Exp Biol 200:2893–2906Google Scholar
  9. 9.
    Roberts SD, Powell MD (2005) The viscosity and glycoprotein biochemistry of salmonid mucus varies with species, salinity and the presence of amoebic gill disease. J Comp Physiol B 175:1–11CrossRefGoogle Scholar
  10. 10.
    Shadwick RE, Lauder GV (eds) (2005) Fish biomechanics. Academic Press, CaliforniaGoogle Scholar
  11. 11.
    Helfman GS, Collette BB, Facey DF (2009) The diversity of fishes: biology, evolution and ecology, 2nd edn. Wiley, ChichesterGoogle Scholar
  12. 12.
    Vatsos IN, Kotzamanis Y, Henry M, Angelidis P, Alexis M (2010) Monitoring stress in fish by applying image analysis to their skin mucous cells. Eur J Histochem 54:e22CrossRefGoogle Scholar
  13. 13.
    Palstra AP, Planas JV (eds) (2013) Swimming physiology of fish: towards using exercise to farm a fit fish in sustainable aquaculture. Springer, HeidelbergGoogle Scholar
  14. 14.
    Nagamine H, Yamahata K, Hagiwara Y, Matsubara R (2004) Turbulence modification by compliant skin and strata-corneas desquamation of a swimming dolphin. J Turbul 5:1–25CrossRefGoogle Scholar
  15. 15.
    Jakowska S (1963) Mucus secretion in fish. Ann NY Acad Sci 106:458–562CrossRefGoogle Scholar
  16. 16.
    Negus VE (1963) The function of mucus. Acta Oto-Laryngol 56:204–214CrossRefGoogle Scholar
  17. 17.
    Ingrain GA (1980) Substances involved in the natural resistance of fish to infection: a review. J Fish Biol 16:23–60CrossRefGoogle Scholar
  18. 18.
    Ellis AE (1981) Non-specific defence mechanisms in fish and their role in disease processes. Dev Biol Stand 49:337–352Google Scholar
  19. 19.
    Daniel TL (1981) Fish mucus: in situ mearurements of polymer drag reduction. Biol Bull 160:376–382CrossRefGoogle Scholar
  20. 20.
    Dean B, Bhushan B (2010) Shark-skin surfaces for fluid-drag reduction in turbulent flow: a review. Philos Trans R Soc A 368:4775–4806CrossRefGoogle Scholar
  21. 21.
    Tezduyar TE, Behr M, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces: the deforming-spatial-domain/space-time procedure: I. The concept and the preliminary numerical tests. Comput Methods Appl Mech Eng 94:339–351MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Tezduyar TE, Behr M, Mittal S, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces: the deforming-spatial-domain/space–time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput Methods Appl Mech Eng 94:353–371MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28:1–44MathSciNetzbMATHGoogle Scholar
  24. 24.
    Mittal S, Tezduyar T (1992) A finite element study of incompressible flows past oscillating cylinders and airfoils. Int J Numer Methods Fluids 15:1073–1118CrossRefGoogle Scholar
  25. 25.
    Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43:555–575MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Tezduyar TE, Sathe S, Keedy R, Stein K (2006a) Space–time finite element techniques for computation of fluid–structure interactions. Comput Methods Appl Mech Eng 195:2002–2027MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Tezduyar TE, Sathe S, Stein K (2006b) Solution techniques for the fully-discretized equations in computation of fluid–structure interactions with the space–time formulations. Comput Methods Appl Mech Eng 195:5743–5753MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Tezduyar TE (2006) Interface-tracking and interface-capturing techniques for finite element computation of moving boundaries and interfaces. Comput Methods Appl Mech Eng 195:2983–3000MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    Tezduyar TE (2007) Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids 36:191–206MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Tezduyar TE, Sathe S (2007) Modeling of fluid–structure interactions with the space–time finite elements: solution techniques. Int J Numer Methods Fluids 54:855–900zbMATHCrossRefGoogle Scholar
  31. 31.
    Wang SY, Tian FB, Jia LB, Lu XY, Yin XZ (2010) The secondary vortex street in the wake of two tandem circular cylinders at low Reynolds number. Phys Rev E 81:036305CrossRefGoogle Scholar
  32. 32.
    Takizawa K, Tezduyar TE (2011) Multiscale space–time fluid–structure interaction techniques. Comput Mech 48:247–267MathSciNetzbMATHCrossRefGoogle Scholar
  33. 33.
    Takizawa K, Tezduyar TE (2012) Space–time fluid–structure interaction methods. Math Models Methods Appl Sci 22(supp02):1230001MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    Tian FB, Lu XY, Luo H (2012) Propulsive performance of a body with a traveling wave surface. Phys Rev E 86:016304CrossRefGoogle Scholar
  35. 35.
    Bazilevs Y, Takizawa K, Tezduyar TE (2013) Challenges and directions in computational fluid–structure interaction. Math Models Methods Appl Sci 23:215–221MathSciNetzbMATHCrossRefGoogle Scholar
  36. 36.
    Takizawa K, Montes D, McIntyre S, Tezduyar TE (2013) Space–time VMS methods for modeling of incompressible flows at high Reynolds numbers. Math Models Methods Appl Sci 23:223–248MathSciNetzbMATHCrossRefGoogle Scholar
  37. 37.
    Dong GJ, Lu XY (2005) Numerical analysis on the propulsive performance and vortex shedding of fish-like travelling wavy plate. Int J Numer Methods Fluids 48:1351–1373zbMATHCrossRefGoogle Scholar
  38. 38.
    Yu C-L, Ting S-C, Yeh M-K, Yang J-T (2011) Three-dimensional numerical simulation of hydrodynamic interactions between pectoral-fin vortices and body undulation in a swimming fish. Phys Fluids 23:091901CrossRefGoogle Scholar
  39. 39.
    Mittal S, Tezduyar TE (1995) Parallel finite element simulation of 3D incompressible flows-fluid–structure interactions. Int J Numer Methods Fluids 21:933–953zbMATHCrossRefGoogle Scholar
  40. 40.
    Johnson AA, Tezduyar TE (1999) Advanced mesh generation and update methods for 3D flow simulations. Comput Mech 23:130–143zbMATHCrossRefGoogle Scholar
  41. 41.
    Takizawa K, Henicke B, Puntel A, Kostov N, Tezduyar TE (2012a) Space–time techniques for computational aerodynamics modeling of flapping wings of an actual locust. Comput Mech 50:743–760zbMATHCrossRefGoogle Scholar
  42. 42.
    Takizawa K, Kostov N, Puntel A, Henicke B, Tezduyar TE (2012b) Space–time computational analysis of bio-inspired flapping-wing aerodynamics of a micro aerial vehicle. Comput Mech 50:761–778zbMATHCrossRefGoogle Scholar
  43. 43.
    Takizawa K, Henicke B, Puntel A, Kostov N, Tezduyar TE (2013) Computer modeling techniques for flapping-wing aerodynamics of a locust. Comput Fluids 85:125–134MathSciNetzbMATHCrossRefGoogle Scholar
  44. 44.
    Takizawa K, Henicke B, Puntel A, Spielman T, Tezduyar TE (2012) Space–time computational techniques for the aerodynamics of flapping wings. J Appl Mech 79:010903zbMATHCrossRefGoogle Scholar
  45. 45.
    Tian FB, Xu YQ, Tang XY, Deng YL (2013) Study on a self-propelled fish swimming in viscous fluid by a finite element method. J Mech Med Biol 13:1340012CrossRefGoogle Scholar
  46. 46.
    Takizawa K, Tezduyar TE, Kostov N (2014) Sequentially-coupled space-time FSI analysis of bio-inspired flapping-wing aerodynamics of an MAV. Comput Mech 54:213–233MathSciNetCrossRefGoogle Scholar
  47. 47.
    Takizawa K, Tezduyar TE, Buscher A (2015) Space–time computational analysis of MAV flapping-wing aerodynamics with wing clapping. Comput Mech 55:1131–1141CrossRefGoogle Scholar
  48. 48.
    Tian FB (2015) A numerical study of linear and nonlinear kinematic models in fish swimming with the DSD/SST method. Comput Mech 55:469–477MathSciNetzbMATHCrossRefGoogle Scholar
  49. 49.
    Tian FB, Wang W, Wu J, Sui Y (2016) Swimming performance and vorticity structures of a mother–calf pair of fish. Comput Fluids 124:1–11MathSciNetzbMATHCrossRefGoogle Scholar
  50. 50.
    Stewart WJ, Tian FB, Akanyeti O, Walker C, Liao JC (2016) Refusing rainbow trout selectively exploit flows behind tandem cylinders. J Exp Biol 219:2182–2191CrossRefGoogle Scholar
  51. 51.
    Xu YQ, Jiang YQ, Wu J, Sui Y, Tian FB (2018) Benchmark numerical solutions for two-dimensional fluid–structure interaction involving large displacements with the deforming-spatial-domain/stabilized space-time and immersed boundary-lattice Boltzmann methods. J Mech Eng Sci 232:2500–2514CrossRefGoogle Scholar
  52. 52.
    Kalro V, Aliabadi S, Garrard W, Tezduyar T, Mittal S, Stein K (1997) Parallel finite element simulation of large ram-air parachutes. Int J Numer Methods Fluids 24:1353–1369zbMATHCrossRefGoogle Scholar
  53. 53.
    Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008a) Interface projection techniques for fluid–structure interaction modeling with moving-mesh methods. Comput Mech 43:39–49zbMATHCrossRefGoogle Scholar
  54. 54.
    Tezduyar TE, Sathe S, Schwaab M, Pausewang J, Christopher J, Crabtree J (2008b) Fluid–structure interaction modeling of ringsail parachutes. Comput Mech 43:133–142zbMATHCrossRefGoogle Scholar
  55. 55.
    Takizawa K, Spielman T, Tezduyar TE (2011) Space–time FSI modeling and dynamical analysis of spacecraft parachutes and parachute clusters. Comput Mech 48:345–364zbMATHCrossRefGoogle Scholar
  56. 56.
    Takizawa K, Fritze M, Montes D, Spielman T, Tezduyar TE (2012) Fluid–structure interaction modeling of ringsail parachutes with disreefing and modified geometric porosity. Comput Mech 50:835–854CrossRefGoogle Scholar
  57. 57.
    Takizawa K, Tezduyar TE (2012) Computational methods for parachute fluid–structure interactions. Arch Comput Methods Eng 19:125–169MathSciNetzbMATHCrossRefGoogle Scholar
  58. 58.
    Takizawa K, Spielman T, Moorman C, Tezduyar TE (2012) Fluid–structure interaction modeling of spacecraft parachutes for simulation-based design. J Appl Mech 79:010907CrossRefGoogle Scholar
  59. 59.
    Takizawa K, Montes D, Fritze M, McIntyre S, Boben J, Tezduyar TE (2013a) Methods for FSI modeling of spacecraft parachute dynamics and cover separation. Math Models Methods Appl Sci 23:307–338MathSciNetzbMATHCrossRefGoogle Scholar
  60. 60.
    Takizawa K, Tezduyar TE, Boben J, Kostov N, Boswell C, Buscher A (2013b) Fluid–structure interaction modeling of clusters of spacecraft parachutes with modified geometric porosity. Comput Mech 52:1351–1364zbMATHCrossRefGoogle Scholar
  61. 61.
    Takizawa K, Tezduyar TE, Kolesar R, Boswell C, Kanai T, Montel K (2014a) Multiscale methods for gore curvature calculations from FSI modeling of spacecraft parachutes. Comput Mech 54:1461–1476MathSciNetzbMATHCrossRefGoogle Scholar
  62. 62.
    Takizawa K, Tezduyar TE, Boswell C, Kolesar R, Montel K (2014b) FSI modeling of the reefed stages and disreefing of the Orion spacecraft parachutes. Comput Mech 54:1203–1220CrossRefGoogle Scholar
  63. 63.
    Takizawa K, Tezduyar TE, Kolesar R (2015a) FSI modeling of the Orion spacecraft drogue parachutes. Comput Mech 55:1167–1179zbMATHCrossRefGoogle Scholar
  64. 64.
    Takizawa K, Tezduyar TE, Boswell C, Tsutsui Y, Montel K (2015b) Special methods for aerodynamic-moment calculations from parachute FSI modeling. Comput Mech 55:1059–1069CrossRefGoogle Scholar
  65. 65.
    Takizawa K, Tezduyar TE, Terahara T (2016) Ram-air parachute structural and fluid mechanics computations with the space–time isogeometric analysis (ST-IGA). Comput Fluids 141:191–200MathSciNetzbMATHCrossRefGoogle Scholar
  66. 66.
    Takizawa K, Tezduyar TE, Kanai T (2017) Porosity models and computational methods for compressible-flow aerodynamics of parachutes with geometric porosity. Math Models Methods Appl Sci 27:771–806MathSciNetzbMATHCrossRefGoogle Scholar
  67. 67.
    Kanai T, Takizawa K, Tezduyar TE, Tanaka T, Hartmann A (2019) Compressible-flow geometric-porosity modeling and spacecraft parachute computation with isogeometric discretization. Comput Mech 63:301–321MathSciNetzbMATHCrossRefGoogle Scholar
  68. 68.
    Tezduyar TE, Takizawa K, Brummer T, Chen PR (2011) Space-time fluid–structure interaction modeling of patient-specific cerebral aneurysms. Int J Numer Methods Biomed Eng 27:1665–1710MathSciNetzbMATHCrossRefGoogle Scholar
  69. 69.
    Takizawa K, Bazilevs Y, Tezduyar TE (2012a) Space–time and ALE-VMS techniques for patient-specific cardiovascular fluid–structure interaction modeling. Arch Comput Methods Eng 19:171–225MathSciNetzbMATHCrossRefGoogle Scholar
  70. 70.
    Takizawa K, Schjodt K, Puntel A, Kostov N, Tezduyar TE (2012b) Patient-specific computer modeling of blood flow in cerebral arteries with aneurysm and stent. Comput Mech 50:675–686MathSciNetzbMATHCrossRefGoogle Scholar
  71. 71.
    Takizawa K, Schjodt K, Puntel A, Kostov N, Tezduyar TE (2013) Patient-specific computational analysis of the influence of a stent on the unsteady flow in cerebral aneurysms. Comput Mech 51:1061–1073MathSciNetzbMATHCrossRefGoogle Scholar
  72. 72.
    Takizawa K, Bazilevs Y, Tezduyar TE, Long CC, Marsden AL, Schjodt K (2014a) ST and ALE-VMS methods for patient-specific cardiovascular fluid mechanics modeling. Math Models Methods Appl Sci 24:2437–2486MathSciNetzbMATHCrossRefGoogle Scholar
  73. 73.
    Takizawa K, Tezduyar TE, Buscher A, Asada S (2014b) Space–time fluid mechanics computation of heart valve models. Comput Mech 54:973–986zbMATHCrossRefGoogle Scholar
  74. 74.
    Takizawa K, Torii R, Takagi H, Tezduyar TE, Xu XY (2014c) Coronary arterial dynamics computation with medical-image-based time-dependent anatomical models and element-based zero-stress state estimates. Comput Mech 54:1047–1053zbMATHCrossRefGoogle Scholar
  75. 75.
    Takizawa K, Tezduyar TE, Terahara T, Sasaki T (2017) Heart valve flow computation with the integrated space–time VMS, slip interface, topology change and isogeometric discretization methods. Comput Fluids 158:176–188MathSciNetzbMATHCrossRefGoogle Scholar
  76. 76.
    Sasaki T, Takizawa K, Tezduyar TE (2019) Medical-image-based aorta modeling with zero-stress-state estimation. Comput Mech 64:249–271MathSciNetzbMATHCrossRefGoogle Scholar
  77. 77.
    Takizawa K, Henicke B, Tezduyar TE, Hsu M-C, Bazilevs Y (2011a) Stabilized space–time computation of wind-turbine rotor aerodynamics. Comput Mech 48:333–344zbMATHCrossRefGoogle Scholar
  78. 78.
    Takizawa K, Henicke B, Montes D, Tezduyar TE, Hsu M-C, Bazilevs Y (2011b) Numerical-performance studies for the stabilized space–time computation of wind-turbine rotor aerodynamics. Comput Mech 48:647–657zbMATHCrossRefGoogle Scholar
  79. 79.
    Bazilevs Y, Hsu M-C, Takizawa K, Tezduyar TE (2012) ALE-VMS and ST-VMS methods for computer modeling of wind-turbine rotor aerodynamics and fluid-structure interaction. Math Models Methods Appl Sci 22(supp02):1230002zbMATHCrossRefGoogle Scholar
  80. 80.
    Takizawa K, Tezduyar TE, McIntyre S, Kostov N, Kolesar R, Habluetzel C (2014) Space–time VMS computation of wind-turbine rotor and tower aerodynamics. Comput Mech 53:1–15zbMATHCrossRefGoogle Scholar
  81. 81.
    Bazilevs Y, Takizawa K, Tezduyar TE, Hsu M-C, Kostov N, McIntyre S (2014) Aerodynamic and FSI analysis of wind turbines with the ALE-VMS and ST-VMS methods. Arch Comput Methods Eng 21:359–398MathSciNetzbMATHCrossRefGoogle Scholar
  82. 82.
    Castorrini A, Corsini A, Rispoli F, Venturini P, Takizawa K, Tezduyar TE (2016) Computational analysis of wind-turbine blade rain erosion. Comput Fluids 141:175–183MathSciNetzbMATHCrossRefGoogle Scholar
  83. 83.
    Korobenko A, Bazilevs Y, Takizawa K, Tezduyar TE (2018) Computer modeling of wind turbines: 1. ALE-VMS and ST-VMS aerodynamic and FSI analysis. Arch Comput Methods Eng. Available online  https://doi.org/10.1007/s11831-018-9292-1 MathSciNetCrossRefGoogle Scholar
  84. 84.
    Korobenko A, Bazilevs Y, Takizawa K, Tezduyar TE (2018) Computer modeling of wind turbines: 2. free-surface FSI and fatigue-damage. Arch Comput Methods Eng. Available online  https://doi.org/10.1007/s11831-018-9287-y MathSciNetCrossRefGoogle Scholar
  85. 85.
    Castorrini A, Corsini A, Rispoli F, Venturini P, Takizawa K, Tezduyar TE (2019) Computational analysis of performance deterioration of a wind turbine blade strip subjected to environmental erosion. Comput MechGoogle Scholar
  86. 86.
    Takizawa K, Bazilevs Y, Tezduyar TE, Hsu M-C, Øiseth O, Mathisen KM, Kostov N, McIntyre S (2014) Engineering analysis and design with ALE-VMS and space–time methods. Arch Comput Methods Eng 21:481–508MathSciNetzbMATHCrossRefGoogle Scholar
  87. 87.
    Tezduyar TE, Takizawa K (2019) Space–time computations in practical engineering applications: a summary of the 25-year history. Comput Mech 63:747–753zbMATHCrossRefGoogle Scholar
  88. 88.
    Tian FB, Bharti RP, Xu YQ (2013) Deforming-spatial-domain/stabilized space-time (DSD/SST) method in computation of non-Newtonian fluid flow and heat transfer with moving boundaries. Comput Mech 53:257–271MathSciNetzbMATHCrossRefGoogle Scholar
  89. 89.
    Tian FB, Dai H, Luo H, Doyle JF, Rousseau B (2014) Fluid–structure interaction involving large deformations: 3D simulations and applications to biological systems. J Comput Phys 258:451–469MathSciNetzbMATHCrossRefGoogle Scholar
  90. 90.
    Wang L, Currao GMD, Han F, Neely AJ, Young J, Tian FB (2017) An immersed boundary method for fluid-structure interaction with compressible multiphase flows. J Comput Phys 346:131–151MathSciNetzbMATHCrossRefGoogle Scholar
  91. 91.
    Xu L, Tian FB, Young J, Lai JCS (2018) A novel geometry-adaptive Cartesian grid based immersed boundary-lattice Boltzmann method for fluid-structure interactions at moderate and high Reynolds numbers. J Comput Phys 375:22–56MathSciNetzbMATHCrossRefGoogle Scholar
  92. 92.
    Tian FB, Tobing S, Young J, Lai JCS, Walker SM, Taylor GK, Thomas ALR (2019) Aerodynamic characteristics of hoverflies during hovering flight. Comput Fluids 183:75–83MathSciNetzbMATHCrossRefGoogle Scholar
  93. 93.
    Ma J, Tian FB, Young J, Lai JCS (2019) Dynamic characteristics of a deformable capsule in a simple shear flow. Phys Rev E 99:023101CrossRefGoogle Scholar
  94. 94.
    Wang L, Tian FB (2019) Numerical simulation of flow over a parallel cantilevered flag in the vicinity of a rigid wall. Phys Rev E 99:053111CrossRefGoogle Scholar
  95. 95.
    Huang WX, Tian FB (2019) Recent trends and progresses in the immersed boundary method. J Mech Eng Sci Available online.  https://doi.org/10.1177/0954406219842606
  96. 96.
    Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite element computation of 3D flows. Computer 26:27–36zbMATHCrossRefGoogle Scholar
  97. 97.
    Johnson AA, Tezduyar TE (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interface. Comput Methods Appl Mech Eng 119:73–94zbMATHCrossRefGoogle Scholar
  98. 98.
    Johnson AA, Tezduyar TE (1996) Simulation of multiple spheres falling in a liquid-filled tube. Comput Methods Appl Mech Eng 134:351–373MathSciNetzbMATHCrossRefGoogle Scholar
  99. 99.
    Johnson AA, Tezduyar TE (1997a) Parallel computation of incompressible flows with complex geometries. Int J Numer Methods Fluids 24:1321–1340zbMATHCrossRefGoogle Scholar
  100. 100.
    Johnson AA, Tezduyar TE (1997b) 3D simulation of fluid-particle interactions with the number of particles reaching 100. Comput Methods Appl Mech Eng 145:301–321zbMATHCrossRefGoogle Scholar
  101. 101.
    Johnson A, Tezduyar T (2001) Methods for 3D computation of fluid-object interactions in spatially-periodic flows. Comput Methods Appl Mech Eng 190:3201–3221zbMATHCrossRefGoogle Scholar
  102. 102.
    Tian FB (2014) FSI modeling with the DSD/SST method for the fluid and finite difference method for the structure. Comput Mech 54:581–589MathSciNetzbMATHCrossRefGoogle Scholar
  103. 103.
    Shen L, Zhang X, Yue DKP, Triantafyllou MS (2003) Turbulent flow over a flexible wall undergoing a streamwise travelling wave motion. J Fluid Mech 484:197–221zbMATHCrossRefGoogle Scholar
  104. 104.
    Wu JZ, Ma HY, Zhou MD (2006) Vorticity and vortex dynamics. Springer, BerlinCrossRefGoogle Scholar
  105. 105.
    Tian FB, Luo H, Zhu L, Lu XY (2011) Coupling modes of three filaments in side-by-side arrangement. Phys Fluids 23:111903CrossRefGoogle Scholar
  106. 106.
    Lighthill MJ (1952) On sound generated aerodynamically. I. General theory. Proc R Soc Lond A 211:564–587MathSciNetzbMATHCrossRefGoogle Scholar
  107. 107.
    Barrett DS, Triantafyllou MS, Yue DPK, Grosenbaugh MA, Wolfgang MJ (1999) Drag reduction in fish-like locomotion. J Fluid Mech 392:183–212MathSciNetzbMATHCrossRefGoogle Scholar
  108. 108.
    Tian FB, Zhu L, Fok PW, Lu XY (2013) Simulation of a pulsatile non-Newtonian flow past a stenosed 2D artery with atherosclerosis. Comput Biol Med 43:1098–1113CrossRefGoogle Scholar
  109. 109.
    Moulton JM (1960) Swimming sounds and the schooling of fishes. Biol Bull 119:210–223CrossRefGoogle Scholar
  110. 110.
    Farassat F (2007) Derivation of formulations 1 and 1A of Farassat, NASA Tech. Rep. TM-2007-214853Google Scholar
  111. 111.
    Wang L, Tian FB (2018) Heat transfer in non-newtonian flows by a hybrid immersed boundary-lattice boltzmann and finite difference method. Appl Sci 8:559CrossRefGoogle Scholar
  112. 112.
    Wang L, Tian FB (2019) Numerical study of flexible flapping wings with an immersed boundary method: fluid–structure–acoustics interaction. J Fluids Struct 90:396–409CrossRefGoogle Scholar

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Engineering and Information TechnologyUniversity of New South WalesCanberraAustralia

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