Advertisement

Computational Mechanics

, 48:293 | Cite as

Space–time SUPG finite element computation of shallow-water flows with moving shorelines

  • Shinsuke Takase
  • Kazuo Kashiyama
  • Seizo Tanaka
  • Tayfun E. Tezduyar
Original Paper

Abstract

We show that combination of the Deforming-Spatial-Domain/Stabilized Space–Time and the Streamline-Upwind/Petrov–Galerkin formulations can be used quite effectively for computation of shallow-water flows with moving shorelines. The combined formulation is supplemented with a stabilization parameter that was originally introduced for compressible flows, a compressible-flow shock-capturing parameter adapted for shallow-water flows, and remeshing based on using a background mesh. We present a number of test computations and provide comparisons to theoretical results, experimental data and results computed with nonmoving meshes.

Keywords

Shallow-water equations Space–time finite element method SUPG formulation Moving shorelines Background mesh Wave runup 

References

  1. 1.
    Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian–Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29: 329–349MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28: 1–44. doi: 10.1016/S0065-2156(08)70153-4 MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    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: 339–351. doi: 10.1016/0045-7825(92)90059-S MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    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: 353–371. doi: 10.1016/0045-7825(92)90060-W MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26: 27–36. doi: 10.1109/2.237441 CrossRefGoogle Scholar
  6. 6.
    Behr M, Johnson A, Kennedy J, Mittal S, Tezduyar T (1993) Computation of incompressible flows with implicit finite element implementations on the connection machine. Comput Methods Appl Mech Eng 108: 99–118. doi: 10.1016/0045-7825(93)90155-Q MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Tezduyar TE, Aliabadi SK, Behr M, Mittal S (1994) Massively parallel finite element simulation of compressible and incompressible flows. Comput Methods Appl Mech Eng 119: 157–177. doi: 10.1016/0045-7825(94)00082-4 zbMATHCrossRefGoogle Scholar
  8. 8.
    Mittal S, Tezduyar TE (1994) Massively parallel finite element computation of incompressible flows involving fluid-body interactions. Comput Methods Appl Mech Eng 112: 253–282. doi: 10.1016/0045-7825(94)90029-9 MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Mittal S, Tezduyar TE (1995) Parallel finite element simulation of 3D incompressible flows—fluid-structure interactions. Int J Numer Methods Fluids 21: 933–953. doi: 10.1002/fld.1650211011 zbMATHCrossRefGoogle Scholar
  10. 10.
    Aliabadi SK, Tezduyar TE (1995) Parallel fluid dynamics computations in aerospace applications. Int J Numer Methods Fluids 21: 783–805. doi: 10.1002/fld.1650211003 MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Tezduyar T, Aliabadi S, Behr M, Johnson A, Kalro V, Litke M (1996) Flow simulation and high performance computing. Comput Mech 18: 397–412. doi: 10.1007/BF00350249 zbMATHCrossRefGoogle Scholar
  12. 12.
    Johnson AA, Tezduyar TE (1997) Parallel computation of incompressible flows with complex geometries. Int J Numer Methods Fluids 24: 1321–1340. doi: 10.1002/(SICI)1097-0363(199706)24:12<1321::AID-FLD562>3.3.CO;2-C zbMATHCrossRefGoogle Scholar
  13. 13.
    Guler I, Behr M, Tezduyar T (1999) Parallel finite element computation of free-surface flows. Comput Mech 23: 117–123. doi: 10.1007/s004660050391 CrossRefGoogle Scholar
  14. 14.
    Johnson AA, Tezduyar TE (1999) Advanced mesh generation and update methods for 3D flow simulations. Comput Mech 23: 130–143. doi: 10.1007/s004660050393 zbMATHCrossRefGoogle Scholar
  15. 15.
    Behr M, Tezduyar T (1999) The shear-slip mesh update method. Comput Methods Appl Mech Eng 174: 261–274. doi: 10.1016/S0045-7825(98)00299-0 zbMATHCrossRefGoogle Scholar
  16. 16.
    Kalro V, Tezduyar TE (2000) A parallel 3D computational method for fluid–structure interactions in parachute systems. Comput Methods Appl Mech Eng 190: 321–332. doi: 10.1016/S0045-7825(00)00204-8 zbMATHCrossRefGoogle Scholar
  17. 17.
    Stein K, Benney R, Kalro V, Tezduyar TE, Leonard J, Accorsi M (2000) Parachute fluid–structure interactions: 3-D computation. Comput Methods Appl Mech Eng 190: 373–386. doi: 10.1016/S0045-7825(00)00208-5 zbMATHCrossRefGoogle Scholar
  18. 18.
    Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8: 83–130. doi: 10.1007/BF02897870 zbMATHCrossRefGoogle Scholar
  19. 19.
    Tezduyar T, Osawa Y (2001) Fluid–structure interactions of a parachute crossing the far wake of an aircraft. Comput Methods Appl Mech Eng 191: 717–726. doi: 10.1016/S0045-7825(01)00311-5 zbMATHCrossRefGoogle Scholar
  20. 20.
    Stein K, Benney R, Tezduyar T, Potvin J (2001) Fluid–structure interactions of a cross parachute: Numerical simulation. Comput Methods Appl Mech Eng 191: 673–687. doi: 10.1016/S0045-7825(01)00312-7 zbMATHCrossRefGoogle Scholar
  21. 21.
    Ohayon R (2001) Reduced symmetric models for modal analysis of internal structural-acoustic and hydroelastic-sloshing systems. Comput Methods Appl Mech Eng 190: 3009–3019zbMATHCrossRefGoogle Scholar
  22. 22.
    Stein K, Tezduyar T, Benney R (2003) Mesh moving techniques for fluid–structure interactions with large displacements. J Appl Mech 70: 58–63. doi: 10.1115/1.1530635 zbMATHCrossRefGoogle Scholar
  23. 23.
    Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43: 555–575. doi: 10.1002/fld.505 MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Stein K, Tezduyar TE, Benney R (2004) Automatic mesh update with the solid-extension mesh moving technique. Comput Methods Appl Mech Eng 193: 2019–2032. doi: 10.1016/j.cma.2003.12.046 zbMATHCrossRefGoogle Scholar
  25. 25.
    van Brummelen EH, de Borst R (2005) On the nonnormality of subiteration for a fluid-structure interaction problem. SIAM J Sci Comput 27: 599–621MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Tezduyar TE, Sathe S, Keedy R, Stein K (2006) Space–time finite element techniques for computation of fluid–structure interactions. Comput Methods Appl Mech Eng 195: 2002–2027. doi: 10.1016/j.cma.2004.09.014 MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Tezduyar TE, Sathe S, Stein K (2006) Solution techniques for the fully-discretized equations in computation of fluid–structure interactions with the space–time formulations. Comput Methods Appl Mech Eng 195: 5743–5753. doi: 10.1016/j.cma.2005.08.023 MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Computer modeling of cardiovascular fluid–structure interactions with the deforming-spatial-domain/stabilized space–time formulation. Comput Methods Appl Mech Eng 195: 1885–1895. doi: 10.1016/j.cma.2005.05.050 MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Fluid–structure interaction modeling of aneurysmal conditions with high and normal blood pressures. Comput Mech 38: 482–490. doi: 10.1007/s00466-006-0065-6 zbMATHCrossRefGoogle Scholar
  30. 30.
    Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid–structure interaction analysis with applications to arterial blood flow. Comput Mech 38: 310–322MathSciNetzbMATHCrossRefGoogle Scholar
  31. 31.
    Khurram RA, Masud A (2006) A multiscale/stabilized formulation of the incompressible Navier–Stokes equations for moving boundary flows and fluid–structure interaction. Comput Mech 38: 403–416zbMATHCrossRefGoogle Scholar
  32. 32.
    Tezduyar TE (2007) Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids 36: 191–206. doi: 10.1016/j.compfluid.2005.02.011 MathSciNetzbMATHCrossRefGoogle Scholar
  33. 33.
    Brenk M, Bungartz H-J, Mehl M, Neckel T (2006) Fluid–structure interaction on Cartesian grids: flow simulation and coupling environment. In: Bungartz H-J, Schafer M (eds) Fluid–structure interaction. Lecture notes in computational science and engineering, vol 53. Springer, Berlin, pp 233–269Google Scholar
  34. 34.
    Tezduyar TE, Sathe S, Cragin T, Nanna B, Conklin BS, Pausewang J, Schwaab M (2007) Modeling of fluid–structure interactions with the space–time finite elements: arterial fluid mechanics. Int J Numer Methods Fluids 54: 901–922. doi: 10.1002/fld.1443 MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2007) Influence of wall elasticity in patient-specific hemodynamic simulations. Comput Fluids 36: 160–168. doi: 10.1016/j.compfluid.2005.07.014 zbMATHCrossRefGoogle Scholar
  36. 36.
    Cruchaga MA, Celentano DJ, Tezduyar TE (2007) Collapse of a liquid column: numerical simulation and experimental validation. Comput Mech 39: 453–476. doi: 10.1007/s00466-006-0043-z zbMATHCrossRefGoogle Scholar
  37. 37.
    Sawada T, Hisada T (2007) Fluid–structure interaction analysis of the two dimensional flag-in-wind problem by an interface tracking ALE finite element method. Comput Fluids 36: 136–146zbMATHCrossRefGoogle Scholar
  38. 38.
    Tezduyar TE, Sathe S (2007) Modeling of fluid–structure interactions with the space–time finite elements: solution techniques. Int J Numer Methods Fluids 54: 855–900. doi: 10.1002/fld.1430 MathSciNetzbMATHCrossRefGoogle Scholar
  39. 39.
    Takizawa K, Yabe T, Tsugawa Y, Tezduyar TE, Mizoe H (2007) Computation of free–surface flows and fluid–object interactions with the CIP method based on adaptive meshless Soroban grids. Comput Mech 40: 167–183. doi: 10.1007/s00466-006-0093-2 zbMATHCrossRefGoogle Scholar
  40. 40.
    Takizawa K, Tanizawa K, Yabe T, Tezduyar TE (2007) Ship hydrodynamics computations with the CIP method based on adaptive Soroban grids. Int J Numer Methods Fluids 54: 1011–1019. doi: 10.1002/fld.1466 zbMATHCrossRefGoogle Scholar
  41. 41.
    Yabe T, Takizawa K, Tezduyar TE, Im H-N (2007) Computation of fluid–solid and fluid–fluid interfaces with the CIP method based on adaptive Soroban grids—an overview. Int J Numer Methods Fluids 54: 841–853. doi: 10.1002/fld.1473 MathSciNetzbMATHCrossRefGoogle Scholar
  42. 42.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2007) Numerical investigation of the effect of hypertensive blood pressure on cerebral aneurysm—dependence of the effect on the aneurysm shape. Int J Numer Methods Fluids 54: 995–1009. doi: 10.1002/fld.1497 MathSciNetzbMATHCrossRefGoogle Scholar
  43. 43.
    Manguoglu M, Sameh AH, Tezduyar TE, Sathe S (2008) A nested iterative scheme for computation of incompressible flows in long domains. Comput Mech 43: 73–80. doi: 10.1007/s00466-008-0276-0 MathSciNetzbMATHCrossRefGoogle Scholar
  44. 44.
    Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008) Interface projection techniques for fluid–structure interaction modeling with moving-mesh methods. Comput Mech 43: 39–49. doi: 10.1007/s00466-008-0261-7 zbMATHCrossRefGoogle Scholar
  45. 45.
    Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008) Fluid–structure interaction modeling of ringsail parachutes. Comput Mech 43: 133–142. doi: 10.1007/s00466-008-0260-8 zbMATHCrossRefGoogle Scholar
  46. 46.
    Tezduyar TE, Sathe S, Schwaab M, Conklin BS (2008) Arterial fluid mechanics modeling with the stabilized space–time fluid–structure interaction technique. Int J Numer Methods Fluids 57: 601–629. doi: 10.1002/fld.1633 MathSciNetzbMATHCrossRefGoogle Scholar
  47. 47.
    Sathe S, Tezduyar TE (2008) Modeling of fluid–structure interactions with the space–time finite elements: contact problems. Comput Mech 43: 51–60. doi: 10.1007/s00466-008-0299-6 MathSciNetzbMATHCrossRefGoogle Scholar
  48. 48.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2008) Fluid–structure interaction modeling of a patient-specific cerebral aneurysm: influence of structural modeling. Comput Mech 43: 151–159. doi: 10.1007/s00466-008-0325-8 zbMATHCrossRefGoogle Scholar
  49. 49.
    Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid–structure interaction: theory, algorithms, and computations. Comput Mech 43: 3–37MathSciNetzbMATHCrossRefGoogle Scholar
  50. 50.
    Isaksen JG, Bazilevs Y, Kvamsdal T, Zhang Y, Kaspersen JH, Waterloo K, Romner B, Ingebrigtsen T (2008) Determination of wall tension in cerebral artery aneurysms by numerical simulation. Stroke 39: 3172–3178CrossRefGoogle Scholar
  51. 51.
    Dettmer WG, Peric D (2008) On the coupling between fluid flow and mesh motion in the modelling of fluid–structure interaction. Comput Mech 43: 81–90zbMATHCrossRefGoogle Scholar
  52. 52.
    Tezduyar TE, Schwaab M, Sathe S (2009) Sequentially-coupled arterial fluid–structure interaction (SCAFSI) technique. Comput Methods Appl Mech Eng 198: 3524–3533. doi: 10.1016/j.cma.2008.05.024 MathSciNetzbMATHCrossRefGoogle Scholar
  53. 53.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2009) Fluid–structure interaction modeling of blood flow and cerebral aneurysm: significance of artery and aneurysm shapes. Comput Methods Appl Mech Eng 198: 3613–3621. doi: 10.1016/j.cma.2008.08.020 MathSciNetzbMATHCrossRefGoogle Scholar
  54. 54.
    Manguoglu M, Sameh AH, Saied F, Tezduyar TE, Sathe S (2009) Preconditioning techniques for nonsymmetric linear systems in computation of incompressible flows. J Appl Mech 76: 021204. doi: 10.1115/1.3059576 CrossRefGoogle Scholar
  55. 55.
    Bazilevs Y, Gohean JR, Hughes TJR, Moser RD, Zhang Y (2009) Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device. Comput Methods Appl Mech Eng 198: 3534–3550MathSciNetzbMATHCrossRefGoogle Scholar
  56. 56.
    Bazilevs Y, Hsu M-C, Benson D, Sankaran S, Marsden A (2009) Computational fluid–structure interaction: methods and application to a total cavopulmonary connection. Comput Mech 45: 77–89MathSciNetzbMATHCrossRefGoogle Scholar
  57. 57.
    Takizawa K, Christopher J, Tezduyar TE, Sathe S (2010) Space–time finite element computation of arterial fluid–structure interactions with patient-specific data. Int J Numer Methods Biomed Eng 26: 101–116. doi: 10.1002/cnm.1241 zbMATHCrossRefGoogle Scholar
  58. 58.
    Takizawa K, Moorman C, Wright S, Christopher J, Tezduyar TE (2010) Wall shear stress calculations in space–time finite element computation of arterial fluid–structure interactions. Comput Mech 46: 31–41. doi: 10.1007/s00466-009-0425-0 MathSciNetzbMATHCrossRefGoogle Scholar
  59. 59.
    Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Multiscale sequentially-coupled arterial FSI technique. Comput Mech 46: 17–29. doi: 10.1007/s00466-009-0423-2 MathSciNetzbMATHCrossRefGoogle Scholar
  60. 60.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2010) Influence of wall thickness on fluid–structure interaction computations of cerebral aneurysms. Int J Numer Methods Biomed Eng 26: 336–347. doi: 10.1002/cnm.1289 MathSciNetzbMATHCrossRefGoogle Scholar
  61. 61.
    Manguoglu M, Takizawa K, Sameh AH, Tezduyar TE (2010) Solution of linear systems in arterial fluid mechanics computations with boundary layer mesh refinement. Comput Mech 46: 83–89. doi: 10.1007/s00466-009-0426-z zbMATHCrossRefGoogle Scholar
  62. 62.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2010) Role of 0D peripheral vasculature model in fluid–structure interaction modeling of aneurysms. Comput Mech 46: 43–52. doi: 10.1007/s00466-009-0439-7 zbMATHCrossRefGoogle Scholar
  63. 63.
    Bazilevs Y, Hsu M-C, Zhang Y, Wang W, Liang X, Kvamsdal T, Brekken R, Isaksen J (2010) A fully-coupled fluid–structure interaction simulation of cerebral aneurysms. Comput Mech 46: 3–16MathSciNetzbMATHCrossRefGoogle Scholar
  64. 64.
    Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Space–time finite element computation of complex fluid–structure interactions. Int J Numer Methods Fluids 64: 1201–1218. doi: 10.1002/fld.2221 zbMATHCrossRefGoogle Scholar
  65. 65.
    Bazilevs Y, Hsu M-C, Zhang Y, Wang W, Kvamsdal T, Hentschel S, Isaksen J (2010) Computational fluid–structure interaction: methods and application to cerebral aneurysms. Biomech Model Mechanobiol 9: 481–498CrossRefGoogle Scholar
  66. 66.
    Kiendl J, Bazilevs Y, Hsu M-C, Wüchner R, Bletzinger K-U (2010) The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches. Comput Methods Appl Mech Eng 199: 2403–2416CrossRefGoogle Scholar
  67. 67.
    Bazilevs Y, Hsu M-C, Akkerman I, Wright S, Takizawa K, Henicke B, Spielman T, Tezduyar TE (2011) 3D simulation of wind turbine rotors at full scale. Part I: geometry modeling and aerodynamics. Int J Numer Methods Fluids 65: 207–235. doi: 10.1002/fld.2400 zbMATHCrossRefGoogle Scholar
  68. 68.
    Bazilevs Y, Hsu M-C, Kiendl J, Wüchner R, Bletzinger K-U (2011) 3D simulation of wind turbine rotors at full scale. Part II: fluid–structure interaction modeling with composite blades. Int J Numer Methods Fluids 65: 236–253zbMATHCrossRefGoogle Scholar
  69. 69.
    Takizawa K, Moorman C, Wright S, Spielman T, Tezduyar TE (2011) Fluid–structure interaction modeling and performance analysis of the Orion spacecraft parachutes. Int J Numer Methods Fluids 65: 271–285. doi: 10.1002/fld.2348 zbMATHCrossRefGoogle Scholar
  70. 70.
    Takizawa K, Moorman C, Wright S, Purdue J, McPhail T, Chen PR, Warren J, Tezduyar TE (2011) Patient-specific arterial fluid–structure interaction modeling of cerebral aneurysms. Int J Numer Methods Fluids 65: 308–323. doi: 10.1002/fld.2360 zbMATHCrossRefGoogle Scholar
  71. 71.
    Hsu M-C, Bazilevs Y (2011) Blood vessel tissue prestress modeling for vascular fluid–structure interaction simulations. Finite Elem Anal Des 47: 593–599CrossRefMathSciNetGoogle Scholar
  72. 72.
    Akkerman I, Bazilevs Y, Kees CE, Farthing MW (2011) Isogeometric analysis of free-surface flow. J Comput Phys 230: 4137–4152zbMATHCrossRefMathSciNetGoogle Scholar
  73. 73.
    Takizawa K, Wright S, Moorman C, Tezduyar TE (2011) Fluid–structure interaction modeling of parachute clusters. Int J Numer Methods Fluids 65: 286–307. doi: 10.1002/fld.2359 zbMATHCrossRefGoogle Scholar
  74. 74.
    Manguoglu M, Takizawa K, Sameh AH, Tezduyar TE (2011) Nested and parallel sparse algorithms for arterial fluid mechanics computations with boundary layer mesh refinement. Int J Numer Methods Fluids 65: 135–149. doi: 10.1002/fld.2415 MathSciNetzbMATHCrossRefGoogle Scholar
  75. 75.
    Kees CE, Akkerman I, Farthing MW, Bazilevs Y (2011) A conservative level set method suitable for variable-order approximations and unstructured meshes. J Comput Phys 230: 4536–4558zbMATHCrossRefMathSciNetGoogle Scholar
  76. 76.
    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 (published online). doi: 10.1002/cnm.1433, Feb 2011
  77. 77.
    Takizawa K, Tezduyar TE (2011) Multiscale space–time fluid–structure interaction techniques. Computat Mech (published online). doi: 10.1007/s00466-011-0571-z, Feb 2011
  78. 78.
    Takizawa K, Henicke B, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Stabilized space–time computation of wind-turbine rotor aerodynamics. Comput Mech (published online). doi: 10.1007/s00466-011-0589-2, March 2011
  79. 79.
    Takizawa K, Spielman T, Tezduyar TE (2011) Space–time FSI modeling and dynamical analysis of spacecraft parachutes and parachute clusters. Comput Mech (published online). doi: 10.1007/s00466-011-0590-9, April 2011
  80. 80.
    Takizawa K, Spielman T, Moorman C, Tezduyar TE (2011) Fluid–structure interaction modeling of spacecraft parachutes for simulation-based design. J Appl Mech (to appear)Google Scholar
  81. 81.
    Takizawa K, Brummer T, Tezduyar TE, Chen PR (2011) A comparative study based on patient-specific fluid–structure interaction modeling of cerebral aneurysms. J Appl Mech (to appear)Google Scholar
  82. 82.
    Takizawa K, Henicke B, Puntel A, Spielman T, Tezduyar TE (2011) Space–time computational techniques for the aerodynamics of flapping wings. J Appl Mech (to appear)Google Scholar
  83. 83.
    Takizawa K, Henicke B, Montes D, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Numerical-performance studies for the stabilized space–time computation of wind-turbine rotor aerodynamics. Comput Mech (published online). doi: 10.1007/s00466-011-0614-5, July 2011
  84. 84.
    Akkerman I, Bazilevs Y, Benson DJ, Farthing MW, Kees CE (2011) Free-surface flow and fluid–object interaction modeling with emphasis on ship hydrodynamics. J Appl Mech (accepted)Google Scholar
  85. 85.
    Hsu M-C, Akkerman I, Bazilevs Y (2011) High-performance computing of wind turbine aerodynamics using isogeometric analysis. Comput Fluids (published online). doi: 10.1016/j.compfluid.2011.05.002
  86. 86.
    Bazilevs Y, Hsu M-C, Kiendl J, Benson DJ (2011) A computational procedure for pre-bending of wind turbine blades. Int J Numer Methods Eng (accepted)Google Scholar
  87. 87.
    Tezduyar T, Aliabadi S, Behr M (1998) Enhanced-discretization interface-capturing technique (EDICT) for computation of unsteady flows with interfaces. Comput Methods Appl Mech Eng 155: 235–248. doi: 10.1016/S0045-7825(97)00194-1 zbMATHCrossRefGoogle Scholar
  88. 88.
    Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng 32: 199–259MathSciNetzbMATHCrossRefGoogle Scholar
  89. 89.
    Hughes TJR, Tezduyar TE (1984) Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. Comput Methods Appl Mech Eng 45: 217–284. doi: 10.1016/0045-7825(84)90157-9 MathSciNetzbMATHCrossRefGoogle Scholar
  90. 90.
    Tezduyar TE, Mittal S, Ray SE, Shih R (1992) Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput Methods Appl Mech Eng 95: 221–242. doi: 10.1016/0045-7825(92)90141-6 zbMATHCrossRefGoogle Scholar
  91. 91.
    Hughes TJR (1995) Multiscale phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles, and the origins of stabilized methods. Comput Methods Appl Mech Eng 127: 387–401zbMATHCrossRefGoogle Scholar
  92. 92.
    Hughes TJR, Oberai AA, Mazzei L (2001) Large eddy simulation of turbulent channel flows by the variational multiscale method. Phys Fluids 13: 1784–1799CrossRefGoogle Scholar
  93. 93.
    Bazilevs Y, Calo VM, Cottrel JA, Hughes TJR, Reali A, Scovazzi G (2007) Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng 197: 173–201zbMATHCrossRefGoogle Scholar
  94. 94.
    Johnson AA, Tezduyar TE (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput Methods Appl Mech Eng 119: 73–94. doi: 10.1016/0045-7825(94)00077-8 zbMATHCrossRefGoogle Scholar
  95. 95.
    Behr M, Tezduyar T (2001) Shear-slip mesh update in 3D computation of complex flow problems with rotating mechanical components. Comput Methods Appl Mech Eng 190: 3189–3200. doi: 10.1016/S0045-7825(00)00388-1 zbMATHCrossRefGoogle Scholar
  96. 96.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2004) Influence of wall elasticity on image-based blood flow simulation. Jpn Soc Mech Eng J Ser A 70:1224–1231 (in Japanese)Google Scholar
  97. 97.
    Aliabadi SK, Tezduyar TE (1993) Space–time finite element computation of compressible flows involving moving boundaries and interfaces. Comput Methods Appl Mech Eng 107: 209–223. doi: 10.1016/0045-7825(93)90176-X zbMATHCrossRefGoogle Scholar
  98. 98.
    Le Beau GJ, Ray SE, Aliabadi SK, Tezduyar TE (1993) SUPG finite element computation of compressible flows with the entropy and conservation variables formulations. Comput Methods Appl Mech Eng 104: 397–422. doi: 10.1016/0045-7825(93)90033-T zbMATHCrossRefGoogle Scholar
  99. 99.
    Tezduyar TE, Hughes TJR (1982) Development of time-accurate finite element techniques for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. NASA technical report NASA-CR-204772, NASA. http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19970023187_1997034954.pdf
  100. 100.
    Tezduyar TE, Hughes TJR (1983) Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations. In: Proceedings of AIAA 21st aerospace sciences meeting, AIAA paper 83-0125, Reno, NevadaGoogle Scholar
  101. 101.
    Hughes TJR, Mallet M (1986) A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems. Comput Methods Appl Mech Eng 58: 329–339MathSciNetzbMATHCrossRefGoogle Scholar
  102. 102.
    Hughes TJR, Franca LP, Mallet M (1987) A new finite element formulation for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multi-dimensional advective-diffusive systems. Comput Methods Appl Mech Eng 63: 97–112MathSciNetzbMATHCrossRefGoogle Scholar
  103. 103.
    Le Beau GJ, Tezduyar TE (1991) Finite element computation of compressible flows with the SUPG formulation. In: Advances in finite element analysis in fluid dynamics, FED-vol 123. ASME, New York, pp 21–27Google Scholar
  104. 104.
    Tezduyar TE, Park YJ (1986) Discontinuity capturing finite element formulations for nonlinear convection-diffusion-reaction equations. Comput Methods Appl Mech Eng 59: 307–325. doi: 10.1016/0045-7825(86)90003-4 zbMATHCrossRefGoogle Scholar
  105. 105.
    Tezduyar TE, Osawa Y (2000) Finite element stabilization parameters computed from element matrices and vectors. Comput Methods Appl Mech Eng 190: 411–430. doi: 10.1016/S0045-7825(00)00211-5 zbMATHCrossRefGoogle Scholar
  106. 106.
    Catabriga L, Coutinho ALGA, Tezduyar TE (2005) Compressible flow SUPG parameters computed from element matrices. Commun Numer Methods Eng 21: 465–476. doi: 10.1002/cnm.759 MathSciNetzbMATHCrossRefGoogle Scholar
  107. 107.
    Catabriga L, Coutinho ALGA, Tezduyar TE (2006) Compressible flow SUPG parameters computed from degree-of-freedom submatrices. Comput Mech 38: 334–343. doi: 10.1007/s00466-006-0033-1 zbMATHCrossRefGoogle Scholar
  108. 108.
    Tezduyar TE (2004) Finite element methods for fluid dynamics with moving boundaries and interfaces. In: Stein E, Borst RD, Hughes TJR (eds) Encyclopedia of computational mechanics. Fluids, vol 3, Chap 17. Wiley, New YorkGoogle Scholar
  109. 109.
    Tezduyar TE, Senga M (2006) Stabilization and shock-capturing parameters in SUPG formulation of compressible flows. Comput Methods Appl Mech Eng 195: 1621–1632. doi: 10.1016/j.cma.2005.05.032 MathSciNetzbMATHCrossRefGoogle Scholar
  110. 110.
    Tezduyar TE, Senga M (2007) SUPG finite element computation of inviscid supersonic flows with YZβ shock-capturing. Comput Fluids 36: 147–159. doi: 10.1016/j.compfluid.2005.07.009 zbMATHCrossRefGoogle Scholar
  111. 111.
    Tezduyar TE, Senga M, Vicker D (2006) Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and YZβ shock-capturing. Comput Mech 38: 469–481. doi: 10.1007/s00466-005-0025-6 zbMATHCrossRefGoogle Scholar
  112. 112.
    Corsini A, Rispoli F, Santoriello A (2005) A variational multiscale high-order finite element formulation for turbomachinery flow computations. Comput Methods Appl Mech Eng 194: 4797–4823MathSciNetzbMATHCrossRefGoogle Scholar
  113. 113.
    Rispoli F, Saavedra R (2006) A stabilized finite element method based on SGS models for compressible flows. Comput Methods Appl Mech Eng 196: 652–664zbMATHCrossRefGoogle Scholar
  114. 114.
    Rispoli F, Saavedra R, Corsini A, Tezduyar TE (2007) Computation of inviscid compressible flows with the V-SGS stabilization and YZβ shock-capturing. Int J Numer Methods Fluids 54: 695–706. doi: 10.1002/fld.1447 MathSciNetzbMATHCrossRefGoogle Scholar
  115. 115.
    Rispoli F, Saavedra R, Menichini F, Tezduyar TE (2009) Computation of inviscid supersonic flows around cylinders and spheres with the V-SGS stabilization and YZβ shock-capturing. J Appl Mech 76: 021209. doi: 10.1115/1.3057496 CrossRefGoogle Scholar
  116. 116.
    Catabriga L, de Souza DAF, Coutinho ALGA, Tezduyar TE (2009) Three-dimensional edge-based SUPG computation of inviscid compressible flows with YZβ shock-capturing. J Appl Mech 76: 021208. doi: 10.1115/1.3062968 CrossRefGoogle Scholar
  117. 117.
    Kawahara M, Takeuchi N, Yoshida T (1978) Two step explicit finite element method for tsunami wave-propagation analysis. Int J Numer Methods Eng 12: 331–351zbMATHCrossRefGoogle Scholar
  118. 118.
    Kawahara M, Hirano H, Tsubota K, Inagaki K (1982) Selective lumping finite element method for shallow water flow. Int J Numer Methods Fluids 2: 89–112zbMATHCrossRefGoogle Scholar
  119. 119.
    Gopalakrishnan TC, Tung CC (1983) Numerical analysis of moving boundary problem in coastal hydrodynamics. Int J Numer Methods Fluids 3: 179–200zbMATHCrossRefGoogle Scholar
  120. 120.
    Kawahara M, Kashiyama K (1984) Selective lumping finite element method for nearshore current. Int J Numer Methods Fluids 4: 71–97zbMATHCrossRefGoogle Scholar
  121. 121.
    Kawahara M, Umetsu T (1986) Finite element method for moving boundary problems in river flow. Int J Numer Methods Fluids 6: 365–386zbMATHCrossRefGoogle Scholar
  122. 122.
    Okamoto T, Kawahara M, Ioki N, Nagaoka H (1992) Two-dimensional wave runup analysis by selective lumping finite element method. Int J Numer Methods Fluids 14: 1219–1243zbMATHCrossRefGoogle Scholar
  123. 123.
    Kashiyama K, Ito H, Behr M, Tezduyar T (1995) Three-step explicit finite element computation of shallow water flows on a massively parallel computer. Int J Numer Methods Fluids 21: 885–900. doi: 10.1002/fld.1650211009 zbMATHCrossRefGoogle Scholar
  124. 124.
    Luettich RA, Westerink JJ (1995) Implementation and testing of elemental flooding and drying in the ADCIRC hydrodynamic model. Final contract report DACW39-94-M-5869, US Army Corps of EngineersGoogle Scholar
  125. 125.
    Kashiyama K, Saitoh K, Behr M, Tezduyar TE (1997) Parallel finite element methods for large-scale computation of storm surges and tidal flows. Int J Numer Methods n Fluids 24: 1371–1389. doi: 10.1002/(SICI)1097-0363(199706)24:12<1371::AID-FLD565>3.0.CO;2-7 zbMATHCrossRefGoogle Scholar
  126. 126.
    Kashiyama K, Ohba Y, Takagi T, Behr M, Tezduyar T (1999) Parallel finite element method utilizing the mode splitting and sigma coordinate for shallow water flows. Comput Mech 23: 144–150. doi: 10.1007/s004660050394 zbMATHCrossRefGoogle Scholar
  127. 127.
    Kashiyama K, Sugano S, Behr M, Tezduyar TE (1999) Space–time finite element method for shallow water flows considering moving boundaries. In: Proceedings of the 3rd ASME/JSME joint fluids engineering conference, San Francisco, California (1999)Google Scholar
  128. 128.
    Heniche M, Secretan Y, Boudreau P, Leclerc M (2000) A two-dimensional finite element drying-wetting shallow water model for rivers and estuaries. Adv Water Resour 23: 360–371CrossRefGoogle Scholar
  129. 129.
    Dawson C, Westerink JJ, Feyen JC, Pothian D (2006) Edge-based finite element method for shallow water equations. Int J Numer Methods Fluids 52: 63–88zbMATHCrossRefGoogle Scholar
  130. 130.
    Kubatko EJ, Bunya S, Dawson C, Westerink JJ (2009) Dynamic p-adaptive Runge-Kutta discontinuous Galerkin methods for the shallow water equations. Comput Methods Appl Mech Eng 198: 1766–1774MathSciNetCrossRefGoogle Scholar
  131. 131.
    Bunya S, Kubatko EJ, Westerink JJ, Dawson C (2009) Wetting and drying treatment for the Runge–Kutta discontinuous Galerkin solution to the shallow water equations. Comput Methods Appl Mech Eng 198: 1548–1562MathSciNetCrossRefGoogle Scholar
  132. 132.
    Takase S, Kashiyama K, Tanaka S, Tezduyar TE (2010) Space–time SUPG formulation of the shallow-water equations. Int J Numer Methods Fluids 64: 1379–1394. doi: 10.1002/fld.2464 MathSciNetzbMATHCrossRefGoogle Scholar
  133. 133.
    Rispoli F, Corsini A, Tezduyar TE (2007) Finite element computation of turbulent flows with the discontinuity-capturing directional dissipation (DCDD). Comput Fluids 36: 121–126. doi: 10.1016/j.compfluid.2005.07.004 zbMATHCrossRefGoogle Scholar
  134. 134.
    Tanaka S, Kashiyama K (2006) A new mesh re-generation technique for free surface flow analysis based on interface-tracking method. J Struct Mech Earthq Eng 2: 269–277CrossRefGoogle Scholar
  135. 135.
    Tanaka S, Kashiyama K (2006) ALE finite element method for FSI problems with free surface using mesh re-generation method based on background mesh. Int J Comput Fluid Dyn 20: 229–236zbMATHCrossRefGoogle Scholar
  136. 136.
    Dean RG, Dalrymple RA (1984) Water wave mechanics for engineers and scientists. Prentice-Hall, New JerseyGoogle Scholar
  137. 137.
    Mittal S, Aliabadi S, Tezduyar T (1999) Parallel computation of unsteady compressible flows with the EDICT. Comput Mech 23: 151–157. doi: 10.1007/s004660050395 zbMATHCrossRefGoogle Scholar
  138. 138.
    Tezduyar TE, Sathe S (2006) Enhanced-discretization selective stabilization procedure (EDSSP). Comput Mech 38: 456–468. doi: 10.1007/s00466-006-0056-7 zbMATHCrossRefGoogle Scholar
  139. 139.
    Corsini A, Rispoli F, Santoriello A, Tezduyar TE (2006) Improved discontinuity-capturing finite element techniques for reaction effects in turbulence computation. Comput Mech 38: 356–364. doi: 10.1007/s00466-006-0045-x MathSciNetzbMATHCrossRefGoogle Scholar
  140. 140.
    Corsini A, Menichini C, Rispoli F, Santoriello A, Tezduyar TE (2009) A multiscale finite element formulation with discontinuity capturing for turbulence models with dominant reactionlike terms. J Appl Mech 76: 021211. doi: 10.1115/1.3062967 CrossRefGoogle Scholar
  141. 141.
    Corsini A, Iossa C, Rispoli F, Tezduyar TE (2010) A DRD finite element formulation for computing turbulent reacting flows in gas turbine combustors. Comput Mech 46: 159–167. doi: 10.1007/s00466-009-0441-0 MathSciNetzbMATHCrossRefGoogle Scholar
  142. 142.
    Tanaka N (1999) The CIVA method for mesh-free approaches: improvement of the CIP method for n-simplex. Comput Fluid Dyn J 8: 121–127Google Scholar
  143. 143.
    Carrier GF, Greenspan HP (1958) Water waves of finite amplitude on a sloping beach. J Fluid Mech 4: 97–109MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Shinsuke Takase
    • 1
  • Kazuo Kashiyama
    • 2
  • Seizo Tanaka
    • 3
  • Tayfun E. Tezduyar
    • 4
  1. 1.Research Center of Computational Mechanics, Inc.Togoshi, Shinagawa-kuJapan
  2. 2.Department of Civil and Environmental EngineeringChuo UniversityBunkyo-kuJapan
  3. 3.Earthquake Research InstituteUniversity of TokyoBunkyo-ku, TokyoJapan
  4. 4.Mechanical EngineeringRice UniversityHoustonUSA

Personalised recommendations