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Toward free-surface modeling of planing vessels: simulation of the Fridsma hull using ALE-VMS

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Abstract

In this paper we focus on a class of applications involving surface vessels moving at high speeds, or “planing”. We introduce a Fridsma planing hull benchmark problem, and simulate it using the finite-element-based ALE-VMS (Bazilevs et al. in Math Models Methods Appl Sci 2012; Takizawa et al. in Arch Comput Methods Eng 19: 171–225, 2012) approach. The major reasons for selecting this problem is the relative simplicity of the hull geometry and the existence of high-quality experimental data used for the purposes of validation. The ALE-VMS approach is formulated in the context of the Mixed Interface-Tracking/Interface-Capturing Technique (MITICT) (Tezduyar in Arch Comput Methods Eng 8:83–130, 2001; Akin et al. in Comput Fluids 36:2–11, 2007; Cruchaga et al. in Int J Numer Methods Fluids 54:1021–1031, 2007), where the level set technique is used for capturing the air–water interface, and the Arbitrary Lagrangian Eulerian (ALE) method is employed to track the interface between the fluid and structure. In this work, the planing hull structure is treated as a six-degree-of-freedom rigid object. The computational results obtained for the Fridsma hull, which include convergence of the trim angle and drag under mesh refinement, match well with the experimental data.

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References

  1. Fridsma G (1968) A systematic study of the rough-water performance of planing boats. Davidson Laboratory Report 1275

  2. Savitsky D, Brown PW (1976) Procedures for hydrodynamics evaluation of planing hulls in smooth and rough water. Mar Technol 13: 381–400

    Google Scholar 

  3. Sun H, Faltinsen O (2007) The influence of gravity on the performance of planing vessels in calm water. J Eng Math 58: 91–107

    Article  MathSciNet  MATH  Google Scholar 

  4. Garme K, Rosén A (2006) Time-domain simulations and full-scale trials on planing craft in waves. J Int Shipbuilding Progress 50: 177–208

    Google Scholar 

  5. Sun H, Faltinsen O (2011) Predictions of porpoising inception for planing vessels. J Mar Sci Technol 16: 270–282

    Article  Google Scholar 

  6. 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. Accepted for publication. doi:10.1142/S0218202512300025

  7. Takizawa K, Bazilevs Y, Tezduyar TE (2012) Space–time and ALE-VMS techniques for patient-specific cardiovascular fluid–structure interaction modeling. Arch Comput Methods Eng 19: 171–225

    Article  MathSciNet  Google Scholar 

  8. Akkerman I, Bazilevs Y, Benson DJ, Farthing CE, Kees MW (2012) Free-surface flow and fluid–object interaction modeling with emphasis on ship hydrodynamics. J Appl Mech 79(1): 010909

    Article  Google Scholar 

  9. Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8: 83–130

    Article  MATH  Google Scholar 

  10. Akin JE, Tezduyar TE, Ungor M (2007) Computation of flow problems with the mixed interface-tracking/interface-capturing technique (MITICT). Comput Fluids 36: 2–11

    Article  MATH  Google Scholar 

  11. Cruchaga MA, Celentano DJ, Tezduyar TE (2007) A numerical model based on the mixed interface-tracking/interface-capturing technique (MITICT) for flows with fluid–solid and fluid–fluid interfaces. Int J Numer Methods Fluids 54: 1021–1031

    Article  MATH  Google Scholar 

  12. Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian- Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29: 329–349

    Article  MathSciNet  MATH  Google Scholar 

  13. 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

    Article  MATH  Google Scholar 

  14. 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(3): 339–351

    Article  MathSciNet  MATH  Google Scholar 

  15. 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(3): 353–371

    Article  MathSciNet  MATH  Google Scholar 

  16. Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43: 555–575

    Article  MathSciNet  MATH  Google Scholar 

  17. Cruchaga M, Celentano D, Tezduyar T (2001) A moving Lagrangian interface technique for flow computations over fixed meshes. Comput Methods Appl Mech Eng 191: 525–543

    Article  MATH  Google Scholar 

  18. Sethian JA (1999) Level set methods and fast marching methods. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  19. Sussman M, Smereka P, Osher SJ (1994) A level set approach for computing solutions to incompressible two-phase flows. J Comput Phys 114: 146–159

    Article  MATH  Google Scholar 

  20. Nagrath S, Jansen KE, Lahey RT (2005) Computation of incompressible bubble dynamics with a stabilized finite element level set method. Comput Methods Appl Mech Eng 194: 4565–4587

    Article  MathSciNet  MATH  Google Scholar 

  21. 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: 173–201

    Article  MATH  Google Scholar 

  22. Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid–structure interaction analysis with applications to arterial blood flow. Comput Mech 38: 310–322

    Article  MathSciNet  MATH  Google Scholar 

  23. Akkerman I, Bazilevs Y, Calo VM, Hughes TJR, Hulshoff S (2008) The role of continuity in residual-based variational multiscale modeling of turbulence. Comput Mech 41: 371–378

    Article  MathSciNet  MATH  Google Scholar 

  24. Bazilevs Y, Michler C, Calo VM, Hughes TJR (2007) Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Comput Methods Appl Mech Eng 196: 4853–4862

    Article  MathSciNet  MATH  Google Scholar 

  25. Bazilevs Y, Michler C, Calo VM, Hughes TJR (2010) Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly-enforced boundary conditions on unstretched meshes. Comput Methods Appl Mech Eng 199(13–16): 780–790

    Article  MathSciNet  MATH  Google Scholar 

  26. 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: 3534–3550

    Article  MathSciNet  MATH  Google Scholar 

  27. Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid–structure interaction: theory, algorithms, and computations. Comput Mech 43: 3–37

    Article  MathSciNet  MATH  Google Scholar 

  28. Hsu MC, Bazilevs Y, Calo VM, Tezduyar TE, Hughes TJR (2010) Improving stability of multiscale formulations of fluid flow at small time steps. Comput Methods Appl Mech Eng 199: 828–840

    Article  MathSciNet  MATH  Google Scholar 

  29. 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

    Article  MATH  Google Scholar 

  30. Bazilevs Y, Hsu M-C, Kiendl J, Wuechner R, Bletzinger K-U (2011) 3D simulation of wind turbine rotors at full scale. Part II: fluid–structure interaction. Int J Numer Methods Fluids 65: 236–253

    Article  MATH  Google Scholar 

  31. Kees C, Akkerman I, Farthing M, Bazilevs Y (2011) A conservative level set method suitable for variable-order approximations and unstructured meshes. J Comput Phys 230(12): 3402–3414

    Article  MathSciNet  Google Scholar 

  32. Lins EF, Elias RN, Rochinha FA, Coutinho ALGA (2010) Residual-based variational multiscale simulation of free surface flows. Comput Mech 46: 545–557

    Article  MathSciNet  MATH  Google Scholar 

  33. Akkerman I, Bazilevs Y, Kees C, Farthing M (2011) Isogeometric analysis of free-surface flow. J Comput Phys 230(11): 4137–4152

    Article  MathSciNet  MATH  Google Scholar 

  34. 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: 199–259

    Article  MathSciNet  MATH  Google Scholar 

  35. Tezduyar TE, Osawa Y (2000) Finite element stabilization parameters computed from element matrices and vectors. Comput Methods Appl Mech Eng 190: 411–430

    Article  MATH  Google Scholar 

  36. Tezduyar TE (2004) Finite element methods for fluid dynamics with moving boundaries and interfaces. In Stein E, De Borst R, Hughes TJR (eds) Encyclopedia of computational mechanics, vol 3: fluids, chapter 17. Wiley, New York

  37. 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

    Article  MathSciNet  MATH  Google Scholar 

  38. Nitsche J (1971) Uber ein variationsprinzip zur losung von Dirichlet-problemen bei verwendung von teilraumen, die keinen randbedingungen unterworfen sind. Abh Math Univ Hamburg 36: 9–15

    Article  MathSciNet  MATH  Google Scholar 

  39. Bazilevs Y, Hughesm TJR (2007) Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput Fluids 36: 12–26

    Article  MathSciNet  MATH  Google Scholar 

  40. Bazilevs Y, Akkerman I (2010) Large eddy simulation of turbulent taylor-couette flow using isogeometric analysis and the residual-based variational multiscale method. J Comput Phys 229(9): 3402–3414

    Article  MathSciNet  MATH  Google Scholar 

  41. Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, Chichester

    MATH  Google Scholar 

  42. Hughes TJR, Winget J (1980) Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis. Int J Numer Methods Eng 15: 1862–1867

    Article  MathSciNet  MATH  Google Scholar 

  43. Tezduyar TE, Behr M, Mittal S, Johnson AA (1992) Computation of unsteady incompressible flows with the finite element methods—space–time formulations, iterative strategies and massively parallel implementations. In: New methods in transient analysis, PVP-Vol 246/AMD-Vol 143. ASME, New York, pp 7–24

  44. Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26(10): 27–36

    Article  Google Scholar 

  45. 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

    Article  MATH  Google Scholar 

  46. Cruchaga M, Celentano D, Tezduyar T (2002) Computation of mould filling processes with a moving Lagrangian interface technique. Commun Numer Methods Eng 18: 483–493

    Article  MATH  Google Scholar 

  47. Cruchaga MA, Celentano DJ, Tezduyar TE (2005) Moving-interface computations with the edge-tracked interface locator technique (ETILT). Int J Numer Methods Fluids 47: 451–469

    Article  MATH  Google Scholar 

  48. Cruchaga MA, Celentano DJ, Tezduyar TE (2007) Collapse of a liquid column: numerical simulation and experimental validation. Comput Mech 39: 453–476

    Article  MATH  Google Scholar 

  49. Tezduyar TE, Senga M (2006) Stabilization and shock-capturing parameters in SUPG formulation of compressible flows. Comput Methods Appl Mech Eng 195: 1621–1632

    Article  MathSciNet  MATH  Google Scholar 

  50. Tezduyar TE, Senga M (2007) SUPG finite element computation of inviscid supersonic flows with YZ β shock-capturing. Comput Fluids 36: 147–159

    Article  MATH  Google Scholar 

  51. Tezduyar TE, Senga M, Vicker D (2006) Computation of inviscid supersonic flows around cylinders and spheres with the supg formulation and YZ β shock-capturing. Comput Mech 38: 469–481

    Article  MATH  Google Scholar 

  52. Bazilevs Y, Calo VM, Tezduyar TE, Hughes TJR (2007) YZ β discontinuity-capturing for advection-dominated processes with application to arterial drug delivery. Int J Numer Methods Fluids 54: 593–608

    Article  MathSciNet  MATH  Google Scholar 

  53. Rispoli F, Saavedra R, Corsini A, Tezduyar TE (2007) Computation of inviscid compressible flows with the V-SGS stabilization and YZ β shock-capturing. Int J Numer Methods Fluids 54: 695–706

    Article  MathSciNet  MATH  Google Scholar 

  54. Catabriga L, de Souza DAF, Coutinho ALGA, Tezduyar TE (2009) Three-dimensional edge-based supg computation of inviscid compressible flows with YZ β shock-capturing. J Appl Mech 76: 021208

    Article  Google Scholar 

  55. Galeao AC, Dutra do Carmo EG (1988) A consistent approximate upwind Petrov–Galerkin method for convection-dominated problems. Comput Methods Appl Mech Eng 68(1): 83–95

    Article  MathSciNet  MATH  Google Scholar 

  56. 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

    Article  MATH  Google Scholar 

  57. Tezduyar TE, Ramakrishnan S, Sathe S (2008) Stabilized formulations for incompressible flows with thermal coupling. Int J Numer Methods Fluids 57: 1189–1209

    Article  MathSciNet  MATH  Google Scholar 

  58. Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. J Appl Mech 60: 371–375

    Article  MathSciNet  MATH  Google Scholar 

  59. Jansen KE, Whiting CH, Hulbert GM (1999) A generalized- α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190: 305–319

    Article  MathSciNet  Google Scholar 

  60. 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

    Article  MathSciNet  MATH  Google Scholar 

  61. 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

    Article  MathSciNet  MATH  Google Scholar 

  62. Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194: 4135–4195

    Article  MathSciNet  MATH  Google Scholar 

  63. Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, Chichester

    Google Scholar 

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Authors and Affiliations

  1. Department of Structural Engineering, University of California, San Diego, 9500 Gilman Drive, Mail Code 0085, La Jolla, CA, 92093, USA

    I. Akkerman, J. Dunaway, J. Kvandal, J. Spinks & Y. Bazilevs

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  1. I. Akkerman
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  2. J. Dunaway
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  3. J. Kvandal
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  4. J. Spinks
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  5. Y. Bazilevs
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Correspondence to Y. Bazilevs.

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Akkerman, I., Dunaway, J., Kvandal, J. et al. Toward free-surface modeling of planing vessels: simulation of the Fridsma hull using ALE-VMS. Comput Mech 50, 719–727 (2012). https://doi.org/10.1007/s00466-012-0770-2

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