Abstract
We present our free-surface flow and fluid-object interaction computational framework. The framework is an instantiation of the Mixed Interface-Tracking/Interface-Capturing Technique (MITICT) (Akin et al. in Comput. Fluids 36:2–11, 2007; Cruchaga et al. in Int. J. Numer. Methods Fluids 54:1021–1031, 2007; Tezduyar in Arch. Comput. Methods Eng. 8:83–130, 2001) where the level-set method is used for the air-water interface description and the ALE (Hughes et al. in Comput. Methods Appl. Mech. Eng. 29:329–349, 1981) technique is employed to track the moving fluid-object interface. We discuss the definition of the local mesh size used in the level-set formulation, which is an important aspect of this work. We show two example computations, the dam break and Fridsma hull, and validate our methodology using the experimental data available for these cases.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In [22] the results were reported in terms of the Speed-Length Ratio (SLR), \(u/\sqrt{L}\), which is a dimensional quantity. Here report the results in terms of the Froude number, which is non-dimensional.
References
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
Akkerman I, Bazilevs Y, Benson DJ, Farthing MW, Kees CE (2012) Free-surface flow and fluid-object interaction modeling with emphasis on ship hydrodynamics. J Appl Mech 79:010905. doi:10.1115/1.4005072
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
Akkerman I, Bazilevs Y, Kees C, Farthing M (2011) Isogeometric analysis of free-surface flow. J Comput Phys 230:4137–4152. doi:10.1016/j.jcp.2010.11.044
Akkerman I, Dunaway J, Kvandal J, Spinks J, Bazilevs Y (2012) Toward free-surface modeling of planing vessels: simulation of the Fridsma hull using ALE-VMS. Comput Mech. doi:10.1007/s00466-012-0770-2
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
Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37
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
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
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
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
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 22:1230002. doi:10.1142/S0218202512300025
Bazilevs Y, Hughes TJR (2007) Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput Fluids 36:12–26
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
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
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
Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, Chichester
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
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
Eca L, Hoekstra M, Hay A, Pelletier D (2007) Verification of RANS solvers with manufactured solutions. Eng Comput 23:253–270
Elias RN, Coutinho ALGA (2007) Stabilized edge-based finite element simulation of free-surface flows. Int J Numer Methods Fluids 54:965–993
Fridsma G (1968) A systematic study of the rough-water performance of planing boats. Davidson Laboratory report 1275
Hsu M-C, Akkerman I, Bazilevs Y (2012) Wind turbine aerodynamics using ALE–VMS: validation and the role of weakly enforced boundary conditions. Comput Mech 50:499–511
Hsu M-C, 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
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
Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29:329–349
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
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
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 230:4536–4558. doi:10.1016/j.jcp.2011.02.030
Kleefsman KMT, Fekken G, Veldman AEP, Iwanowski B, Buchner B (2005) A volume-of-fluid based simulation method for wave impact problems. J Comput Phys 206:363–393
Lins EF, Elias RN, Rochinha FA, Coutinho ALGA (2010) Residual-based variational multiscale simulation of free surface flows. Comput Mech 46:545–557
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
Osher S, Fedkiw R (2003) Level set methods and dynamic implicit surfaces. Applied mathematical sciences, vol 153. Springer, New York
Sethian JA (1999) Level set methods and fast marching methods. Cambridge University Press, Cambridge
Söderlind G (2002) Automatic control and adaptive time-stepping. Numer Algorithms 31:281–310
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
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
Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8:83–130
Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43:555–575
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
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
Valli AMP, Carey GF, Coutinho ALGA (2005) Control strategies for timestep selection in finite element simulation of compressible flows and coupled reaction-convection-diffusion processes. Int J Numer Methods Fluids 47:201–231
Acknowledgements
This research was supported through ARO Award W911NF-10-1-0247. This support is gratefully acknowledged. We also wish to thank the Texas Advanced Computing Center (TACC) at the University of Texas at Austin and San Diego Supercomputer Center (SDSC) at the University of California, San Diego for providing HPC resources that contributed to the research results reported in this paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Akkerman, I., Benner, K., Bazilevs, Y. (2013). Free-Surface Flow and Fluid-Object Interaction. In: Eça, L., Oñate, E., García-Espinosa, J., Kvamsdal, T., Bergan, P. (eds) MARINE 2011, IV International Conference on Computational Methods in Marine Engineering. Computational Methods in Applied Sciences, vol 29. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6143-8_3
Download citation
DOI: https://doi.org/10.1007/978-94-007-6143-8_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-6142-1
Online ISBN: 978-94-007-6143-8
eBook Packages: EngineeringEngineering (R0)