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A volume-of-fluid based simulation method for wave impact problems. (English) Zbl 1087.76539

Summary: Some aspects of water impact and green water loading are considered by numerically investigating a dambreak problem and water entry problems. The numerical method is based on the Navier-Stokes equations that describe the flow of an incompressible viscous fluid. The equations are discretised on a fixed Cartesian grid using the finite volume method. Even though very small cut cells can appear when moving an object through the fixed grid, the method is stable. The free surface is displaced using the Volume-of-Fluid method together with a local height function, resulting in a strictly mass conserving method. The choice of boundary conditions at the free surface appears to be crucial for the accuracy and robustness of the method. For validation, results of a dambreak simulation are shown that can be compared with measurements. A box has been placed in the flow, as a model for a container on the deck of an offshore floater on which forces are calculated. The water entry problem has been investigated by dropping wedges with different dead-rise angles, a cylinder and a cone into calm water with a prescribed velocity. The resulting free surface dynamics, with the sideways jets, has been compared with photographs of experiments. Also a comparison of slamming coefficients with theory and experimental results has been made. Finally, a drop test with a free falling wedge has been simulated.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D33 Waves for incompressible viscous fluids
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References:

[1] Battistin, D.; Iafrati, A., Hydrodynamic loads during water entry of two-dimensional and axisymmetric bodies, J. Fluid Struct., 17, 643-664 (2003)
[2] Botta, E. F.F.; Ellenbroek, M. H.M., A modified SOR method for the poisson equation in unsteady free-surface flow calculations, J. Comput. Phys., 60, 119-134 (1985) · Zbl 0598.65076
[5] Clément, A., Coupling of two absorbing boundary conditions for 2D time-domain simulations of free surface gravity waves, J. Comput. Phys., 126, 139-151 (1996) · Zbl 0853.76057
[9] Faltinsen, O. M., Sea Loads on Ships and Offshore Structures (1990), Cambridge University Press: Cambridge University Press Cambridge
[14] Gerrits, J.; Veldman, A. E.P., Transient dynamics of containers partially filled with liquid, (Sarler, B.; Brebbia, C. A., Moving Boundaries, vol. VI (2001)), 63-72
[15] Gerrits, J.; Veldman, A. E.P., Dynamics of liquid-filled spacecraft, J. Eng. Math., 45, 21-38 (2003) · Zbl 1112.76337
[19] Greenhow, M., Wedge entry into initially calm water, Appl. Ocean Res., 9, 214-223 (1987)
[20] Harlow, F. H.; Welch, J. E., Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluid, 8, 2182-2189 (1965) · Zbl 1180.76043
[21] Harvie, D. J.E.; Fletcher, D. F., A new volume of fluid advection algorithm: the stream scheme, J. Comput. Phys., 162, 1-32 (2000) · Zbl 0964.76068
[22] Hirsch, C., Numerical Computation of Internal and External Flow, Section 23.3 (1990), Wiley: Wiley New York
[23] Hirt, C. R.; Nichols, B. D., Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys., 39, 201-225 (1981) · Zbl 0462.76020
[24] Iafrati, A.; Di Mascio, A.; Campana, E. F., A level set technique applied to unsteady free surface flows, Int. J. Num. Meth. Fluid, 35, 281-297 (2001) · Zbl 1043.76052
[25] Israeli, M.; Orszag, S. A., Approximation of radiation boundary conditions, J. Comput. Phys., 41, 115-135 (1981) · Zbl 0469.65082
[26] Juric, D.; Tryggvason, G., A front tracking method for dendritic solidification, J. Comput. Phys., 123, 127-148 (1996) · Zbl 0843.65093
[27] Kan, H.-C.; Udaykumar, H. S.; Shyy, W.; Tran-Son-Tay, R., Hydrodynamics of a compound drop with application to leukocyte modeling, Phys. Fluid, 10, 760-774 (1998)
[29] Loots, G. E.; Hillen, B.; Veldman, A. E.P., The role of hemodynamics in the development of the outflow tract of the heart, J. Eng. Math., 45, 91-104 (2003) · Zbl 1112.76516
[30] Loots, E.; Hillen, B.; Hoogstraten, H.; Veldman, A., Fluid-structure interaction in the basilar artery, (Herbin, R.; Kroener, D., Finite Volumes for Complex Applications III (2002)), 607-614 · Zbl 1177.76478
[33] Osher, S.; Sethian, J. A., Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79, 12-49 (1988) · Zbl 0659.65132
[34] Peskin, C. S., Numerical analysis of blood flow in the heart, J. Comput. Phys., 25, 220-252 (1977) · Zbl 0403.76100
[35] Rider, W. J.; Kothe, D. B., Reconstructing volume tracking, J. Comput. Phys., 141, 112-152 (1998) · Zbl 0933.76069
[36] Rudman, M., Volume-tracking methods for interfacial flow calculations, Int. J. Num. Meth. Fluid, 24, 671-691 (1997) · Zbl 0889.76069
[37] Scardovelli, R.; Zaleski, S., Direct numerical simulation of free-surface and interfacial flow, Annu. Rev. Fluid Mech., 31, 567-603 (1999)
[38] Schiffman, M.; Spencer, D. C., The force of impact on a cone striking a water surface vertical entry, Comm. Pure Appl. Math., 4, 379-417 (1951) · Zbl 0043.19003
[40] Orlanski, I., A simple boundary condition for unbounded hyperbolic flows, J. Comput. Phys., 21, 251-269 (1976) · Zbl 0403.76040
[41] Sussman, M.; Fatemi, E., An efficient, interface preserving level set re-distancing algorithm and its application to interfacial incompressible fluid flow, SIAM J. Sci. Comput., 20, 1165-1191 (1999) · Zbl 0958.76070
[42] Sussman, M.; Puckett, E. G., A coupled level set and volume-of-fluid method for computing 3d and axisymmetric incompressible two-phase flows, J. Comput. Phys., 162, 301-337 (2000) · Zbl 0977.76071
[43] Verstappen, R. W.C. P.; Veldman, A. E.P., Symmetry-preserving discretization of turbulent flow, J. Comput. Phys., 187, 343-368 (2003) · Zbl 1062.76542
[46] Zalesak, S. T., Fully multi-dimensional flux corrected transport algorithms for fluid flow, J. Comput. Phys., 31, 335-362 (1979) · Zbl 0416.76002
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