In this paper, a VOF method called RHRIC (refined high resolution intertace capturing) is introduced for solving the motion of the free surface and applied to the simulation of the advection of rigid interiaces of different shapes and a 20 dam-break problem, which are typical benchmark test cases. The numerical results for the interface advection cases are compared to the analytic solutions, while the available experimental data and other numerical results of various free surface methods for the dam-break problem are provided for the validation of the proposed VOF method. The same simulations were also carried out using the original HRIC scheme and a modified HRIC scheme called MHRIC for comparison. Although the RHRIC uses a simple order scheme, a basis of the original HRIC scheme, lower than the third-order ULTIMATE-QUICKEST used by the MHRIC, it provides an improved accuracy over the two previous HRIC methods.
Colicchio G, Colagrossi A, Greco M, Landrini M., 2002, " Free-surface flow after a dam break: a comparative study," Ship Technology Research: 49(3):95-204.
Colaorossi, A. and Landrini, M, 2003, " Numerical simulation of interfacial flows by smoothed particle hydrodynamics," J. Comput. Phys. 191, pp.448-475.
Ferziger, J.H., and Peric, M., 1996, Computational Methods for Fluid Dynamics, Springer-Verlag, Berlin.
Fluent, 2006, Fluent 6.3 users guide, fluent inc.
Hirt, C.R., and Nichols, B.D., 1981, " Volume of fluid (VOF) method for the dynamics of free boundaries," J. Comput. Phys. 39, pp.201-225.
Hong, C.B., 2003, " Numerical Investigation of High-Speed Ship Wash in Restricted Waterway," Ph.D thesis, Hiroshima University, Japan.
Hong, S.Y. and Choi, H.S., 1995, " Analysis of Steady and Unsteady Flow Around a Ship Using a Higher-Order Boundary Element Method," Journal of the Society of Naval Architects of Korea, Vol. 32, No.1, pp.42-57.
Jeong, U.C., Yasuaki Doi, and Kasu-hiro Mori, 1998, "Numerical Investigations on Vortical Flows and Turbulence beneath the Free Surface around Bow," Journal of the Society of Naval Architects of Korea, Vol. 35, No.1, pp.15-23.
Kim, H.E., and Lee, Y.G., 2003, " A Basic Research of Air Bubble Locus around the Ship Hull," Journal of the Society of Naval Architects of Korea, Vol. 37, No.4, pp.48-55.
Kim, J.J. and Kim, H.T., 2001, " Computation of Turbulent Flow around a Ship Model with Free-Surface," Journal of the Society of Naval Architects of Korea, Vol. 38, No.1, pp.1-8.
Kim, W.J., Kim, D.H. and Van, S.H., 2000, " Development of Computational Methods for Viscous Flow around a commercial Ship Using Finite-Volume Methods," Journal of the Society of Naval Architects of Korea, Vol. 37, No.4, pp.19-31.
Kim, Y.J., Ha, Y.R., and Hong, S.Y., 2003, "Numerical Calculation of the free-Surface Flows around a Submerged Body," Journal of the Society of Naval Architects of Korea, Vol. 40, No.2, pp.11-20.
Lafaurie, B., Nardone, C., Scardovelli, R., Zaleski, S., and Zanetti, G., 1994, " Modelling merging and fragmentation in multiphase flows with SURFER," J. Comput. Phys. 113, pp.134-147.
Lee, D.Y. and Choi, H.S., 1998, " A Study on the Sloshing of Cargo Tanks Including Hydroelastic Effects," Journal of the Society of Naval Architects of Korea, Vol. 35, No.4, pp.27-37.
Leonard, B.P., 1991, "The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection," Comput. Methods Appl. Mech. Engrg. 88, pp.17-74.
Martin, J.C., and Moyce, W.J., 1952, " An experimental study of the collapsed liquid columns on a rigid horizontal plate," Phil. Trans. Roy. Soc. London A. Math., Phys. Eng. Sci., 244, pp.312-324.
Muzaferija, S. and Peric, M., 1999, "Computation of Free Surface Flows Using Interface-Tracking and Interface-Capturing Methods," Chap. 2, in Mahrenholtz, O. and Markewicz, M., Nonlinear Water Wave Interaction, Computational Mechanics Publications.
Nielsen, K.B., 2003, " Numerical prediction of green water loads on ships," Ph.D thesis, Technical University of Denmark.
Park, I.R., Kim, K.S., Kim, J. and Van, S.H., 2008, "UnsteadY RANS Analysis of the Hydrodynamic Response for a Ship with Forward Speed in Regular Wave," Journal of the Society of Naval Architects of Korea, Vol. 45, No.1, pp.29-41.
Park, I.R., Kim, K.S., Kim, J., and Van, S.H., 2009, "A volume-of-fluid method for incompressible free surface flows," Int. J. Numer. Meth. Fluids 61, pp.1331-1362.
Park, I.R., Kim, W.J., Kim, J. and Van, S.H., 2005, "A Study on a VOF Method for the Improvement of Free Surface Capturing," Journal of the Society of Naval Architects of Korea, Vol. 42, No.2, pp.88-97.
Rudman, M., 1998, "A volume tracking method for interfacial flows with large density variations," Int. J. Numer. Methods Fluids 28, pp.357-378.
Shin, M.S. and Kang, K.J., 1996, " Numerical Simulation of Free-Surface Flows around a Series 60$ (C_B =0.6)$ model ship," Journal of the Society of Naval Architects of Korea, Vol. 33, No. 2, pp.13-29.
Shin, S.M., and Kim, D.H., 2004, " Internal Wave Computations based on a Discontinuity in Dynamic Pressure," Journal of the Society of Naval Architects of Korea, Vol. 41, No.4, pp.17-29
Son, G, 2003, " Efficient implementation of a coupled level-set and volume-of-fluid method for three-dimensional incompressible two-phase flows," Numer. Heat Transf. B 43, pp.549- 565.
Stone, H. L., 1968, "Iterative Solution of Implicit Approximations of Multi-directional Partial Differential Equations," SIAM J. Numer. Anal., Vol. 5, po. 530-558.
Sussman M., Smith K.M., Hussaini M.Y., Ohta M., and Zhi-Wei R., 2007, " A sharp interface method for incompressible two-phase flows," J. Comput. Phys. 221, pp. 469- 505.
Ubbink, O. and lssay, R.I., 1999, " A method for capturing sharp fluid interfaces on arbitrary meshes," J. Comput. Phys. 153, pp. 26- 50.
Van Leer, B., 1979, " Towards the Ultimate Conservative Difference Scheme, V:A Second-Order Sequel to Godunov' s Method," J. Comput. Phys., Vol. 32, pp. 101-136.
Yum, D.J., and Yoon, B.S., 2008, " Numerical Simulation of Slamming Phenomena for 2-D Wedges," Journal of the Society of Naval Architects of Korea, Vol. 45, No.5, pp.477-486.
• Zalesak, S.T., 1979, " Fully multi-dimensional flux corrected transport algorithms for fluids," J. Comput. Phys. 31, pp.335- 362.
Zhou, Z.O., De Kat, J.O., and Buchner, B., 1999, " A nonlinear 3-D approach to simulate green water dynamics on deck," in: Proceedings of the 7th International Conference on Numerical Ship Hydrodynamics, Nantes, FRANCE. pp. 5.1-1,15.
이 논문을 인용한 문헌 (2)
Park, Il-Ryong ; Jung, Kwang-Hyo 2012. "Study on the Effects of Surface Roughness and Turbulence Intensity on Dam-break Flows" 大韓造船學會 論文集 = Journal of the Society of Naval Architects of Korea, 49(3): 247~253
Park, Il-Ryong 2013. "Study on Improvement in Numerical Method for Two-phase Flows Including Surface Tension Effects" 韓國海洋工學會誌 = Journal of ocean engineering and technology, 27(5): 70~76