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http://dx.doi.org/10.3744/SNAK.2010.47.1.011

Numerical Simulation of Free Surface Flows Using the Roe's Flux-difference Splitting Scheme  

Shin, Sang-Mook (Dept. of Naval Architecture and Marine Systems Engineering, Pukyong National University)
Kim, In-Chul (Dept. of Naval Architecture and Marine Systems Engineering, Pukyong National University)
Kim, Yong-Jig (Dept. of Naval Architecture and Marine Systems Engineering, Pukyong National University)
Publication Information
Journal of the Society of Naval Architects of Korea / v.47, no.1, 2010 , pp. 11-19 More about this Journal
Abstract
A code is developed to simulate incompressible free surface flows using the Roe's flux-difference splitting scheme. An interface of two fluids is considered as a moving contact discontinuity. The continuities of pressure and normal velocity across the interface are enforced by the conservation law in the integral sense. The fluxes are computed using the Roe's flux-difference splitting scheme for two incompressible fluids. The interface can be identified based on the computed density distribution. However, no additional treatment is required along the interface during the whole computations. Complicated time evolution of the interface including topological change can be captured without any difficulties. The developed code is applied to simulate the Rayleigh-Taylor instability of two incompressible fluids in the density ratio of 7.2:1 and the broken dam problem of water-air. The present results are compared with other available results and good agreements are achieved for the both cases.
Keywords
Free surface; Contact discontinuity; Rayleigh-Taylor instability; Broken dam; Incompressible fluids;
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Times Cited By KSCI : 4  (Citation Analysis)
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1 Popinet, S. and Zaleski S., 1999, "A Front-Tracking Algorithm for Accurate Representation of Surface Tension," International Journal for Numerical Methods in Fluids, Vol. 30(6), pp. 775-793.   DOI
2 Qian, L., Causon, D.M., Mingham, C.G. and Ingram, D.M., 2006, "A Free-surface Capturing Method for Two Fluid Flows with Moving Bodies," Proceedings of the Royal Society, Vol. 422, pp. 21-42.
3 Roe, P.L., 1981, "Approximate Riemann Solvers, Parameter Vectors and Difference Schemes," Journal of Computational Physics, Vol. 43(2), pp. 357-372.   DOI   ScienceOn
4 Shin, S. 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.   과학기술학회마을   DOI   ScienceOn
5 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.   과학기술학회마을   DOI   ScienceOn
6 Gao, F., Ingram, D.M., Causon, D.M., Mingham, C.G., 2007, "The Development of a Cartesian Cut Cell Method for Incompressible Viscous Flows," International Journal for Numerical Methods in Fluids, Vol. 54(9), pp. 1033-1053.   DOI   ScienceOn
7 Kelecey, F.J. and Pletcher, R.H., 1997, "The Development of a Free Surface Capturing Approach for Multidimensional Free Surface Flows in Closed Containers," Journal of Computational Physics, Vol. 138(2), pp. 939-980.   DOI   ScienceOn
8 Martin, J. and Moyce, W., 1952, "An Experi Mental Study of the Collapse of Liquid Columns on a Rigid Horizontal Plane," Philosophical Transactions of the Royal Society A, Vol. 244, No. 882, pp. 312-324.   DOI
9 Shin, S., Bae, S.Y., Kim, I.C. and Kim, Y.J., 2009, "Effects of Flexibility on Propulsive Force Acting on a Heaving Foil," Ocean Engineering,Vol. 36(3-4), pp. 285-294.   DOI   ScienceOn
10 Sheu, T.W.H., Yu, C.H. and Chiu, P.H., 2009, "Development of a Dispersively Accurate Conservative Level Set Scheme for Capturing Interface in Two-phase Flows," Journal of Computational Physics, Vol. 228(3), pp. 661-686.   DOI   ScienceOn
11 Shin, S. and Kim, H.T., 2006, "Numerical Simulation of a Viscous Flow Field Around a Deforming Foil Using the Hybrid Cartesian/Immersed Boundary Method," Journal of the Society of Naval Architects of Korea, Vol. 43,No. 5, pp. 538-549.   과학기술학회마을   DOI   ScienceOn
12 Shin, S., Kim, C.K. and Bai, K.J., 2004, "Numerical Simulation on an Interaction of a Vortex Street with an Elliptic Leading Edge Using an Unstructured Grid," International Journal for Numerical Methods in Fluids, Vol. 44(3), pp. 331-346.   DOI   ScienceOn
13 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. 4, pp. 477-486.   과학기술학회마을   DOI   ScienceOn