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http://dx.doi.org/10.3741/JKWRA.2012.45.4.349

Application of Non-hydrostatic Free Surface Model for Three-Dimensional Viscous Flows  

Choi, Doo-Yong (K-water Institute, Korea Water Resources Corporation)
Publication Information
Journal of Korea Water Resources Association / v.45, no.4, 2012 , pp. 349-360 More about this Journal
Abstract
A horizontally curvilinear non-hydrostatic free surface model that was applicable to three-dimensional viscous flows was developed. The proposed model employed a top-layer equation to close kinematic free-surface boundary condition, and an isotropic k-${\varepsilon}$ model to close turbulence viscosity in the Reynolds averaged Navier-Stokes equation. The model solved the governing equations with a fractional step method, which solved intermediate velocities in the advection-diffusion step, and corrects these provisional velocities by accounting for source terms including pressure gradient and gravity acceleration. Numerical applications were implemented to the wind-driven currents in a two-dimensional closed basin, the flow in a steep-sided trench, and the flow in a strongly-curved channel accounting for secondary current by the centrifugal force. Through the numerical simulations, the model showed its capability that were in good agreement with experimental data with respect to free surface elevation, velocity, and turbulence characteristics.
Keywords
non-hydrostatic model; free surface closure; viscous flows; top-layer equation; curved channel;
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1 Molls, T., and Chaudhry, M.H. (1995). "Depth-averaged open-channel flow model." Journal of Hydraulic Engineering, Vol. 121, No. 6, pp. 453-465.   DOI   ScienceOn
2 Nichols, B.D., and Hirt, C.W. (1975). Methods for calculating multi-dimensional, transient free surface flows past bodies. Technical Report LA-UR-75-1932, Los Alamos National Laboratory, LM.
3 Pacanowski, R.C., and Gnanadesikan, A. (1998). "Transient response in a z-level ocean model that resolves topography with partial cell." MonthlyWeather Review, Vol. 126, No. 12, pp. 3248-3270.
4 Rozovskii, I.L. (1957). Flow of water in bends of open channels. Transl. 1961, Israel Program for Scientific Translations, Jerusalem.
5 Spillane, K.T., and Hess, G.D. (1978). "Wind-induced drift in contained bodies of water." Journal of Physical Oceanography, Vol. 8, No. 5, pp. 930-935.   DOI
6 Stansby, P.L., and Zhou, J.G. (1998). "Shallow-water flow solver with non-hydrostatic pressure: 2D vertical plane problems." Int. J. Numer. Meth. Fluids, Vol. 28, No. 3, pp. 541-563.   DOI   ScienceOn
7 Stelling, G.S., and Zijlema, M. (2003). "An accurate and efficient finite-difference algorithm for non-hydrostatic free-surface flow with application to wave propagation." Int. J. Numer. Meth. Fluids, Vol. 43, No. 1, pp. 1-23.   DOI   ScienceOn
8 Tannehill, J.C., Anderson, D.A., and Pletcher, R.H. (1998). Computational fluid mechanics and heat transfer, Taylor & Francis.
9 Tsanis, I.K. (1989). "Simulation of wind-induced water currents." Journal of Hydraulic Engineering, Vol. 115, No. 8, pp. 1113-1134.   DOI
10 van Rijn, L.C. (1982). The computation of the flow and turbulence field in dredged trenches. Report S 488-1, Delft Hydraulics Laboratory, Delft, The Netherlands
11 Yuan, H., and Wu, C.H. (2004). "An implicit 3D fully non-hydrostatic model for free-surface flows." Int. J. Numer. Meth. Fluids, Vol. 46, No. 7, pp. 709-733.   DOI   ScienceOn
12 Choi, D.Y., Wu, C.H., and Young, C.C. (2011). "An efficient curvilinear non-hydrostatic model for simulating surface water waves." Int. J. Numer. Meth. Fluids, Vol. 66, No. 9, pp. 1093-1115.   DOI   ScienceOn
13 Choi, D.Y., and Yuan, H. (2011). "A horizontally curvilinear non-hydrostatic model for simulating nonlinear wave motion in curved boundaries." Int. J. Numer. Meth. Fluids, DOI: 10.1002/fld.2676, published online.   DOI
14 Harlow, F.H., and Welch, J.E. (1965). "Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface." Physics of Fluids, Vol. 8, No. 12, pp. 2182-2189.   DOI
15 Launder, B.E., and Spaulding, D.B. (1974). "The numerical computation of turbulence flows." Compt. Methods Appl. Mech. Eng., Vol. 3, No. 2, pp. 269-289.   DOI   ScienceOn
16 Lee, J.W., Teubner, M.D., Nixon, J.B., and Gill, P.M. (2006). "A 3-D non-hydrostatic pressure model for small amplitude free surface flows." Int. J. Numer. Meth. Fluids, Vol. 50, No. 6, pp. 649-672.   DOI   ScienceOn
17 Lin, P., and Li, C.W. (2002). "A ${\sigma}$-coordinate threedimensional numerical model for surface wave propagation." Int. J. Numer. Meth. Fluids, Vol. 38, No. 11, pp. 1045-1068.   DOI   ScienceOn
18 Leschziner, M.A., and Rodi, W. (1979). "Calculation of strongly curved open channel flow." Journal ofHydraulic Division, ASCE, Vol. 105, No. 10, pp. 1297-1314.
19 Leupi, C., and Altinakar, M.S. (2005). "Finite element modelling of free-surface flows with non-hydrostatic pressure and k-epsilon turbulence model." Int. J. Numer. Meth. Fluids, Vol. 49, No. 2, pp. 149-170.   DOI   ScienceOn
20 Lien, H.C., Hsieh, T.Y., Yang, J.C., and Yeh, K.C. (1999). "Bend-flow simulation using 2D depth-averaged model." Journal of Hydraulic Engineering, Vol. 125, No. 10, pp. 1097-1108.   DOI
21 Marshall, J., Hill, C., Perelman, L., and Adcroft, A. (1997). "Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling." Journal of Geophysical Research, Vol. 102, No. 3, pp. 5733-5752.   DOI
22 Casulli, V., and Stelling, G.S. (1998). "Numerical simulation of 3D quasi-hydrostatic, free-surface flows." Journal of Hydraulic Engineering, Vol. 124, No. 7, pp. 678-686.   DOI   ScienceOn
23 Baines, D., and Knapp, D.J. (1965). "Wind driven water currents." Journal of Hydraulic Division, ASCE, Vol. 91, No. 2, pp. 205-221.
24 Browning, G.L., Holland, W.R., Kreiss, H.O., and Worley, S.J. (1990). "An accurate hyperbolic system for approximately hydrostatic and incompressible oceanographic flows." Dyn. Atmos. Oceans, Vol. 14, pp. 303-332.
25 Casulli, V. (1999). "A semi-implicit finite difference method for non-hydrostatic, free-surface flows." Int. J. Numer. Meth. Fluids, Vol. 30, No. 4, pp. 425-440.   DOI   ScienceOn
26 Choi, D.Y., and Wu, C.H. (2006). "A new efficient 3D non-hydrostatic free-surface flow model for simulating water wave motions." Ocean Engineering, Vol. 33, pp. 587-609.   DOI   ScienceOn
27 Young, C.-C., Wu, C.H., Liu, W.-C., and Kuo, J.-T. (2009). "A higher-order non-hydrostatic σ model for simulating non-linear refraction-diffraction of water waves." Coastal Engineering, Vol. 56, No. 9, pp. 919-930.   DOI   ScienceOn