Hello..

I am Ph.D student at Kyoto University in Japan. I want to know some information related to following topic.

"The modeling of free surface in the Computational Fluid Dynamics."

My major is coastal engineering. so, it is based on sea wave. so, now I am looking for some data for studying.

Would you please inform me some information and papaer'references index for studyng above topic ?

This is my master thesis title if you want to order

A Finite Volume Model for the Study of Surface-Induced Motions author. Tamer EL-Soukkary Graduate Program in Engineering Science The Department of Mechanical \& Materials Engineering Submitted in partial fulfillment of the requirements for the degree of Master of Engineering Science

Faculty of Graduate Studies University {\em of} Western Ontario London, Ontario, CANADA December 2000 __________________________________________________ ___ Thesis are the citation

\begin{thebibliography}{10}

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\bibitem{HS94} Harris, J.A. and Street, R.L., 1994,`` Numerical simulation of turbulent flow over a moving wavy boundary: Norris and Renolds extended,"{\it Physics of fluids},Vol. 6, pp.924--943.

\bibitem{HS96} Harris, J.A. and Street, R.L., 1996,`` Linear dynamics of wind waves in coupled turbulent air-water flow. Part 2. Numerical model,"{\it Journal of fluid Mechanics},Vol. 308, pp. 219--254.

\bibitem{SP00} Sullivan, P.P., McWilliams, J.C. and Moeng, C.H., 2000,`` Simulation of turbulent flow over idealized water waves,"{\it Journal of Fluid Mechanics},Vol. 404, pp.47--85.

\bibitem{SP80} Patanker, S.V., 1980,``Numerical heat transfer and fluid flow," Hemispere Publishing Corporation., Washington, D.C.

\bibitem{FP96} Ferziger, J.H. and Peri\'c, M., 1996,``Computational Methods for Fluid Dynamics," Springer Pub., Germany.

\bibitem{MP99} Muzaferija, S. and Peri\`c, M. 1999,`` Computation of free-surface flows using interface-tracking and interface-capturing methods,"{\it Nonlinear Water Wave Interaction, Advances in Fluid Mechanics series, edited by Mahrenholtz, O. and Markiewicz, M.} WITpress, UK., Vol. 24, pp.59--100.

\bibitem{DP90} Demird\u zi\'c, I. and Peri\'c, M., 1990,``Finite Volume Method For Prediction of Fluid Flow in Arbitrarily Shaped Domains with Moving Boundaries,"{\it International Journal of Numerical Methods In Fluids}, Vol. 10, pp.771--790.

\bibitem{SP98} Shyy, W., Pal, S., Udaykumar, H.S. and Choi, D., 1998,``Structured Moving Grid and Geometeric Conservation Laws for Fluid Flow Computation,"{\it Numerical Heat Transfer, Part A}, Vol. 34, pp.369--397.

\bibitem{RC83} Rhie, C. M. and Chow, W. L., 1983,``Numerical study of the turbulent flow past an airfoil with trailing edge seperation,"{\it AIAA J.,}, Vol. 21, pp.1525--1532.

\bibitem{PK88} Peri\`c, M., Kessler, R., Scheuerer, G., 1988,``Comparison of Finite-Volume Numerical Methods with Staggered and Colocated Grids,"{\it Computer \& Fluids}, Vol. 16, No. 4, pp.389--403.

\bibitem{LB79} Leonard, B.P., 1988,``A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream Interpolation,"{\it Computer Methods in Applied Mechanics and Engineering}, Vol. 19, pp.59--98.

\bibitem{KR74} Khosla, P.K. and Rubin, S.G., 1974,``A diagonally dominant second-order accurate implicit scheme,"{\it Computer \& Fluids,}, Vol. 2, pp.207--209.

\bibitem{DP88} Demird\u zi\'c, I. and Peri\'c, M., 1988,``Space Conservation Law in Finite Volume Calculations of Fluid Flow,"{\it International Journal for Numerical Methods in Fluids}, Vol. 8, pp.1037--1050.

\bibitem{JL72} Jones, W. P. and Launder, D. E., 1972,``The Prediction of Laminarization with a Two-Equation Model of Turbulence,"{\it International Journal of Heat and Mass Transfer}, Vol. 15, pp.301--314.

\bibitem{TT61} Trulio, J.G. and Trigger, K.R., 1961,``Numerical solution of the one-dimensional hydrodynamic equations in an arbitrary time-dependent coordinate system,"{\it University of California Lawrence Radiation Laboratory Report UCLR-6522}.

\bibitem{RP84} Panton, R.L., 1984,`` Incompressible Flow," John Wiley.

\bibitem{VM95} Versteeg, H.K., Malalasekera, W., 1995,``An Introduction to Computational Fluid Dynamics: The Finite Volume Method," Longman Scientific \& Technical, U.K.

\bibitem{FC88} Fletcher, C. A. J., 1988,``Computational Techniques for Fluid Dynamics," Springer-Verlag, Vol. 1, p.302, Germany.

\bibitem{RT74} Raithby, G. D. and Torrance, K. E., 1974,``Upstream-Weighted Differencing Schemes and Their Application to Elliptic Problems Involving Fluid Flow,"{\it Computer \& Fluids}, Vol. 2, pp. 191--206.

\bibitem{RX95} Raithby, G.D., XU, W.X. and Stubley, G.D., 1995,``Prediction of Incompressible Free Surface Flows with An Element-Based Finite Volume Method,"{\it Computational Fluid Dynamics Journal}, Vol. 4, no. 3, pp.353--371.

\bibitem{WD94} Wilcox, D., 1994,``Turbulence Modeling for CFD," Second Ed., DCW Industries, Inc. La Ca\~{n}ada, California.

\bibitem{SH79} Schlichting, H., 1979,``Boundary Layer Theory," Seventh Ed., McGraw-Hill, New York.

\bibitem{RR84} Dean, R.G. and Dalrymple, R.A., 1984,``Water Wave Mechanics for Engineers and Scientists," Prentice-Hall,Inc.

\bibitem{GG82} Ghia, U., Ghia, K. N. and Shin., C. T., 1982,``High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method,"{\it Journal of Computational Physics}, Vol. 48, pp.387--411.

\bibitem{KJ80} Kim, J., Kline, S.J. and Johnston, J.P., 1980,``Investigation of a Reattaching Turbulent Shear Layer: Flow over a Backward-Facing Step,"{\it ASME Journal of Fluids Engineering}, Vol. 102, pp.302--308.

\bibitem{OP91} Obi, S. and Peri\'c, M., 1991,``Second-Moment Calculation Procedure for Turbulent Flows with Collocated Variable Arrangement,"{\it AIAA Journal}, Vol. 29, No. 4 , pp.585--590.

\bibitem{AG99} Straatman, A.G., 1999,``A modified Model for Diffusion in Second-Moment Turbulence Closures,"{\it ASME Journal of Fluids Engineering}, Vol. 121, pp.747--756.

\bibitem{ZW94} Zijlema, M., Segal, A. and Wesseling, P., 1994,``Finite volume computation of 2D incompressible turbulent flows in general coordinates on staggered grids,"{\it Faculty of Technical Mathematics and Informatics, Delft University of Technology},Report 94-24, 1994.

\bibitem{HN84} Heaps, N.S., 1984,`` Vertical Struture of Current in Homogeneous and Stratified Waters,"{\it Hydrodynamics of Lakes, CISM courses and lecturees No.286, International center for mechanical sciences, edited by. Hutter, K.}, Springer-Verlag, Germany., pp.153--207

\bibitem{WT95} Wu, J. and Tsanis, I.K., 1995,``Numerical Study of Wind-Induced Water Currents,"{\it Journal of Hydraulic Engineering}, Vol. 121, pp.388--395.

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\bibitem{BR90} Ramaswamy, B., 1990,`` Numerical Simulation of Unsteady Viscous Free Surface Flow,"{\it Journal of computational Physiscs}, Vol. 90, pp.396--430.

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\end{thebibliography}

Hello...

Thank you for giving me a good guidance of the topic which is posted in cfd-online. Of course, I am looking for data which Mr/Mrs Tamer Elsoukkary told me yesterday. However, It is not easy to approach the topic. So, I would like to know the general concepts for modeling of free surface in CFD. For example, modeling method(like VOF), general concepts of method, and so on. Thank you. I will wait response sincerely.

MAC, VOF, moving grid are to my knowlage the only existing methods for free surface. Method are also classified as surface tracking (moving grid)and surface capturing (VOF). Read chapter 12 of \bibitem{FP96} Ferziger, J.H. and Peri\'c, M., 1996,``Computational Methods for Fluid Dynamics," Springer Pub., Germany.

As well as \bibitem{MP99} Muzaferija, S. and Peri\`c, M. 1999,`` Computation of free-surface flows using interface-tracking and interface-capturing methods,"{\it Nonlinear Water Wave Interaction, Advances in Fluid Mechanics series, edited by Mahrenholtz, O. and Markiewicz, M.} WITpress, UK., Vol. 24, pp.59--100.

These are the best resources as well as some PhD thesis done by Prof. Gosman students in empirial collage in London where the finite volume been first developed. This area of study is really lacking and too difficult. It also depends on what you want to solve. For my master I was interested in sloving the air moving the water in a huge lake and that was really difficlut so I end up solving one fluid and imposing the wavy shape of the surface. I think VOF is to some extent capable of giving an answer whather that good enough I don't know. My advice is to try CFD package like Fluent or Star-CD and the time you invest in learning the software will give you hint to what you need to do when you program your own code. Good Luck, Tamer

By the way what exactly is the phyiscal problem and what forces it involve... e.g gravity , corluis (earth rotation), wind...??

"These are the best resources as well as some PhD thesis done by Prof. Gosman students in empirial collage in London where the finite volume been first developed."

This doesn't seem quite right. Pat Roache's book Computational Fluid Dynamics (the revised edition - copyright 1976) is essentially an encyclopedia of early CFD work. Checking the exhaustive bibliography in that work, I think you'll find that the first reference to Gosman is 1969, while Harlow's work (MAC in particular, which is a Finite Volume technique) starts in 1959 (!) with free surface (MAC) calculations first reported in 1966.

I think, subject to correction, that Gosman and his students developed the SIMPLE technique for solving the coupled equations.

I will say that there is another method for free surface simulation which is called mode-splitting method. This method uses vertically integrated N-S equations to solve the water surface fluctuations which represent the free surface movement. CH3D and POM both use this method. But this method is used only for hydrostatic modeling which is quasi-3D. So far, I have not seen any articles using this method for fully 3D modeling. If anybody knows, please tell me where to find such papers.

What is the references of mode-splitting method ? Would you please tell me a paper'name, year, and so on ? and also what is the CH3D and POM ?

Additional urgent question.

Please tell me a recent paper on modeling of free surface.

Dear Kim

Try this address: http://www.lmm.jussieu.fr/~zaleski/zaleski.html

See into the publications link. Proffesor Zaleski has a lot of papers on free surface dynamics.

Just to pointed out, if you are looking for VOF to use it to track your interface then, I think, you can't consider it as FREE. If you have a real FREE (almost free) interface, then try "Level Set Methods" they have no numerical diffusion and you don't need to recontruct the inteface.

Regards

Kike

Hi, Kim,

Here are two links to CH3D and POM respectively: http://hlnet.wes.army.mil/software/ch3d/ http://www.aos.princeton.edu/WWWPUBLIC/htdocs.pom/

Have fun!

What is the problem you interested to solve describe it?

Do you need to account for viscousity and model turbulence? Because to my knowlage noone was succesful in turbulence modelling using VOF. MAC mechod of Harlow was based on the finte difference method on orthogonal grids

POM uses a two and half equation turbulence model by Mellor and Yamada to compute the viscosity at the vertical direction and uses Smagorinsky model to compute the viscosity coefficient at the horizontal direction. CH3D uses K-epsilon model to compute the viscosity at the vertical direction and takes a constant viscosity at horizontal direction.

please include citation in your reply as I am not accounted with the methods CH3D and POM

Actually, you want to solve free-surface flow on coastal areas. Right? So, I will confine my comment to research trends in civil and coastal engineering. They are somewhat different from that of mechanical engineering.

There are several ways to solve free-surface flows (in civil engineering).

First is to solve shallow water equation which is based on hydrostaic and long-wave approximation. Mode-splitting is also belong to this class. Mode-splitting is sometimes called multi-layer or layer-integrated shallow water equation. The advantage of shallow water equations are that they can be applied to very large areas, which is essential in real flow calculation. In addition, when tide or flooding is a main problem these provide so called drying/wetting techniques which enable moving shoreline process. The disadvantage is they do not capture short-waves.

The second is, to solve Boussinesq equations which takes into account hydrodynamic pressure and dispersive waves. Therefore solitary wave modeling is possible. Solving Boussinesq equation is more expensive than shallow water equations but provides very good results for short-wave motion such as those associate with shoaling, nearshore-tsunamis, run-up etc. Boussinesq equations have the same form with shallow water equations except for the Boussinesq terms. These terms are, generally, space-time mixed third order derivatve term. They make the work extremely difficult. Generally, 1-D Boussinesq equation or 2D equation on rectangular mesh is studied. Studies on 2D Boussinesq equation on unstructured meshes are gradually progressing now.

The third is to solve potential function. Since this approach is limited to very small region, no-one use this nowdays.

Finally, the most expensive is solving Navier-Stokes equations. Becuase of solving 3D equation on large sea is impossible, 2D equation is used. 2D NS equation was originally adopted to simulate wave breaking in coastal areas. Aforementioned VOF method combined with turbulence model is used by some researchers and showed excellent reuslts in modeling wave-breaking. Using VOF without turbulence model cannot simulate breaking waves properly. VOF is especially useful for calculating breaking waves, since the free-surface is not necessarily required to be single. Several studies based on VOF method to simulate breaking waves have been reported recently.

Some references are listed below

1. multi-layer shallow water equations :

1) 3D layer-integrated modelling of estuarine flows with flooding and drying, 'Estuarine, Coastal and Shelf Science' (1997), 44, 737-751

2) Modeling a limited region of the ocean, Journal of Computational Physics (1998), 145, 555-574.

3) 3D numerical model for Pearl river estuary, Journal of hydraulic engineering (2001), 127(1), 72-82.

4) Sigma coordinate pressure gradient errors and the seamount problem, Journal of Atmospheric and Ocean Technology (1997), 15(5), 1122-1131.

4. NS equations (VOF & turbulence model) :

1) A numerical study of breaking waves in surf zone, Journal of Fluid Mechanics (1998), 359, 239-264.

2) Numerical simulation of breaking waves by large eddy simulation and VOF method, Proc. 26th Int. Conf. on Coastal Eng. (1998), ASCE, 892-905.

3) Numerical simulation of wave motion on and in coastal sturctures, Proc. 23rd Int. Conf. on Coastal Eng. (1992), ASCE, 1772-1784.

4) Numerical simulation and validation of plunging breakers using 2D Navier-Stokes model, Proc. 24th Int. Conf. on Coastal Eng. (1994), ASCE, 511-524.

5) Wave action on and in permeable structures, Proc. 24th Int. Conf. on Coastal Eng. (1994), ASCE, 1739-1753.

6) Wave dynamics at coastal structures : development of a numerical model for free surface flow, Proc. 25th Int. Conf. on Coastal Eng. (1996), ASCE, 339-402.

7) Numerical analysis of two-dimensional plane wave deformation due to submerged structure (in Japanese), Proc. of Coastal Engineering (199?), JSCE, 44(1), 81-85

Thank you for giving me a good advice. It is very useful to me. If you don't mind, I want to know some references related to 2.(Boussinesq equaion), 3.(potential function). Thank you very much. I will wait your response.

Some references of Boussinesq equations are

Alternative form of Boussinesq equations for nearshore wave propagation, J. Waterway, Port, Coastal, and Ocean Engineering, 119(6), 618-

Boussinesq modeling of wave transformation, beraking, and runup, J. Waterway, Port, Coastal, and Ocean Engineering, 126(1), 39-

Boussinesq type model with boundary-fitted coordinate system, J. Waterway, Port, Coastal, and Ocean Engineering, 127(3), 152-

A Taylor-Galerkin method for simulating nonlinear dispersive water waves, J. Computational Physics, 146, 546-.

Those references contain many other references. Please try to find them also.

Boundary element method is frequently used for the solution of potential function to model free surface flows. The governing equation is Laplace equation or Poisson equation, etc. Unfortunately, I don't know references. Please find papers of Phillip L.-F. Liu who is a professor of Dept. of Civil Engineering of Cornell Univ.

Best Regards,

Hi,

There is a deformable mesh option in CFX 4.4 so that the grid deforms as a function of pressure at each new iteration or time step. Work on estuaries and rivers have been conducted with this code. Alternatively there's a VOF method and a free-surface sharpenening algorithm available.

Herve

Hi,

Does CFX4.4 implement a nonhydrostatic simulation(The NS equation is not simplified to Dv/Dt=-g at vertical direction and full N-S equation is solved)? Could you give me a quantitative example of how much CPU is consumed for the simulation of a real problem(the CPU time, the real time simulated, the mesh size, the maximum flow speed, the physical domain)?